Incremental Social Learning in Particle Swarms
by Marco A. Montes de Oca, Thomas Stützle, Ken Van den Enden, and Marco Dorigo
February 2010
This page contains all supplementary information that, for the sake of conciseness, was not included in the paper.
Table of Contents
- Paper Abstract
- Benchmark functions
- Solution quality distribution
- Results after 100 function evaluations
- Results after 1,000 function evaluations
- Results after 10,000 function evaluations
- Results after 100,000 function evaluations
- Results after 1,000,000 function evaluations
- Solution quality development and population size growth over time (mean)
- Ackley function
- Double sum function
- Griewank function
- Penalized function
- Rastrigin function
- Rosenbrock function
- Salomon function
- Schaffer function
- Schwefel function
- Sphere function
- Step function
- Weierstrass function
- Statistical significance results (alternative hypothesis = "less")
- Differences after 100 function evaluations
- Differences after 1,000 function evaluations
- Differences after 10,000 function evaluations
- Differences after 100,000 function evaluations
- Differences after 1,000,000 function evaluations
- Effect size analysis
- Results after 100 function evaluations
- Results after 1,000 function evaluations
- Results after 10,000 function evaluations
- Results after 100,000 function evaluations
- Results after 1,000,000 function evaluations
- IPSOLS original vs. new version
- Results after 100 function evaluations
- Results after 1,000 function evaluations
- Results after 10,000 function evaluations
- Results after 100,000 function evaluations
- Results after 1,000,000 function evaluations
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Paper Abstract
Incremental social learning (ISL) was proposed as a way to improve the scalability of systems composed of multiple learning agents. In this article, we show that ISL can be very useful to improve the performance of population-based optimization algorithms. Our study focuses on two particle swarm optimization (PSO) algorithms: a) the incremental particle swarm optimizer (IPSO), which is a PSO algorithm with a growing population size in which the initial position of new particles is biased toward the best-so-far solution, and b) the incremental particle swarm optimizer with local search (IPSOLS), in which solutions are further improved through a local search procedure.
We first derive analytically the probability density function induced by the proposed initialization rule applied to new particles. We then compare the performance of IPSO and IPSOLS on a set of benchmark functions with that of other PSO algorithms (with and without local search) and a random restart local search algorithm. Finally, we measure the benefits of using incremental social learning on PSO algorithms by running IPSO and IPSOLS on problems with different fitness distance correlations.
Keywords: Particle Swarm Optimization, Local Search, Continuous Optimization, Swarm Intelligence, Social Learning.
The following table shows the mathematical definition of the benchmark functions used in this study
Solution quality distribution
The following figures show the boxplots of the solution quality distribution after a certain number of function evaluations. A symbol on top of a box plot denotes a statistically significant difference at the 5% level between the results obtained with the indicated algorithm and those obtained with IPSO (in favor of IPSO, marked with a "+" symbol) or with IPSOLS (in favor of IPSOLS, marked with a "x" symbol).
Results after 100 function evaluations
Ackley function - 100 dimensions |
Fully-connected topology | Ring topology |
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Double sum function - 100 dimensions |
Fully-connected topology | Ring topology |
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Griewank function - 100 dimensions |
Fully-connected topology | Ring topology |
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Penalized function - 100 dimensions |
Fully-connected topology | Ring topology |
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Rastrigin function - 100 dimensions |
Fully-connected topology | Ring topology |
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Rosenbrock function - 100 dimensions |
Fully-connected topology | Ring topology |
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Salomon function - 100 dimensions |
Fully-connected topology | Ring topology |
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Schaffer function - 100 dimensions |
Fully-connected topology | Ring topology |
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Schwefel function - 100 dimensions |
Fully-connected topology | Ring topology |
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Sphere function - 100 dimensions |
Fully-connected topology | Ring topology |
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Step function - 100 dimensions |
Fully-connected topology | Ring topology |
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Weierstrass function - 100 dimensions |
Fully-connected topology | Ring topology |
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Results after 1000 function evaluations
Ackley function - 100 dimensions |
Fully-connected topology | Ring topology |
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Double sum function - 100 dimensions |
Fully-connected topology | Ring topology |
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Griewank function - 100 dimensions |
Fully-connected topology | Ring topology |
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Penalized function - 100 dimensions |
Fully-connected topology | Ring topology |
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Rastrigin function - 100 dimensions |
Fully-connected topology | Ring topology |
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Rosenbrock function - 100 dimensions |
Fully-connected topology | Ring topology |
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Salomon function - 100 dimensions |
Fully-connected topology | Ring topology |
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Schaffer function - 100 dimensions |
Fully-connected topology | Ring topology |
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Schwefel function - 100 dimensions |
Fully-connected topology | Ring topology |
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Sphere function - 100 dimensions |
Fully-connected topology | Ring topology |
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Step function - 100 dimensions |
Fully-connected topology | Ring topology |
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Weierstrass function - 100 dimensions |
Fully-connected topology | Ring topology |
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Results after 10,000 function evaluations
Ackley function - 100 dimensions |
Fully-connected topology | Ring topology |
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Double sum function - 100 dimensions |
Fully-connected topology | Ring topology |
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Griewank function - 100 dimensions |
Fully-connected topology | Ring topology |
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Penalized function - 100 dimensions |
Fully-connected topology | Ring topology |
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Rastrigin function - 100 dimensions |
Fully-connected topology | Ring topology |
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Rosenbrock function - 100 dimensions |
Fully-connected topology | Ring topology |
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Salomon function - 100 dimensions |
Fully-connected topology | Ring topology |
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Schaffer function - 100 dimensions |
Fully-connected topology | Ring topology |
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Schwefel function - 100 dimensions |
Fully-connected topology | Ring topology |
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Sphere function - 100 dimensions |
Fully-connected topology | Ring topology |
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Step function - 100 dimensions |
Fully-connected topology | Ring topology |
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Weierstrass function - 100 dimensions |
Fully-connected topology | Ring topology |
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Results after 100,000 function evaluations
Ackley function - 100 dimensions |
Fully-connected topology | Ring topology |
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Double sum function - 100 dimensions |
Fully-connected topology | Ring topology |
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Griewank function - 100 dimensions |
Fully-connected topology | Ring topology |
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Penalized function - 100 dimensions |
Fully-connected topology | Ring topology |
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Rastrigin function - 100 dimensions |
Fully-connected topology | Ring topology |
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Rosenbrock function - 100 dimensions |
Fully-connected topology | Ring topology |
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Salomon function - 100 dimensions |
Fully-connected topology | Ring topology |
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Schaffer function - 100 dimensions |
Fully-connected topology | Ring topology |
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Schwefel function - 100 dimensions |
Fully-connected topology | Ring topology |
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Sphere function - 100 dimensions |
Fully-connected topology | Ring topology |
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Step function - 100 dimensions |
Fully-connected topology | Ring topology |
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Weierstrass function - 100 dimensions |
Fully-connected topology | Ring topology |
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Results after 1,000,000 function evaluations
Ackley function - 100 dimensions |
Fully-connected topology | Ring topology |
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Double sum function - 100 dimensions |
Fully-connected topology | Ring topology |
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Griewank function - 100 dimensions |
Fully-connected topology | Ring topology |
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Penalized function - 100 dimensions |
Fully-connected topology | Ring topology |
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Rastrigin function - 100 dimensions |
Fully-connected topology | Ring topology |
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Rosenbrock function - 100 dimensions |
Fully-connected topology | Ring topology |
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Salomon function - 100 dimensions |
Fully-connected topology | Ring topology |
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Schaffer function - 100 dimensions |
Fully-connected topology | Ring topology |
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Schwefel function - 100 dimensions |
Fully-connected topology | Ring topology |
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Sphere function - 100 dimensions |
Fully-connected topology | Ring topology |
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Step function - 100 dimensions |
Fully-connected topology | Ring topology |
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Weierstrass function - 100 dimensions |
Fully-connected topology | Ring topology |
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Solution quality development and population size growth over time (mean)
The following figures show the development of the solution quality and of the population size growth over time. The plots correspond to the mean value (out of 100 independent runs).
Results on the Ackley function
Ackley function - 100 dimensions |
Fully-connected topology | Ring topology |
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Results on the double sum function
Double sum function - 100 dimensions |
Fully-connected topology | Ring topology |
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Results on the Griewank function
Griewank function - 100 dimensions |
Fully-connected topology | Ring topology |
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Results on the Penalized function
Penalized function - 100 dimensions |
Fully-connected topology | Ring topology |
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Results on the Rastrigin function
Rastring function - 100 dimensions |
Fully-connected topology | Ring topology |
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Results on the Rosenbrock function
Rosenbrock function - 100 dimensions |
Fully-connected topology | Ring topology |
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Results on the Salomon function
Salomon function - 100 dimensions |
Fully-connected topology | Ring topology |
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Results on the Schaffer function
Schaffer function - 100 dimensions |
Fully-connected topology | Ring topology |
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Results on the Schwefel function
Schwefel function - 100 dimensions |
Fully-connected topology | Ring topology |
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Results on the Sphere function
Sphere function - 100 dimensions |
Fully-connected topology | Ring topology |
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Results on the Step function
Step function - 100 dimensions |
Fully-connected topology | Ring topology |
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Results on the Weierstrass function
Weierstrass function - 100 dimensions |
Fully-connected topology | Ring topology |
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Statistical significance results (alternative hypothesis = "less")
The following tables show all pairwise p values obtained after applying Wilcoxon's test using Holm's correction method for multiple comparisons.
Differences after 100 function evaluations
Ackley function - 100 dimensions |
Fully-connected topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.0e+00 | 6.5e-03 | 6.5e-03 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 8.4e-07 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 2.3e-07 | 4.1e-03 | NA | NA | NA | NA |
H-EPUSLS | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA |
I-RLS | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA |
J-ISL | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA |
Z-IPSO | 5.5e-07 | 2.7e-16 | 2.7e-16 | 8.3e-11 | 1.2e-16 | 1.2e-16 | 1.2e-16 | 1.5e-16 | 1.2e-16 | 1.2e-16 |
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Ring topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.0e+00 | 6.3e-03 | 6.3e-03 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 8.4e-07 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 2.3e-07 | 4.1e-03 | NA | NA | NA | NA |
H-EPUSLS | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA |
I-RLS | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA |
J-ISL | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA |
Z-IPSO | 1.7e-08 | 4.6e-16 | 4.6e-16 | 1.7e-12 | 1.6e-16 | 2.0e-16 | 2.2e-16 | 1.6e-16 | 1.5e-16 | 1.5e-16 |
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Griewank function - 100 dimensions |
Fully-connected topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.0e+00 | 1.7e-15 | 1.7e-15 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.7e-03 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 2.2e-05 | 4.0e-02 | NA | NA | NA | NA |
H-EPUSLS | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA |
I-RLS | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA |
J-ISL | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA |
Z-IPSO | 2.7e-09 | 1.1e-16 | 1.1e-16 | 2.8e-14 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 |
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Ring topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.0e+00 | 2.8e-15 | 2.8e-15 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.7e-03 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 2.2e-05 | 4.0e-02 | NA | NA | NA | NA |
H-EPUSLS | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA |
I-RLS | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA |
J-ISL | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA |
Z-IPSO | 6.5e-13 | 1.1e-16 | 1.1e-16 | 9.7e-15 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 |
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Rastrigin function - 100 dimensions |
Fully-connected topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.0e+00 | 6.4e-15 | 6.4e-15 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.5e-03 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.1e-06 | 6.3e-04 | NA | NA | NA | NA |
H-EPUSLS | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA |
I-RLS | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA |
J-ISL | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA |
Z-IPSO | 7.8e-11 | 1.1e-16 | 1.1e-16 | 1.6e-14 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 |
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Ring topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.0e+00 | 6.8e-15 | 6.8e-15 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.5e-03 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.1e-06 | 6.3e-04 | NA | NA | NA | NA |
H-EPUSLS | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA |
I-RLS | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA |
J-ISL | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA |
Z-IPSO | 7.7e-12 | 1.1e-16 | 1.1e-16 | 1.9e-13 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 |
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Rosenbrock function - 100 dimensions |
Fully-connected topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.0e+00 | 1.1e-16 | 1.1e-16 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 3.1e-05 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.2e-11 | 1.5e-08 | NA | NA | NA | NA |
H-EPUSLS | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA |
I-RLS | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA |
J-ISL | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA |
Z-IPSO | 6.0e-14 | 1.1e-16 | 1.1e-16 | 2.1e-15 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 |
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Ring topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.0e+00 | 2.3e-16 | 2.3e-16 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 3.1e-05 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.2e-11 | 1.5e-08 | NA | NA | NA | NA |
H-EPUSLS | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA |
I-RLS | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA |
J-ISL | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA |
Z-IPSO | 1.5e-15 | 1.1e-16 | 1.1e-16 | 1.5e-15 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 |
|
Salomon function - 100 dimensions |
Fully-connected topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.0e+00 | 1.1e-14 | 1.1e-14 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 5.6e-08 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 2.6e-12 | 8.1e-09 | NA | NA | NA | NA |
H-EPUSLS | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA |
I-RLS | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA |
J-ISL | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA |
Z-IPSO | 8.8e-10 | 1.1e-16 | 1.1e-16 | 5.3e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 |
|
Ring topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.0e+00 | 1.6e-14 | 1.6e-14 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 5.6e-08 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 2.6e-12 | 8.1e-09 | NA | NA | NA | NA |
H-EPUSLS | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA |
I-RLS | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA |
J-ISL | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA |
Z-IPSO | 9.8e-14 | 1.1e-16 | 1.1e-16 | 4.3e-15 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 |
|
Schaffer function - 100 dimensions |
Fully-connected topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 2.0e-06 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 2.3e-09 | 1.4e-04 | NA | NA | NA | NA |
H-EPUSLS | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA |
I-RLS | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA |
J-ISL | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA |
Z-IPSO | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.3e-13 | 2.3e-11 | 4.2e-08 | 3.0e-16 | 8.7e-15 | 8.7e-15 |
|
Ring topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 2.0e-06 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 2.3e-09 | 1.4e-04 | NA | NA | NA | NA |
H-EPUSLS | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA |
I-RLS | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA |
J-ISL | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA |
Z-IPSO | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.1e-13 | 6.6e-12 | 4.3e-08 | 8.0e-16 | 6.4e-15 | 6.4e-15 |
|
Schwefel function - 100 dimensions |
Fully-connected topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 8.7e-02 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.5e-01 | 2.4e-06 | 4.8e-03 | NA | NA | NA | NA |
H-EPUSLS | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA |
I-RLS | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA |
J-ISL | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA |
Z-IPSO | 1.0e+00 | 2.7e-07 | 2.7e-07 | 4.8e-15 | 4.1e-15 | 9.6e-15 | 1.3e-13 | 2.3e-15 | 1.4e-15 | 1.4e-15 |
|
Ring topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 8.5e-02 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 2.2e-02 | 2.6e-06 | 5.0e-03 | NA | NA | NA | NA |
H-EPUSLS | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA |
I-RLS | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA |
J-ISL | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA |
Z-IPSO | 1.0e+00 | 1.4e-02 | 1.4e-02 | 2.5e-14 | 9.1e-14 | 2.7e-13 | 1.3e-12 | 1.2e-13 | 8.9e-15 | 8.9e-15 |
|
Sphere function - 100 dimensions |
Fully-connected topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.0e+00 | 1.7e-15 | 1.7e-15 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.7e-03 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 2.2e-05 | 4.0e-02 | NA | NA | NA | NA |
H-EPUSLS | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA |
I-RLS | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA |
J-ISL | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA |
Z-IPSO | 2.7e-09 | 1.1e-16 | 1.1e-16 | 2.8e-14 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 |
|
Ring topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.0e+00 | 2.8e-15 | 2.8e-15 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.7e-03 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 2.2e-05 | 4.0e-02 | NA | NA | NA | NA |
H-EPUSLS | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA |
I-RLS | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA |
J-ISL | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA |
Z-IPSO | 6.5e-13 | 1.1e-16 | 1.1e-16 | 9.7e-15 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 |
|
Step function - 100 dimensions |
Fully-connected topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 5.9e-01 | 1.2e-03 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 4.5e-06 | 1.4e-08 | 1.0e-05 | NA | NA | NA | NA |
H-EPUSLS | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA |
I-RLS | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA |
J-ISL | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA |
Z-IPSO | 1.0e+00 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 |
|
Ring topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 7.9e-01 | 1.2e-03 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 4.8e-06 | 1.4e-08 | 1.0e-05 | NA | NA | NA | NA |
H-EPUSLS | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA |
I-RLS | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA |
J-ISL | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA |
Z-IPSO | 1.0e+00 | 2.6e-16 | 2.6e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.2e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 |
|
Weierstrass function - 100 dimensions |
Fully-connected topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA |
H-EPUSLS | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA |
I-RLS | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 8.9e-01 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA |
J-ISL | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 8.9e-01 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA |
Z-IPSO | 7.3e-03 | 7.6e-15 | 7.6e-15 | 2.9e-15 | 1.3e-14 | 7.3e-15 | 5.1e-15 | 1.2e-15 | 9.9e-15 | 9.9e-15 |
|
Ring topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 4.0e-01 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA |
H-EPUSLS | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA |
I-RLS | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 8.9e-01 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA |
J-ISL | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA |
Z-IPSO | 1.0e+00 | 5.8e-08 | 5.8e-08 | 3.4e-13 | 7.2e-11 | 3.1e-11 | 2.2e-11 | 7.0e-12 | 6.3e-11 | 4.7e-12 |
|
Differences after 1000 function evaluations
Ackley function - 100 dimensions |
Fully-connected topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.0e+00 | 1.0e+00 | 1.6e-11 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA |
H-EPUSLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA |
I-RLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 9.3e-10 | 3.6e-14 | 1.3e-16 | 1.0e+00 | NA | NA |
J-ISL | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 9.3e-10 | 3.6e-14 | 1.3e-16 | 1.0e+00 | 1.0e+00 | NA |
Z-IPSO | 9.1e-03 | 7.5e-05 | 1.1e-16 | 3.5e-11 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 |
|
Ring topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.0e+00 | 1.0e+00 | 7.9e-12 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 8.4e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 8.4e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 9.0e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA |
H-EPUSLS | 9.8e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA |
I-RLS | 8.4e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 8.9e-10 | 3.3e-14 | 1.5e-16 | 1.0e+00 | NA | NA |
J-ISL | 8.4e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 8.9e-10 | 3.3e-14 | 1.5e-16 | 1.0e+00 | 1.0e+00 | NA |
Z-IPSO | 4.9e-01 | 1.2e-16 | 1.1e-16 | 2.4e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 |
|
Griewank function - 100 dimensions |
Fully-connected topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.0e+00 | 4.9e-11 | 1.1e-16 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA |
H-EPUSLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA |
I-RLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA |
J-ISL | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA |
Z-IPSO | 1.0e+00 | 1.1e-16 | 1.1e-16 | 1.4e-14 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 |
|
Ring topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.0e+00 | 1.1e-16 | 1.1e-16 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA |
H-EPUSLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA |
I-RLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA |
J-ISL | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA |
Z-IPSO | 1.0e+00 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 |
|
Rastrigin function - 100 dimensions |
Fully-connected topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.0e+00 | 2.5e-04 | 1.1e-16 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA |
H-EPUSLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 2.2e-01 | 2.1e-02 | 2.9e-04 | NA | NA | NA |
I-RLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 6.5e-13 | 2.4e-16 | 1.1e-16 | 1.0e+00 | NA | NA |
J-ISL | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 6.5e-13 | 2.4e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | NA |
Z-IPSO | 1.0e+00 | 1.6e-14 | 1.1e-16 | 1.6e-03 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 |
|
Ring topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.0e+00 | 1.6e-14 | 1.1e-16 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA |
H-EPUSLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 2.2e-01 | 2.1e-02 | 2.8e-04 | NA | NA | NA |
I-RLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 6.2e-13 | 2.4e-16 | 1.1e-16 | 1.0e+00 | NA | NA |
J-ISL | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 6.2e-13 | 2.4e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | NA |
Z-IPSO | 1.0e+00 | 1.1e-16 | 1.1e-16 | 2.8e-10 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 |
|
Rosenbrock function - 100 dimensions |
Fully-connected topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.0e+00 | 2.0e-14 | 1.1e-16 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.0e+00 | 1.0e+00 | 1.1e-16 | 1.0e+00 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.0e+00 | 1.0e+00 | 1.1e-16 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.0e+00 | 1.0e+00 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA |
H-EPUSLS | 1.0e+00 | 1.0e+00 | 1.1e-16 | 1.0e+00 | 2.4e-01 | 8.6e-02 | 1.7e-02 | NA | NA | NA |
I-RLS | 1.0e+00 | 1.0e+00 | 1.1e-16 | 1.0e+00 | 7.0e-15 | 1.1e-16 | 1.1e-16 | 1.0e+00 | NA | NA |
J-ISL | 1.0e+00 | 1.0e+00 | 1.1e-16 | 1.0e+00 | 7.0e-15 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | NA |
Z-IPSO | 1.0e+00 | 1.1e-16 | 1.1e-16 | 1.1e-13 | 7.8e-16 | 6.5e-16 | 2.2e-16 | 3.5e-14 | 1.1e-15 | 1.1e-15 |
|
Ring topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.0e+00 | 1.1e-16 | 1.1e-16 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.0e+00 | 9.8e-13 | 1.1e-16 | 1.0e+00 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.0e+00 | 3.0e-12 | 1.1e-16 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.0e+00 | 4.0e-11 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA |
H-EPUSLS | 1.0e+00 | 3.1e-15 | 1.1e-16 | 1.0e+00 | 2.0e-01 | 7.2e-02 | 1.4e-02 | NA | NA | NA |
I-RLS | 1.0e+00 | 6.1e-13 | 1.1e-16 | 1.0e+00 | 7.6e-15 | 1.1e-16 | 1.1e-16 | 1.0e+00 | NA | NA |
J-ISL | 1.0e+00 | 6.1e-13 | 1.1e-16 | 1.0e+00 | 7.6e-15 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | NA |
Z-IPSO | 1.0e+00 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 8.9e-07 | 1.5e-07 | 7.1e-09 | 1.1e-02 | 2.5e-06 | 2.5e-06 |
|
Salomon function - 100 dimensions |
Fully-connected topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.0e+00 | 1.0e+00 | 1.3e-16 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 8.3e-06 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 2.8e-10 | 6.3e-07 | NA | NA | NA | NA |
H-EPUSLS | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA |
I-RLS | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA |
J-ISL | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA |
Z-IPSO | 1.0e+00 | 1.1e-16 | 1.1e-16 | 1.5e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 |
|
Ring topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.0e+00 | 1.4e-16 | 1.1e-16 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 8.3e-06 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 2.8e-10 | 6.3e-07 | NA | NA | NA | NA |
H-EPUSLS | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA |
I-RLS | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA |
J-ISL | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA |
Z-IPSO | 1.0e+00 | 1.1e-16 | 1.1e-16 | 1.9e-02 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 |
|
Schaffer function - 100 dimensions |
Fully-connected topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.4e-14 | 3.1e-15 | 1.8e-15 | 1.9e-15 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.4e-14 | 3.2e-15 | 1.9e-15 | 1.9e-15 | 1.0e+00 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 2.0e-14 | 5.3e-15 | 2.3e-15 | 2.1e-15 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA |
H-EPUSLS | 5.3e-15 | 2.1e-15 | 4.4e-16 | 1.7e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA |
I-RLS | 1.0e-14 | 2.3e-15 | 1.5e-15 | 1.5e-15 | 4.9e-08 | 7.8e-13 | 5.3e-15 | 1.0e+00 | NA | NA |
J-ISL | 1.0e-14 | 2.3e-15 | 1.5e-15 | 1.5e-15 | 4.9e-08 | 7.8e-13 | 5.3e-15 | 1.0e+00 | 1.0e+00 | NA |
Z-IPSO | 1.0e+00 | 1.0e+00 | 6.4e-03 | 2.2e-02 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 |
|
Ring topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.9e-14 | 1.2e-15 | 1.5e-15 | 9.2e-16 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.9e-14 | 1.2e-15 | 1.5e-15 | 9.3e-16 | 1.0e+00 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 2.9e-14 | 1.4e-15 | 2.1e-15 | 1.2e-15 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA |
H-EPUSLS | 8.7e-15 | 4.8e-16 | 4.4e-16 | 1.8e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA |
I-RLS | 1.4e-14 | 1.0e-15 | 1.3e-15 | 7.6e-16 | 4.9e-08 | 7.8e-13 | 5.1e-15 | 1.0e+00 | NA | NA |
J-ISL | 1.4e-14 | 1.0e-15 | 1.3e-15 | 7.6e-16 | 4.9e-08 | 7.8e-13 | 5.1e-15 | 1.0e+00 | 1.0e+00 | NA |
Z-IPSO | 1.0e+00 | 3.2e-04 | 6.3e-03 | 5.5e-04 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 |
|
Schwefel function - 100 dimensions |
Fully-connected topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA |
H-EPUSLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA |
I-RLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 2.9e-09 | 1.1e-15 | 1.1e-16 | 1.0e+00 | NA | NA |
J-ISL | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 2.9e-09 | 1.1e-15 | 1.1e-16 | 1.0e+00 | 1.0e+00 | NA |
Z-IPSO | 1.0e+00 | 1.1e-16 | 1.1e-16 | 1.9e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 |
|
Ring topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA |
H-EPUSLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA |
I-RLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 2.9e-09 | 1.1e-15 | 1.1e-16 | 1.0e+00 | NA | NA |
J-ISL | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 2.9e-09 | 1.1e-15 | 1.1e-16 | 1.0e+00 | 1.0e+00 | NA |
Z-IPSO | 1.0e+00 | 1.8e-16 | 1.1e-16 | 2.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 |
|
Sphere function - 100 dimensions |
Fully-connected topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.0e+00 | 1.5e-12 | 1.1e-16 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA |
H-EPUSLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA |
I-RLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA |
J-ISL | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA |
Z-IPSO | 1.0e+00 | 1.1e-16 | 1.1e-16 | 2.7e-12 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 |
|
Ring topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.0e+00 | 1.1e-16 | 1.1e-16 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA |
H-EPUSLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA |
I-RLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA |
J-ISL | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA |
Z-IPSO | 1.0e+00 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 |
|
Step function - 100 dimensions |
Fully-connected topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.0e+00 | 7.4e-01 | 1.1e-16 | 1.1e-16 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.0e+00 | 1.0e+00 | 1.1e-16 | 1.1e-16 | 1.0e+00 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.0e+00 | 1.0e+00 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA |
H-EPUSLS | 1.0e+00 | 1.2e-01 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 2.3e-01 | NA | NA | NA |
I-RLS | 1.0e+00 | 3.7e-01 | 1.1e-16 | 1.1e-16 | 2.4e-06 | 1.6e-10 | 2.8e-13 | 1.0e+00 | NA | NA |
J-ISL | 1.0e+00 | 3.7e-01 | 1.1e-16 | 1.1e-16 | 2.4e-06 | 1.6e-10 | 2.8e-13 | 1.0e+00 | 1.0e+00 | NA |
Z-IPSO | 1.0e+00 | 9.6e-16 | 1.1e-16 | 1.1e-16 | 5.5e-14 | 4.0e-14 | 2.1e-14 | 2.9e-13 | 8.5e-14 | 8.5e-14 |
|
Ring topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.0e+00 | 1.1e-16 | 1.1e-16 | 1.1e-16 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.0e+00 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.0e+00 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA |
H-EPUSLS | 1.0e+00 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 2.4e-01 | NA | NA | NA |
I-RLS | 1.0e+00 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 2.4e-06 | 1.6e-10 | 2.7e-13 | 1.0e+00 | NA | NA |
J-ISL | 1.0e+00 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 2.4e-06 | 1.6e-10 | 2.7e-13 | 1.0e+00 | 1.0e+00 | NA |
Z-IPSO | 1.0e+00 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 |
|
Weierstrass function - 100 dimensions |
Fully-connected topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.0e+00 | 2.2e-03 | 4.5e-10 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA |
H-EPUSLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.2e-01 | 5.3e-06 | NA | NA | NA |
I-RLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 6.9e-15 | 1.1e-16 | 1.1e-16 | 1.0e+00 | NA | NA |
J-ISL | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 6.9e-15 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | NA |
Z-IPSO | 1.0e+00 | 1.1e-16 | 1.1e-16 | 1.8e-08 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 |
|
Ring topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.0e+00 | 1.0e+00 | 1.8e-05 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA |
H-EPUSLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.4e-01 | 6.3e-06 | NA | NA | NA |
I-RLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 7.8e-15 | 1.1e-16 | 1.1e-16 | 1.0e+00 | NA | NA |
J-ISL | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA |
Z-IPSO | 1.0e+00 | 2.0e-10 | 1.1e-16 | 2.0e-11 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 |
|
Differences after 10,000 function evaluations
Ackley function - 100 dimensions |
Fully-connected topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 7.8e-11 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.0e+00 | 1.0e+00 | 1.5e-06 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 5.4e-12 | 1.0e+00 | 1.1e-16 | 1.1e-16 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 5.4e-12 | 1.0e+00 | 1.1e-16 | 1.1e-16 | 1.0e+00 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 5.4e-12 | 1.0e+00 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA |
H-EPUSLS | 4.1e-10 | 1.0e+00 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA |
I-RLS | 8.3e-12 | 1.0e+00 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA |
J-ISL | 5.1e-16 | 3.9e-07 | 1.1e-16 | 1.1e-16 | 2.4e-11 | 2.4e-11 | 2.3e-11 | 9.1e-09 | 4.3e-11 | NA |
Z-IPSO | 6.1e-04 | 1.0e+00 | 1.4e-14 | 1.5e-06 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 |
|
Ring topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.0e+00 | 1.0e+00 | 1.1e-15 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 6.4e-02 | 8.2e-16 | 1.1e-16 | 3.7e-16 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 6.4e-02 | 8.2e-16 | 1.1e-16 | 3.7e-16 | 1.0e+00 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 6.4e-02 | 8.2e-16 | 1.1e-16 | 3.7e-16 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA |
H-EPUSLS | 6.5e-02 | 1.1e-15 | 1.1e-16 | 3.7e-14 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA |
I-RLS | 7.2e-03 | 7.7e-16 | 1.1e-16 | 3.0e-15 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA |
J-ISL | 4.4e-12 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 2.1e-11 | 2.1e-11 | 2.0e-11 | 8.2e-09 | 3.6e-11 | NA |
Z-IPSO | 9.7e-01 | 1.1e-15 | 1.1e-16 | 1.5e-15 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 |
|
Griewank function - 100 dimensions |
Fully-connected topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.5e-13 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 8.1e-10 | 5.0e-07 | 2.3e-13 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA |
H-EPUSLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA |
I-RLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA |
J-ISL | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA |
Z-IPSO | 1.1e-16 | 2.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 |
|
Ring topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.0e+00 | 1.1e-16 | 1.1e-16 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA |
H-EPUSLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA |
I-RLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA |
J-ISL | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA |
Z-IPSO | 1.0e+00 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 |
|
Rastrigin function - 100 dimensions |
Fully-connected topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.0e+00 | 1.0e+00 | 1.1e-14 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA |
H-EPUSLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA |
I-RLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA |
J-ISL | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 8.0e-09 | 8.0e-09 | 8.0e-09 | 4.7e-08 | 4.9e-08 | NA |
Z-IPSO | 1.0e+00 | 1.0e+00 | 1.1e-16 | 1.2e-04 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 |
|
Ring topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.0e+00 | 7.8e-09 | 1.1e-16 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA |
H-EPUSLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA |
I-RLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA |
J-ISL | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 7.7e-09 | 7.7e-09 | 7.7e-09 | 4.3e-08 | 4.5e-08 | NA |
Z-IPSO | 1.0e+00 | 3.4e-09 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 |
|
Rosenbrock function - 100 dimensions |
Fully-connected topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.8e-09 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.1e-16 | 1.1e-16 | 1.1e-16 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA |
H-EPUSLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 2.9e-01 | 2.9e-01 | 2.9e-01 | NA | NA | NA |
I-RLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 2.5e-07 | 8.9e-11 | 9.9e-13 | 1.0e+00 | NA | NA |
J-ISL | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 2.5e-07 | 8.9e-11 | 9.9e-13 | 1.0e+00 | 1.0e+00 | NA |
Z-IPSO | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 |
|
Ring topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.0e+00 | 1.1e-16 | 1.1e-16 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA |
H-EPUSLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 3.4e-01 | 3.4e-01 | 3.4e-01 | NA | NA | NA |
I-RLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 2.9e-07 | 9.7e-11 | 1.1e-12 | 1.0e+00 | NA | NA |
J-ISL | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 2.9e-07 | 9.7e-11 | 1.1e-12 | 1.0e+00 | 1.0e+00 | NA |
Z-IPSO | 1.0e+00 | 2.2e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 |
|
Salomon function - 100 dimensions |
Fully-connected topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.2e-16 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.0e+00 | 1.0e+00 | 3.0e-14 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA |
H-EPUSLS | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA |
I-RLS | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.2e-04 | 1.7e-06 | 7.8e-08 | 1.0e+00 | NA | NA |
J-ISL | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.2e-04 | 1.7e-06 | 7.8e-08 | 1.0e+00 | 1.0e+00 | NA |
Z-IPSO | 1.1e-16 | 5.5e-13 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 |
|
Ring topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.0e+00 | 1.1e-14 | 1.1e-16 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.0e+00 | 1.0e+00 | 1.1e-16 | 1.0e+00 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.0e+00 | 1.0e+00 | 1.1e-16 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.0e+00 | 1.0e+00 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA |
H-EPUSLS | 1.0e+00 | 1.0e+00 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA |
I-RLS | 1.0e+00 | 1.0e+00 | 1.1e-16 | 1.0e+00 | 1.0e-04 | 1.5e-06 | 7.1e-08 | 1.0e+00 | NA | NA |
J-ISL | 1.0e+00 | 1.0e+00 | 1.1e-16 | 1.0e+00 | 1.0e-04 | 1.5e-06 | 7.1e-08 | 1.0e+00 | 1.0e+00 | NA |
Z-IPSO | 1.0e+00 | 1.9e-16 | 1.1e-16 | 1.0e+00 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 |
|
Schaffer function - 100 dimensions |
Fully-connected topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA |
H-EPUSLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA |
I-RLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 3.5e-06 | 2.4e-10 | 1.3e-15 | 1.0e+00 | NA | NA |
J-ISL | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 3.5e-06 | 2.4e-10 | 1.3e-15 | 1.0e+00 | 1.0e+00 | NA |
Z-IPSO | 1.0e+00 | 1.0e+00 | 1.3e-03 | 5.0e-01 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 |
|
Ring topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.0e+00 | 1.0e+00 | 6.5e-11 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA |
H-EPUSLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA |
I-RLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 3.2e-06 | 2.3e-10 | 1.2e-15 | 1.0e+00 | NA | NA |
J-ISL | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 3.2e-06 | 2.3e-10 | 1.2e-15 | 1.0e+00 | 1.0e+00 | NA |
Z-IPSO | 1.0e+00 | 1.0e+00 | 3.1e-16 | 9.2e-04 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 |
|
Schwefel function - 100 dimensions |
Fully-connected topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.0e+00 | 1.0e+00 | 9.5e-10 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA |
H-EPUSLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA |
I-RLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA |
J-ISL | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 4.9e-05 | 4.9e-05 | 4.9e-05 | 3.7e-04 | 9.5e-05 | NA |
Z-IPSO | 1.0e+00 | 1.0e+00 | 1.1e-16 | 1.6e-13 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 |
|
Ring topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.0e+00 | 1.0e+00 | 3.3e-16 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA |
H-EPUSLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA |
I-RLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA |
J-ISL | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 4.9e-05 | 4.9e-05 | 4.9e-05 | 3.7e-04 | 9.5e-05 | NA |
Z-IPSO | 1.0e+00 | 1.3e-03 | 1.1e-16 | 3.4e-05 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 |
|
Sphere function - 100 dimensions |
Fully-connected topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.3e-13 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.7e-14 | 1.3e-13 | 1.7e-14 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA |
H-EPUSLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA |
I-RLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.1e-16 | NA | NA |
J-ISL | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.1e-16 | 1.0e+00 | NA |
Z-IPSO | 1.1e-16 | 1.9e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 |
|
Ring topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.0e+00 | 1.1e-16 | 1.1e-16 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA |
H-EPUSLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA |
I-RLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.1e-16 | NA | NA |
J-ISL | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.1e-16 | 1.0e+00 | NA |
Z-IPSO | 1.0e+00 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 |
|
Step function - 100 dimensions |
Fully-connected topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.1e-16 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 3.9e-01 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.1e-16 | 4.0e-03 | 1.1e-16 | 1.1e-16 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.1e-16 | 4.0e-03 | 1.1e-16 | 1.1e-16 | 1.0e+00 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.1e-16 | 4.0e-03 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA |
H-EPUSLS | 1.1e-16 | 2.2e-03 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA |
I-RLS | 1.1e-16 | 4.0e-03 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA |
J-ISL | 1.1e-16 | 1.0e-05 | 1.1e-16 | 1.1e-16 | 4.3e-03 | 4.3e-03 | 4.3e-03 | 6.9e-01 | 4.3e-03 | NA |
Z-IPSO | 1.9e-16 | 1.0e+00 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 |
|
Ring topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.1e-16 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.8e-15 | 1.0e+00 | 1.1e-16 | 1.1e-16 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.8e-15 | 1.0e+00 | 1.1e-16 | 1.1e-16 | 1.0e+00 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.8e-15 | 1.0e+00 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA |
H-EPUSLS | 1.2e-15 | 1.0e+00 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA |
I-RLS | 1.8e-15 | 1.0e+00 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA |
J-ISL | 6.4e-16 | 1.0e+00 | 1.1e-16 | 1.1e-16 | 4.3e-03 | 4.3e-03 | 4.3e-03 | 6.9e-01 | 4.3e-03 | NA |
Z-IPSO | 1.1e-16 | 2.4e-01 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.8e-16 |
|
Weierstrass function - 100 dimensions |
Fully-connected topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.0e+00 | 2.0e-02 | 4.0e-16 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA |
H-EPUSLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA |
I-RLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 2.7e-02 | 1.1e-03 | 5.3e-06 | 1.0e+00 | NA | NA |
J-ISL | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 2.5e-01 | 1.6e-03 | 6.3e-05 | 1.0e+00 | 1.0e+00 | NA |
Z-IPSO | 2.0e-04 | 1.9e-16 | 1.1e-16 | 1.9e-04 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 |
|
Ring topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.0e+00 | 2.1e-13 | 1.1e-16 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA |
H-EPUSLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA |
I-RLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 3.2e-02 | 1.2e-03 | 5.2e-06 | 1.0e+00 | NA | NA |
J-ISL | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA |
Z-IPSO | 1.0e+00 | 1.5e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 |
|
Differences after 100,000 function evaluations
Ackley function - 100 dimensions |
Fully-connected topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 6.2e-16 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 3.8e-16 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 4.1e-01 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.6e-06 | 1.0e+00 | 1.0e+00 | 2.4e-03 | 1.5e-10 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 4.1e-12 | 1.0e+00 | 1.0e+00 | 2.7e-12 | 2.3e-14 | 1.5e-09 | NA | NA | NA | NA |
H-EPUSLS | 5.5e-04 | 1.0e+00 | 1.0e+00 | 4.3e-05 | 2.0e-02 | 1.0e+00 | 1.0e+00 | NA | NA | NA |
I-RLS | 1.7e-14 | 2.9e-02 | 2.1e-01 | 1.7e-14 | 2.7e-12 | 1.2e-06 | 1.0e+00 | 1.6e-05 | NA | NA |
J-ISL | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 3.1e-16 | 8.0e-15 | 1.9e-12 | 2.3e-14 | 8.4e-16 | NA |
Z-IPSO | 2.3e-14 | 1.0e+00 | 1.0e+00 | 4.5e-14 | 2.9e-06 | 4.7e-01 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 |
|
Ring topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.1e-16 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.0e+00 | 1.0e+00 | 3.0e-03 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.0e+00 | 1.0e+00 | 1.4e-03 | 1.0e+00 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.0e+00 | 1.0e+00 | 7.8e-08 | 3.0e-03 | 4.7e-10 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.1e-05 | 1.0e+00 | 4.6e-14 | 1.2e-10 | 2.7e-14 | 4.0e-09 | NA | NA | NA | NA |
H-EPUSLS | 1.0e+00 | 1.0e+00 | 1.5e-09 | 8.6e-05 | 1.4e-02 | 1.0e+00 | 1.0e+00 | NA | NA | NA |
I-RLS | 1.2e-10 | 1.0e+00 | 7.1e-16 | 2.6e-12 | 2.2e-12 | 9.0e-07 | 1.0e+00 | 1.2e-05 | NA | NA |
J-ISL | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.7e-16 | 1.7e-15 | 1.5e-14 | 2.6e-14 | 5.8e-16 | NA |
Z-IPSO | 1.3e-16 | 1.0e+00 | 1.1e-16 | 4.2e-13 | 1.7e-10 | 1.0e-04 | 1.0e+00 | 9.0e-04 | 1.0e+00 | 1.0e+00 |
|
Griewank function - 100 dimensions |
Fully-connected topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.1e-16 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 2.2e-15 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 9.0e-08 | 8.5e-07 | 8.5e-07 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 5.1e-16 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.9e-16 | 7.8e-01 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 6.8e-01 | 1.0e+00 | NA | NA | NA | NA |
H-EPUSLS | 1.1e-16 | 1.9e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA |
I-RLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 8.0e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 2.1e-16 | NA | NA |
J-ISL | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 6.8e-01 | 1.0e+00 | 1.0e+00 | 1.1e-16 | 1.0e+00 | NA |
Z-IPSO | 1.1e-16 | 1.0e+00 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 |
|
Ring topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 2.5e-04 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.9e-12 | 1.8e-14 | 1.1e-16 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 7.1e-01 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 7.1e-01 | 1.0e+00 | NA | NA | NA | NA |
H-EPUSLS | 2.0e-16 | 1.1e-16 | 1.1e-16 | 7.3e-11 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA |
I-RLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 2.0e-16 | NA | NA |
J-ISL | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 7.1e-01 | 1.0e+00 | 1.0e+00 | 1.1e-16 | 1.0e+00 | NA |
Z-IPSO | 1.0e+00 | 1.0e+00 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 |
|
Rastrigin function - 100 dimensions |
Fully-connected topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.1e-16 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 7.6e-13 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 6.7e-02 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 4.8e-09 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 5.6e-12 | 3.2e-07 | NA | NA | NA | NA |
H-EPUSLS | 1.1e-16 | 1.3e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA |
I-RLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 2.0e-10 | 7.4e-05 | 5.5e-01 | 1.4e-15 | NA | NA |
J-ISL | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | NA |
Z-IPSO | 1.1e-16 | 1.0e+00 | 5.2e-11 | 8.9e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 |
|
Ring topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.5e-10 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 4.6e-09 | 5.6e-01 | 1.1e-16 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 3.6e-09 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 6.1e-12 | 5.2e-07 | NA | NA | NA | NA |
H-EPUSLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA |
I-RLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 2.2e-10 | 9.3e-05 | 5.9e-01 | 9.8e-16 | NA | NA |
J-ISL | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | NA |
Z-IPSO | 1.0e+00 | 1.0e+00 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 |
|
Rosenbrock function - 100 dimensions |
Fully-connected topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.1e-16 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 2.7e-14 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.1e-16 | 3.5e-14 | 1.1e-16 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA |
H-EPUSLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.5e-01 | 9.5e-07 | 9.5e-07 | NA | NA | NA |
I-RLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA |
J-ISL | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 4.1e-03 | 8.5e-13 | 8.5e-13 | 1.0e+00 | 1.2e-12 | NA |
Z-IPSO | 1.1e-16 | 1.0e+00 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 |
|
Ring topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.5e-01 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 8.3e-07 | 2.0e-16 | 1.1e-16 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA |
H-EPUSLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.6e-01 | 1.1e-06 | 1.1e-06 | NA | NA | NA |
I-RLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA |
J-ISL | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 4.7e-03 | 9.9e-13 | 9.9e-13 | 1.0e+00 | 1.5e-12 | NA |
Z-IPSO | 1.0e+00 | 1.0e+00 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 |
|
Salomon function - 100 dimensions |
Fully-connected topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.1e-16 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.1e-16 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 2.0e-14 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.1e-16 | 1.0e+00 | 3.2e-02 | 1.0e+00 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 7.5e-12 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 7.5e-12 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA |
H-EPUSLS | 1.1e-16 | 1.0e+00 | 1.1e-16 | 1.3e-07 | 4.0e-14 | 1.1e-16 | 1.1e-16 | NA | NA | NA |
I-RLS | 8.6e-12 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA |
J-ISL | 1.1e-16 | 1.0e+00 | 1.1e-16 | 8.1e-10 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 2.8e-03 | 1.1e-16 | NA |
Z-IPSO | 1.1e-16 | 2.0e-06 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 |
|
Ring topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 5.5e-14 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 2.1e-09 | 1.0e+00 | 1.1e-16 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.0e+00 | 1.0e+00 | 1.1e-16 | 1.0e+00 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.0e+00 | 1.0e+00 | 1.1e-16 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.0e+00 | 1.0e+00 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA |
H-EPUSLS | 1.6e-09 | 1.0e+00 | 1.1e-16 | 1.0e+00 | 3.3e-13 | 1.1e-16 | 1.1e-16 | NA | NA | NA |
I-RLS | 1.0e+00 | 1.0e+00 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA |
J-ISL | 5.5e-13 | 1.0e+00 | 1.1e-16 | 6.5e-03 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.6e-03 | 1.1e-16 | NA |
Z-IPSO | 1.0e+00 | 1.0e+00 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.1e-16 | 1.0e+00 |
|
Schaffer function - 100 dimensions |
Fully-connected topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.0e+00 | 1.0e+00 | 4.2e-04 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA |
H-EPUSLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 3.9e-16 | 1.1e-16 | 1.1e-16 | NA | NA | NA |
I-RLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA |
J-ISL | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.1e-16 | NA |
Z-IPSO | 1.0e+00 | 1.0e+00 | 2.0e-06 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 |
|
Ring topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.0e+00 | 1.0e+00 | 4.8e-10 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA |
H-EPUSLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 3.9e-16 | 1.1e-16 | 1.1e-16 | NA | NA | NA |
I-RLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA |
J-ISL | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.1e-16 | NA |
Z-IPSO | 1.0e+00 | 1.0e+00 | 2.0e-13 | 8.6e-01 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 |
|
Schwefel function - 100 dimensions |
Fully-connected topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.1e-16 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 3.1e-12 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.2e-07 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.5e-11 | 8.2e-04 | NA | NA | NA | NA |
H-EPUSLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA |
I-RLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.2e-10 | 1.7e-05 | 1.0e+00 | 9.6e-16 | NA | NA |
J-ISL | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | NA |
Z-IPSO | 8.8e-13 | 1.0e+00 | 3.9e-01 | 2.1e-13 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 |
|
Ring topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.4e-02 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.2e-04 | 1.2e-01 | 4.6e-16 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 5.8e-07 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.6e-11 | 8.9e-04 | NA | NA | NA | NA |
H-EPUSLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA |
I-RLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.3e-10 | 1.6e-05 | 1.0e+00 | 9.2e-16 | NA | NA |
J-ISL | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | NA |
Z-IPSO | 1.0e+00 | 1.0e+00 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 |
|
Sphere function - 100 dimensions |
Fully-connected topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.1e-16 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.6e-15 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.6e-14 | 5.6e-12 | 1.6e-14 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA |
H-EPUSLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA |
I-RLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.1e-16 | NA | NA |
J-ISL | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.1e-16 | 1.0e+00 | NA |
Z-IPSO | 1.1e-16 | 4.8e-01 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 |
|
Ring topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 5.8e-05 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 3.0e-12 | 1.7e-14 | 1.1e-16 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA |
H-EPUSLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA |
I-RLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.1e-16 | NA | NA |
J-ISL | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.1e-16 | 1.0e+00 | NA |
Z-IPSO | 1.0e+00 | 1.0e+00 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 |
|
Step function - 100 dimensions |
Fully-connected topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.0e-16 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.0e-16 | 2.5e-14 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.0e-16 | 1.0e-16 | 8.0e-15 | 1.0e-16 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.0e-16 | 1.2e-07 | 1.0e+00 | 1.0e-16 | 1.0e+00 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.0e-16 | 1.2e-07 | 1.0e+00 | 1.0e-16 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA |
H-EPUSLS | 1.0e-16 | 4.5e-05 | 1.0e+00 | 1.0e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA |
I-RLS | 1.0e-16 | 1.2e-07 | 1.0e+00 | 1.0e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 3.5e-11 | NA | NA |
J-ISL | 1.0e-16 | 1.0e-16 | 1.0e-16 | 1.0e-16 | 1.0e-16 | 1.0e-16 | 1.0e-16 | 1.0e-16 | 1.0e-16 | NA |
Z-IPSO | 1.0e-16 | 1.0e-16 | 1.6e-14 | 1.0e-16 | 2.3e-06 | 1.0e-16 | 1.0e-16 | 1.0e-16 | 1.0e-16 | 1.0e+00 |
|
Ring topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 9.2e-17 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 9.2e-17 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 9.2e-17 | 1.0e+00 | 1.0e+00 | 9.2e-17 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 3.0e-16 | 1.0e+00 | 1.0e+00 | 9.2e-17 | 1.0e+00 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 3.0e-16 | 1.0e+00 | 1.0e+00 | 9.2e-17 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA |
H-EPUSLS | 6.9e-16 | 1.0e+00 | 1.0e+00 | 9.2e-17 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA |
I-RLS | 3.3e-16 | 1.0e+00 | 1.0e+00 | 9.2e-17 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 4.1e-11 | NA | NA |
J-ISL | 9.2e-17 | 1.0e+00 | 3.7e-02 | 9.2e-17 | 9.2e-17 | 9.2e-17 | 9.2e-17 | 9.2e-17 | 9.2e-17 | NA |
Z-IPSO | 9.2e-17 | 1.0e+00 | 9.2e-17 | 9.2e-17 | 9.2e-17 | 9.1e-17 | 9.1e-17 | 9.2e-17 | 9.1e-17 | 9.2e-17 |
|
Weierstrass function - 100 dimensions |
Fully-connected topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.1e-16 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 8.4e-16 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.6e-11 | 1.0e+00 | 1.3e-01 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 2.5e-01 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 2.5e-01 | 1.0e+00 | NA | NA | NA | NA |
H-EPUSLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA |
I-RLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.4e-03 | 1.0e+00 | 1.0e+00 | 1.6e-11 | NA | NA |
J-ISL | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 5.2e-02 | 1.0e+00 | 1.0e+00 | 6.0e-08 | 1.0e+00 | NA |
Z-IPSO | 1.1e-16 | 1.1e-01 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 |
|
Ring topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.7e-11 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.1e-16 | 1.1e-16 | 1.1e-16 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 2.4e-01 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 2.4e-01 | 1.0e+00 | NA | NA | NA | NA |
H-EPUSLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA |
I-RLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.5e-03 | 1.0e+00 | 1.0e+00 | 1.7e-11 | NA | NA |
J-ISL | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA |
Z-IPSO | 9.6e-11 | 1.0e+00 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 |
|
Differences after 1,000,000 function evaluations
Ackley function - 100 dimensions |
Fully-connected topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 4.8e-16 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.5e-16 | 2.3e-11 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.8e-01 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 3.3e-01 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.3e-06 | 1.0e+00 | 1.0e+00 | 2.6e-02 | 3.4e-11 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 3.8e-12 | 1.0e+00 | 1.0e+00 | 1.4e-11 | 2.2e-15 | 3.7e-12 | NA | NA | NA | NA |
H-EPUSLS | 2.9e-14 | 2.6e-06 | 4.7e-01 | 1.9e-13 | 5.3e-11 | 1.5e-06 | 3.3e-01 | NA | NA | NA |
I-RLS | 1.1e-16 | 1.1e-16 | 7.2e-16 | 1.1e-16 | 9.2e-16 | 2.2e-12 | 8.2e-05 | 1.0e+00 | NA | NA |
J-ISL | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.5e-16 | 4.2e-15 | 3.8e-09 | 1.1e-03 | 2.8e-16 | NA |
Z-IPSO | 1.2e-15 | 1.0e+00 | 1.0e+00 | 1.3e-15 | 4.5e-12 | 3.7e-06 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 |
|
Ring topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.1e-16 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.1e-16 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.5e-10 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 2.7e-05 | 1.0e+00 | 1.0e+00 | 3.1e-03 | 1.2e-14 | 1.0e-10 | NA | NA | NA | NA |
H-EPUSLS | 2.8e-12 | 1.0e+00 | 1.0e+00 | 1.3e-06 | 1.0e-10 | 8.7e-07 | 2.5e-02 | NA | NA | NA |
I-RLS | 1.1e-16 | 1.5e-13 | 1.1e-16 | 1.1e-16 | 6.5e-16 | 4.3e-14 | 1.0e-10 | 1.0e+00 | NA | NA |
J-ISL | 1.1e-16 | 1.2e-15 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 2.8e-16 | 1.8e-15 | 1.2e-07 | 3.7e-16 | NA |
Z-IPSO | 1.1e-16 | 1.0e+00 | 1.1e-16 | 1.0e-10 | 2.7e-15 | 1.1e-11 | 2.1e-04 | 1.0e+00 | 1.0e+00 | 1.0e+00 |
|
Griewank function - 100 dimensions |
Fully-connected topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.1e-16 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.1e-16 | 3.7e-06 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 9.4e-08 | 4.1e-05 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.1e-16 | 2.0e-16 | 3.4e-15 | 5.4e-16 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 2.0e-16 | 1.0e+00 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA |
H-EPUSLS | 1.1e-16 | 2.0e-10 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA |
I-RLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.1e-16 | NA | NA |
J-ISL | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.1e-16 | 1.0e+00 | NA |
Z-IPSO | 1.1e-16 | 7.5e-13 | 2.8e-04 | 1.2e-02 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 |
|
Ring topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 9.9e-17 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 9.0e-05 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.1e-16 | 1.0e+00 | 9.9e-17 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 9.9e-17 | 8.6e-17 | 9.9e-17 | 2.2e-13 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 9.9e-17 | 3.2e-20 | 9.9e-17 | 1.0e-15 | 1.0e+00 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 9.9e-17 | 4.3e-22 | 9.9e-17 | 9.9e-17 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA |
H-EPUSLS | 1.2e-16 | 1.0e+00 | 9.9e-17 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA |
I-RLS | 9.9e-17 | 4.3e-22 | 9.9e-17 | 9.9e-17 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 9.9e-17 | NA | NA |
J-ISL | 9.9e-17 | 4.3e-22 | 9.9e-17 | 9.9e-17 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 9.9e-17 | 1.0e+00 | NA |
Z-IPSO | 1.0e-12 | 1.0e+00 | 9.9e-17 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 |
|
Rastrigin function - 100 dimensions |
Fully-connected topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.1e-16 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.1e-16 | 4.6e-15 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 2.5e-10 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.1e-16 | 1.1e-16 | 3.6e-01 | 1.1e-16 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.1e-16 | 1.1e-16 | 3.9e-04 | 1.1e-16 | 4.8e-09 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.1e-16 | 1.1e-16 | 1.4e-07 | 1.1e-16 | 3.6e-12 | 3.1e-08 | NA | NA | NA | NA |
H-EPUSLS | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA |
I-RLS | 1.1e-16 | 1.1e-16 | 7.6e-16 | 1.1e-16 | 1.1e-16 | 2.2e-16 | 3.2e-15 | 1.1e-16 | NA | NA |
J-ISL | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | NA |
Z-IPSO | 1.1e-16 | 1.1e-16 | 5.9e-03 | 1.1e-16 | 8.1e-01 | 1.0e+00 | 1.0e+00 | 2.7e-03 | 1.0e+00 | 1.0e+00 |
|
Ring topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.1e-16 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.1e-16 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.2e-16 | 8.6e-01 | 1.8e-03 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.3e-16 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 3.1e-09 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 2.2e-12 | 2.7e-08 | NA | NA | NA | NA |
H-EPUSLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 3.6e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA |
I-RLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.9e-16 | 2.8e-15 | 1.1e-16 | NA | NA |
J-ISL | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | NA |
Z-IPSO | 1.1e-16 | 7.0e-02 | 1.2e-08 | 8.6e-01 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 |
|
Rosenbrock function - 100 dimensions |
Fully-connected topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.1e-16 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.1e-16 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.1e-16 | 1.5e-08 | 2.2e-09 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.4e-08 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 7.6e-12 | 1.1e-07 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 4.0e-16 | 2.9e-10 | 1.1e-05 | NA | NA | NA | NA |
H-EPUSLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.4e-16 | 1.1e-11 | 5.4e-09 | 9.7e-08 | NA | NA | NA |
I-RLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 2.2e-05 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA |
J-ISL | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 8.1e-12 | 5.5e-07 | 1.5e-02 | 1.0e+00 | 1.1e-16 | NA |
Z-IPSO | 1.1e-16 | 1.0e+00 | 8.6e-02 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 |
|
Ring topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 2.9e-14 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 8.8e-03 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 4.7e-14 | 1.0e+00 | 1.1e-16 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 6.0e-08 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 3.6e-10 | 1.8e-06 | NA | NA | NA | NA |
H-EPUSLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 2.1e-11 | 3.0e-08 | 3.5e-05 | NA | NA | NA |
I-RLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA |
J-ISL | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.9e-12 | 1.9e-07 | 1.9e-02 | 1.0e+00 | 1.1e-16 | NA |
Z-IPSO | 9.2e-07 | 1.0e+00 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 |
|
Salomon function - 100 dimensions |
Fully-connected topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.1e-16 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.1e-16 | 7.6e-14 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.1e-14 | 3.1e-04 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.1e-16 | 4.3e-07 | 1.0e+00 | 1.0e+00 | 4.3e-16 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA |
H-EPUSLS | 1.1e-16 | 1.7e-02 | 1.0e+00 | 1.0e+00 | 5.0e-05 | 1.0e+00 | 1.3e-15 | NA | NA | NA |
I-RLS | 2.2e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA |
J-ISL | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.1e-16 | NA |
Z-IPSO | 1.1e-16 | 1.1e-16 | 1.0e-10 | 1.5e-08 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 |
|
Ring topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.1e-16 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 7.3e-15 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.1e-16 | 1.0e+00 | 1.1e-16 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.2e-16 | 1.0e+00 | 1.1e-16 | 1.0e+00 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.1e-16 | 1.0e+00 | 1.1e-16 | 1.0e+00 | 8.0e-10 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.7e-16 | 1.0e+00 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA |
H-EPUSLS | 1.2e-16 | 1.0e+00 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 8.3e-13 | NA | NA | NA |
I-RLS | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA |
J-ISL | 7.0e-16 | 1.0e+00 | 2.9e-14 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.1e-16 | NA |
Z-IPSO | 1.1e-16 | 1.0e+00 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.1e-16 | 1.0e+00 | 1.1e-16 | 1.1e-16 |
|
Schaffer function - 100 dimensions |
Fully-connected topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.4e-16 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 9.9e-09 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 6.6e-05 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 2.4e-04 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 3.0e-05 | 1.0e+00 | NA | NA | NA | NA |
H-EPUSLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 3.4e-05 | 1.0e+00 | 1.0e+00 | NA | NA | NA |
I-RLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA |
J-ISL | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.2e-08 | 1.3e-03 | 1.2e-02 | 2.3e-03 | 1.1e-16 | NA |
Z-IPSO | 3.1e-08 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 |
|
Ring topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.0e+00 | 1.0e+00 | 5.2e-07 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 5.6e-08 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 4.4e-06 | 1.0e+00 | NA | NA | NA | NA |
H-EPUSLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 6.2e-07 | 1.0e+00 | 1.0e+00 | NA | NA | NA |
I-RLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA |
J-ISL | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 2.9e-07 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.1e-16 | NA |
Z-IPSO | 1.0e+00 | 1.0e+00 | 1.3e-08 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 |
|
Schwefel function - 100 dimensions |
Fully-connected topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.1e-16 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.1e-16 | 1.9e-16 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.3e-04 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 7.3e-08 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-14 | 3.7e-11 | NA | NA | NA | NA |
H-EPUSLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA |
I-RLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.3e-16 | 2.6e-15 | 1.1e-16 | NA | NA |
J-ISL | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | NA |
Z-IPSO | 1.1e-16 | 1.7e-16 | 1.0e+00 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 |
|
Ring topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 6.0e-15 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 8.3e-15 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.7e-15 | 1.0e-14 | 6.8e-15 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.5e-08 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 2.6e-14 | 5.1e-11 | NA | NA | NA | NA |
H-EPUSLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA |
I-RLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.5e-16 | 3.2e-15 | 1.1e-16 | NA | NA |
J-ISL | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | NA |
Z-IPSO | 1.7e-16 | 4.2e-06 | 8.6e-09 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 |
|
Sphere function - 100 dimensions |
Fully-connected topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 9.9e-17 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 9.9e-17 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.6e-14 | 9.6e-10 | 1.6e-08 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 9.9e-17 | 6.9e-18 | 9.9e-17 | 9.9e-17 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 9.9e-17 | 6.9e-18 | 9.9e-17 | 9.9e-17 | 1.0e+00 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 9.9e-17 | 6.9e-18 | 9.9e-17 | 9.9e-17 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA |
H-EPUSLS | 9.9e-17 | 9.9e-17 | 9.9e-17 | 9.9e-17 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA |
I-RLS | 9.9e-17 | 6.9e-18 | 9.9e-17 | 9.9e-17 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 9.9e-17 | NA | NA |
J-ISL | 9.9e-17 | 6.9e-18 | 9.9e-17 | 9.9e-17 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 9.9e-17 | 1.0e+00 | NA |
Z-IPSO | 9.9e-17 | 1.0e+00 | 9.9e-17 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 |
|
Ring topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.1e-14 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.4e-04 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.1e-16 | 3.9e-04 | 9.6e-17 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 9.6e-17 | 4.3e-22 | 9.6e-17 | 9.6e-17 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 9.6e-17 | 4.3e-22 | 9.6e-17 | 9.6e-17 | 1.0e+00 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 9.6e-17 | 4.3e-22 | 9.6e-17 | 9.6e-17 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA |
H-EPUSLS | 9.6e-17 | 9.6e-17 | 9.6e-17 | 9.6e-17 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA |
I-RLS | 9.6e-17 | 4.3e-22 | 9.6e-17 | 9.6e-17 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 9.6e-17 | NA | NA |
J-ISL | 9.6e-17 | 4.3e-22 | 9.6e-17 | 9.6e-17 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 9.6e-17 | 1.0e+00 | NA |
Z-IPSO | 1.3e-12 | 1.0e+00 | 9.6e-17 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 |
|
Step function - 100 dimensions |
Fully-connected topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 8.8e-17 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 8.8e-17 | 2.5e-14 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 8.8e-17 | 8.8e-17 | 8.6e-17 | 8.8e-17 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 8.8e-17 | 8.8e-17 | 8.6e-17 | 8.8e-17 | 1.0e+00 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 8.8e-17 | 8.8e-17 | 8.8e-17 | 8.8e-17 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA |
H-EPUSLS | 8.8e-17 | 2.8e-12 | 1.0e+00 | 8.8e-17 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA |
I-RLS | 8.8e-17 | 5.3e-11 | 1.0e+00 | 8.8e-17 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA |
J-ISL | 8.8e-17 | 8.8e-17 | 8.6e-17 | 8.8e-17 | 4.6e-03 | 1.3e-01 | 5.6e-16 | 8.8e-17 | 8.2e-17 | NA |
Z-IPSO | 8.8e-17 | 8.8e-17 | 8.6e-17 | 8.8e-17 | 9.2e-01 | 1.0e+00 | 1.1e-11 | 8.8e-17 | 8.3e-17 | 1.0e+00 |
|
Ring topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 9.7e-17 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 9.7e-17 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 9.7e-17 | 1.0e+00 | 1.0e+00 | 9.7e-17 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 9.7e-17 | 1.0e+00 | 1.0e+00 | 9.7e-17 | 1.0e+00 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 9.7e-17 | 1.0e+00 | 1.0e+00 | 9.7e-17 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA |
H-EPUSLS | 2.3e-16 | 1.0e+00 | 1.0e+00 | 9.7e-17 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA |
I-RLS | 2.0e-16 | 1.0e+00 | 1.0e+00 | 9.7e-17 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.8e-03 | NA | NA |
J-ISL | 9.7e-17 | 1.0e+00 | 1.0e+00 | 9.7e-17 | 1.0e+00 | 1.0e+00 | 1.2e-14 | 9.6e-17 | 8.3e-17 | NA |
Z-IPSO | 9.7e-17 | 1.0e+00 | 1.0e+00 | 9.7e-17 | 1.7e-02 | 5.2e-02 | 5.9e-15 | 9.6e-17 | 8.3e-17 | 7.1e-02 |
|
Weierstrass function - 100 dimensions |
Fully-connected topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.1e-16 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.1e-16 | 1.1e-16 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 5.7e-14 | 1.0e+00 | 1.0e+00 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 2.6e-10 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 2.0e-15 | 2.0e-08 | NA | NA | NA | NA |
H-EPUSLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA |
I-RLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.4e-16 | 9.1e-14 | 2.0e-08 | 1.6e-16 | NA | NA |
J-ISL | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 3.0e-15 | 6.9e-10 | 1.7e-16 | 2.4e-01 | NA |
Z-IPSO | 1.1e-16 | 1.1e-16 | 1.4e-04 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 |
|
Ring topology |
| A-PSO-10 | B-PSO-100 | C-PSO-1000 | D-EPUS | E-PSOLS-5 | F-PSOLS-10 | G-PSOLS-20 | H-EPUSLS | I-RLS | J-ISL |
B-PSO-100 | 1.6e-14 | NA | NA | NA | NA | NA | NA | NA | NA | NA |
C-PSO-1000 | 1.6e-16 | 5.8e-06 | NA | NA | NA | NA | NA | NA | NA | NA |
D-EPUS | 1.1e-16 | 1.1e-16 | 1.1e-16 | NA | NA | NA | NA | NA | NA | NA |
E-PSOLS-5 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | NA | NA | NA | NA | NA | NA |
F-PSOLS-10 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.5e-10 | NA | NA | NA | NA | NA |
G-PSOLS-20 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 6.1e-16 | 3.0e-09 | NA | NA | NA | NA |
H-EPUSLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA | NA | NA |
I-RLS | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.6e-16 | 1.1e-13 | 1.4e-07 | 2.2e-16 | NA | NA |
J-ISL | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | NA |
Z-IPSO | 1.1e-16 | 1.1e-16 | 1.1e-16 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 | 1.0e+00 |
|
Effect size analysis
The following figures show the effect size due to the use of a bias of different strength in the new particles' initialization rule. The experiments were run on functions with different fitness distance correlations.
Results after 100 function evaluations
IPSO |
Fully-connected topology | Ring topology |
|
|
IPSOLS |
Fully-connected topology | Ring topology |
|
|
Results after 1,000 function evaluations
IPSO |
Fully-connected topology | Ring topology |
|
|
IPSOLS |
Fully-connected topology | Ring topology |
|
|
Results after 10,000 function evaluations
IPSO |
Fully-connected topology | Ring topology |
|
|
IPSOLS |
Fully-connected topology | Ring topology |
|
|
Results after 100,000 function evaluations
IPSO |
Fully-connected topology | Ring topology |
|
|
IPSOLS |
Fully-connected topology | Ring topology |
|
|
Results after 1,000,000 function evaluations
IPSO |
Fully-connected topology | Ring topology |
|
|
IPSOLS |
Fully-connected topology | Ring topology |
|
|
IPSOLS original vs. new version
The following figures show the boxplots of the solution quality distribution after a certain number of function evaluations. An asterisk on top of a boxplot denotes a statistically significant difference at the 5\% level between the results obtained with the indicated algorithm and those obtained with the new version (red asterisks) or the original version of IPSOLS (blue asterisks).
Results after 100 function evaluations
Ackley function - 100 dimensions |
Fully-connected topology | Ring topology |
|
|
Griewank function - 100 dimensions |
Fully-connected topology | Ring topology |
|
|
Rastrigin function - 100 dimensions |
Fully-connected topology | Ring topology |
|
|
Rosenbrock function - 100 dimensions |
Fully-connected topology | Ring topology |
|
|
Salomon function - 100 dimensions |
Fully-connected topology | Ring topology |
|
|
Schaffer function - 100 dimensions |
Fully-connected topology | Ring topology |
|
|
Schwefel function - 100 dimensions |
Fully-connected topology | Ring topology |
|
|
Sphere function - 100 dimensions |
Fully-connected topology | Ring topology |
|
|
Step function - 100 dimensions |
Fully-connected topology | Ring topology |
|
|
Weierstrass function - 100 dimensions |
Fully-connected topology | Ring topology |
|
|
Results after 1,000 function evaluations
Ackley function - 100 dimensions |
Fully-connected topology | Ring topology |
|
|
Griewank function - 100 dimensions |
Fully-connected topology | Ring topology |
|
|
Rastrigin function - 100 dimensions |
Fully-connected topology | Ring topology |
|
|
Rosenbrock function - 100 dimensions |
Fully-connected topology | Ring topology |
|
|
Salomon function - 100 dimensions |
Fully-connected topology | Ring topology |
|
|
Schaffer function - 100 dimensions |
Fully-connected topology | Ring topology |
|
|
Schwefel function - 100 dimensions |
Fully-connected topology | Ring topology |
|
|
Sphere function - 100 dimensions |
Fully-connected topology | Ring topology |
|
|
Step function - 100 dimensions |
Fully-connected topology | Ring topology |
|
|
Weierstrass function - 100 dimensions |
Fully-connected topology | Ring topology |
|
|
Results after 10,000 function evaluations
Ackley function - 100 dimensions |
Fully-connected topology | Ring topology |
|
|
Griewank function - 100 dimensions |
Fully-connected topology | Ring topology |
|
|
Rastrigin function - 100 dimensions |
Fully-connected topology | Ring topology |
|
|
Rosenbrock function - 100 dimensions |
Fully-connected topology | Ring topology |
|
|
Salomon function - 100 dimensions |
Fully-connected topology | Ring topology |
|
|
Schaffer function - 100 dimensions |
Fully-connected topology | Ring topology |
|
|
Schwefel function - 100 dimensions |
Fully-connected topology | Ring topology |
|
|
Sphere function - 100 dimensions |
Fully-connected topology | Ring topology |
|
|
Step function - 100 dimensions |
Fully-connected topology | Ring topology |
|
|
Weierstrass function - 100 dimensions |
Fully-connected topology | Ring topology |
|
|
Results after 100,000 function evaluations
Ackley function - 100 dimensions |
Fully-connected topology | Ring topology |
|
|
Griewank function - 100 dimensions |
Fully-connected topology | Ring topology |
|
|
Rastrigin function - 100 dimensions |
Fully-connected topology | Ring topology |
|
|
Rosenbrock function - 100 dimensions |
Fully-connected topology | Ring topology |
|
|
Salomon function - 100 dimensions |
Fully-connected topology | Ring topology |
|
|
Schaffer function - 100 dimensions |
Fully-connected topology | Ring topology |
|
|
Schwefel function - 100 dimensions |
Fully-connected topology | Ring topology |
|
|
Sphere function - 100 dimensions |
Fully-connected topology | Ring topology |
|
|
Step function - 100 dimensions |
Fully-connected topology | Ring topology |
|
|
Weierstrass function - 100 dimensions |
Fully-connected topology | Ring topology |
|
|
Results after 1,000,000 function evaluations
Ackley function - 100 dimensions |
Fully-connected topology | Ring topology |
|
|
Griewank function - 100 dimensions |
Fully-connected topology | Ring topology |
|
|
Rastrigin function - 100 dimensions |
Fully-connected topology | Ring topology |
|
|
Rosenbrock function - 100 dimensions |
Fully-connected topology | Ring topology |
|
|
Salomon function - 100 dimensions |
Fully-connected topology | Ring topology |
|
|
Schaffer function - 100 dimensions |
Fully-connected topology | Ring topology |
|
|
Schwefel function - 100 dimensions |
Fully-connected topology | Ring topology |
|
|
Sphere function - 100 dimensions |
Fully-connected topology | Ring topology |
|
|
Step function - 100 dimensions |
Fully-connected topology | Ring topology |
|
|
Weierstrass function - 100 dimensions |
Fully-connected topology | Ring topology |
|
|