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
  1. Paper Abstract
  2. Benchmark functions
  3. Solution quality distribution
    1. Results after 100 function evaluations
    2. Results after 1,000 function evaluations
    3. Results after 10,000 function evaluations
    4. Results after 100,000 function evaluations
    5. Results after 1,000,000 function evaluations
  4. Solution quality development and population size growth over time (mean)
    1. Ackley function
    2. Double sum function
    3. Griewank function
    4. Penalized function
    5. Rastrigin function
    6. Rosenbrock function
    7. Salomon function
    8. Schaffer function
    9. Schwefel function
    10. Sphere function
    11. Step function
    12. Weierstrass function
  5. Statistical significance results (alternative hypothesis = "less")
    1. Differences after 100 function evaluations
    2. Differences after 1,000 function evaluations
    3. Differences after 10,000 function evaluations
    4. Differences after 100,000 function evaluations
    5. Differences after 1,000,000 function evaluations
  6. Effect size analysis
    1. Results after 100 function evaluations
    2. Results after 1,000 function evaluations
    3. Results after 10,000 function evaluations
    4. Results after 100,000 function evaluations
    5. Results after 1,000,000 function evaluations
  7. IPSOLS original vs. new version
    1. Results after 100 function evaluations
    2. Results after 1,000 function evaluations
    3. Results after 10,000 function evaluations
    4. Results after 100,000 function evaluations
    5. Results after 1,000,000 function evaluations

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

Benchmark functions


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 topologyRing topology
Ackley - FC Ackley - Ring
Double sum function - 100 dimensions
Fully-connected topologyRing topology
Double sum - FC Double sum - Ring
Griewank function - 100 dimensions
Fully-connected topologyRing topology
Griewank - FC Griewank - Ring
Penalized function - 100 dimensions
Fully-connected topologyRing topology
Penalized - FC Penalized - Ring
Rastrigin function - 100 dimensions
Fully-connected topologyRing topology
Rastrigin - FC Rastrigin - Ring
Rosenbrock function - 100 dimensions
Fully-connected topologyRing topology
Rosenbrock - FC Rosenbrock - Ring
Salomon function - 100 dimensions
Fully-connected topologyRing topology
Salomon - FC Salomon - Ring
Schaffer function - 100 dimensions
Fully-connected topologyRing topology
Schaffer - FC Schaffer - Ring
Schwefel function - 100 dimensions
Fully-connected topologyRing topology
Schwefel - FC Schwefel - Ring
Sphere function - 100 dimensions
Fully-connected topologyRing topology
Sphere - FC Sphere - Ring
Step function - 100 dimensions
Fully-connected topologyRing topology
Step - FC Step - Ring
Weierstrass function - 100 dimensions
Fully-connected topologyRing topology
Weierstrass - FC Weierstrass - Ring

Results after 1000 function evaluations

Ackley function - 100 dimensions
Fully-connected topologyRing topology
Ackley - FC Ackley - Ring
Double sum function - 100 dimensions
Fully-connected topologyRing topology
Double sum - FC Double sum - Ring
Griewank function - 100 dimensions
Fully-connected topologyRing topology
Griewank - FC Griewank - Ring
Penalized function - 100 dimensions
Fully-connected topologyRing topology
Penalized - FC Penalized - Ring
Rastrigin function - 100 dimensions
Fully-connected topologyRing topology
Rastrigin - FC Rastrigin - Ring
Rosenbrock function - 100 dimensions
Fully-connected topologyRing topology
Rosenbrock - FC Rosenbrock - Ring
Salomon function - 100 dimensions
Fully-connected topologyRing topology
Salomon - FC Salomon - Ring
Schaffer function - 100 dimensions
Fully-connected topologyRing topology
Schaffer - FC Schaffer - Ring
Schwefel function - 100 dimensions
Fully-connected topologyRing topology
Schwefel - FC Schwefel - Ring
Sphere function - 100 dimensions
Fully-connected topologyRing topology
Sphere - FC Sphere - Ring
Step function - 100 dimensions
Fully-connected topologyRing topology
Step - FC Step - Ring
Weierstrass function - 100 dimensions
Fully-connected topologyRing topology
Weierstrass - FC Weierstrass - Ring

Results after 10,000 function evaluations

Ackley function - 100 dimensions
Fully-connected topologyRing topology
Ackley - FC Ackley - Ring
Double sum function - 100 dimensions
Fully-connected topologyRing topology
Double sum - FC Double sum - Ring
Griewank function - 100 dimensions
Fully-connected topologyRing topology
Griewank - FC Griewank - Ring
Penalized function - 100 dimensions
Fully-connected topologyRing topology
Penalized - FC Penalized - Ring
Rastrigin function - 100 dimensions
Fully-connected topologyRing topology
Rastrigin - FC Rastrigin - Ring
Rosenbrock function - 100 dimensions
Fully-connected topologyRing topology
Rosenbrock - FC Rosenbrock - Ring
Salomon function - 100 dimensions
Fully-connected topologyRing topology
Salomon - FC Salomon - Ring
Schaffer function - 100 dimensions
Fully-connected topologyRing topology
Schaffer - FC Schaffer - Ring
Schwefel function - 100 dimensions
Fully-connected topologyRing topology
Schwefel - FC Schwefel - Ring
Sphere function - 100 dimensions
Fully-connected topologyRing topology
Sphere - FC Sphere - Ring
Step function - 100 dimensions
Fully-connected topologyRing topology
Step - FC Step - Ring
Weierstrass function - 100 dimensions
Fully-connected topologyRing topology
Weierstrass - FC Weierstrass - Ring

Results after 100,000 function evaluations

Ackley function - 100 dimensions
Fully-connected topologyRing topology
Ackley - FC Ackley - Ring
Double sum function - 100 dimensions
Fully-connected topologyRing topology
Double sum - FC Double sum - Ring
Griewank function - 100 dimensions
Fully-connected topologyRing topology
Griewank - FC Griewank - Ring
Penalized function - 100 dimensions
Fully-connected topologyRing topology
Penalized - FC Penalized - Ring
Rastrigin function - 100 dimensions
Fully-connected topologyRing topology
Rastrigin - FC Rastrigin - Ring
Rosenbrock function - 100 dimensions
Fully-connected topologyRing topology
Rosenbrock - FC Rosenbrock - Ring
Salomon function - 100 dimensions
Fully-connected topologyRing topology
Salomon - FC Salomon - Ring
Schaffer function - 100 dimensions
Fully-connected topologyRing topology
Schaffer - FC Schaffer - Ring
Schwefel function - 100 dimensions
Fully-connected topologyRing topology
Schwefel - FC Schwefel - Ring
Sphere function - 100 dimensions
Fully-connected topologyRing topology
Sphere - FC Sphere - Ring
Step function - 100 dimensions
Fully-connected topologyRing topology
Step - FC Step - Ring
Weierstrass function - 100 dimensions
Fully-connected topologyRing topology
Weierstrass - FC Weierstrass - Ring

Results after 1,000,000 function evaluations

Ackley function - 100 dimensions
Fully-connected topologyRing topology
Ackley - FC Ackley - Ring
Double sum function - 100 dimensions
Fully-connected topologyRing topology
Double sum - FC Double sum - Ring
Griewank function - 100 dimensions
Fully-connected topologyRing topology
Griewank - FC Griewank - Ring
Penalized function - 100 dimensions
Fully-connected topologyRing topology
Penalized - FC Penalized - Ring
Rastrigin function - 100 dimensions
Fully-connected topologyRing topology
Rastrigin - FC Rastrigin - Ring
Rosenbrock function - 100 dimensions
Fully-connected topologyRing topology
Rosenbrock - FC Rosenbrock - Ring
Salomon function - 100 dimensions
Fully-connected topologyRing topology
Salomon - FC Salomon - Ring
Schaffer function - 100 dimensions
Fully-connected topologyRing topology
Schaffer - FC Schaffer - Ring
Schwefel function - 100 dimensions
Fully-connected topologyRing topology
Schwefel - FC Schwefel - Ring
Sphere function - 100 dimensions
Fully-connected topologyRing topology
Sphere - FC Sphere - Ring
Step function - 100 dimensions
Fully-connected topologyRing topology
Step - FC Step - Ring
Weierstrass function - 100 dimensions
Fully-connected topologyRing topology
Weierstrass - FC Weierstrass - Ring


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 topologyRing topology
Ackley - FC Ackley - Ring
Ackley - FC Ackley - Ring

Results on the double sum function

Double sum function - 100 dimensions
Fully-connected topologyRing topology
Double sum - FC Double sum - Ring
Double sum - FC Double sum - Ring

Results on the Griewank function

Griewank function - 100 dimensions
Fully-connected topologyRing topology
Griewank - FC Griewank - Ring
Ackley - FC Ackley - Ring

Results on the Penalized function

Penalized function - 100 dimensions
Fully-connected topologyRing topology
Penalized - FC Penalized - Ring
Penalized - FC Penalized - Ring

Results on the Rastrigin function

Rastring function - 100 dimensions
Fully-connected topologyRing topology
Rastrigin - FC Rastrigin - Ring
Ackley - FC Ackley - Ring

Results on the Rosenbrock function

Rosenbrock function - 100 dimensions
Fully-connected topologyRing topology
Rosenbrock - FC Rosenbrock - Ring
Ackley - FC Ackley - Ring

Results on the Salomon function

Salomon function - 100 dimensions
Fully-connected topologyRing topology
Salomon - FC Salomon - Ring
Ackley - FC Ackley - Ring

Results on the Schaffer function

Schaffer function - 100 dimensions
Fully-connected topologyRing topology
Schaffer - FC Schaffer - Ring
Ackley - FC Ackley - Ring

Results on the Schwefel function

Schwefel function - 100 dimensions
Fully-connected topologyRing topology
Schwefel - FC Schwefel - Ring
Ackley - FC Ackley - Ring

Results on the Sphere function

Sphere function - 100 dimensions
Fully-connected topologyRing topology
Sphere - FC Sphere - Ring
Ackley - FC Ackley - Ring

Results on the Step function

Step function - 100 dimensions
Fully-connected topologyRing topology
Step - FC Step - Ring
Ackley - FC Ackley - Ring

Results on the Weierstrass function

Weierstrass function - 100 dimensions
Fully-connected topologyRing topology
Weierstrass - FC Weierstrass - Ring
Ackley - FC Ackley - Ring


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-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.0e+00 NA NA NA NA NA NA NA NA NA
C-PSO-10001.0e+001.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.0e+006.5e-036.5e-03 NA NA NA NA NA NA NA
E-PSOLS-51.0e+001.0e+001.0e+001.0e+00 NA NA NA NA NA NA
F-PSOLS-101.0e+001.0e+001.0e+001.0e+008.4e-07 NA NA NA NA NA
G-PSOLS-201.0e+001.0e+001.0e+001.0e+002.3e-074.1e-03 NA NA NA NA
H-EPUSLS1.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00 NA NA NA
I-RLS1.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00 NA NA
J-ISL1.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00 NA
Z-IPSO5.5e-072.7e-162.7e-168.3e-111.2e-161.2e-161.2e-161.5e-161.2e-161.2e-16
Ring topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.0e+00 NA NA NA NA NA NA NA NA NA
C-PSO-10001.0e+001.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.0e+006.3e-036.3e-03 NA NA NA NA NA NA NA
E-PSOLS-51.0e+001.0e+001.0e+001.0e+00 NA NA NA NA NA NA
F-PSOLS-101.0e+001.0e+001.0e+001.0e+008.4e-07 NA NA NA NA NA
G-PSOLS-201.0e+001.0e+001.0e+001.0e+002.3e-074.1e-03 NA NA NA NA
H-EPUSLS1.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00 NA NA NA
I-RLS1.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00 NA NA
J-ISL1.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00 NA
Z-IPSO1.7e-084.6e-164.6e-161.7e-121.6e-162.0e-162.2e-161.6e-161.5e-161.5e-16
Griewank function - 100 dimensions
Fully-connected topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.0e+00 NA NA NA NA NA NA NA NA NA
C-PSO-10001.0e+001.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.0e+001.7e-151.7e-15 NA NA NA NA NA NA NA
E-PSOLS-51.0e+001.0e+001.0e+001.0e+00 NA NA NA NA NA NA
F-PSOLS-101.0e+001.0e+001.0e+001.0e+001.7e-03 NA NA NA NA NA
G-PSOLS-201.0e+001.0e+001.0e+001.0e+002.2e-054.0e-02 NA NA NA NA
H-EPUSLS1.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00 NA NA NA
I-RLS1.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00 NA NA
J-ISL1.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00 NA
Z-IPSO2.7e-091.1e-161.1e-162.8e-141.1e-161.1e-161.1e-161.1e-161.1e-161.1e-16
Ring topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.0e+00 NA NA NA NA NA NA NA NA NA
C-PSO-10001.0e+001.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.0e+002.8e-152.8e-15 NA NA NA NA NA NA NA
E-PSOLS-51.0e+001.0e+001.0e+001.0e+00 NA NA NA NA NA NA
F-PSOLS-101.0e+001.0e+001.0e+001.0e+001.7e-03 NA NA NA NA NA
G-PSOLS-201.0e+001.0e+001.0e+001.0e+002.2e-054.0e-02 NA NA NA NA
H-EPUSLS1.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00 NA NA NA
I-RLS1.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00 NA NA
J-ISL1.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00 NA
Z-IPSO6.5e-131.1e-161.1e-169.7e-151.1e-161.1e-161.1e-161.1e-161.1e-161.1e-16
Rastrigin function - 100 dimensions
Fully-connected topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.0e+00 NA NA NA NA NA NA NA NA NA
C-PSO-10001.0e+001.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.0e+006.4e-156.4e-15 NA NA NA NA NA NA NA
E-PSOLS-51.0e+001.0e+001.0e+001.0e+00 NA NA NA NA NA NA
F-PSOLS-101.0e+001.0e+001.0e+001.0e+001.5e-03 NA NA NA NA NA
G-PSOLS-201.0e+001.0e+001.0e+001.0e+001.1e-066.3e-04 NA NA NA NA
H-EPUSLS1.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00 NA NA NA
I-RLS1.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00 NA NA
J-ISL1.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00 NA
Z-IPSO7.8e-111.1e-161.1e-161.6e-141.1e-161.1e-161.1e-161.1e-161.1e-161.1e-16
Ring topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.0e+00 NA NA NA NA NA NA NA NA NA
C-PSO-10001.0e+001.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.0e+006.8e-156.8e-15 NA NA NA NA NA NA NA
E-PSOLS-51.0e+001.0e+001.0e+001.0e+00 NA NA NA NA NA NA
F-PSOLS-101.0e+001.0e+001.0e+001.0e+001.5e-03 NA NA NA NA NA
G-PSOLS-201.0e+001.0e+001.0e+001.0e+001.1e-066.3e-04 NA NA NA NA
H-EPUSLS1.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00 NA NA NA
I-RLS1.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00 NA NA
J-ISL1.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00 NA
Z-IPSO7.7e-121.1e-161.1e-161.9e-131.1e-161.1e-161.1e-161.1e-161.1e-161.1e-16
Rosenbrock function - 100 dimensions
Fully-connected topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.0e+00 NA NA NA NA NA NA NA NA NA
C-PSO-10001.0e+001.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.0e+001.1e-161.1e-16 NA NA NA NA NA NA NA
E-PSOLS-51.0e+001.0e+001.0e+001.0e+00 NA NA NA NA NA NA
F-PSOLS-101.0e+001.0e+001.0e+001.0e+003.1e-05 NA NA NA NA NA
G-PSOLS-201.0e+001.0e+001.0e+001.0e+001.2e-111.5e-08 NA NA NA NA
H-EPUSLS1.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00 NA NA NA
I-RLS1.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00 NA NA
J-ISL1.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00 NA
Z-IPSO6.0e-141.1e-161.1e-162.1e-151.1e-161.1e-161.1e-161.1e-161.1e-161.1e-16
Ring topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.0e+00 NA NA NA NA NA NA NA NA NA
C-PSO-10001.0e+001.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.0e+002.3e-162.3e-16 NA NA NA NA NA NA NA
E-PSOLS-51.0e+001.0e+001.0e+001.0e+00 NA NA NA NA NA NA
F-PSOLS-101.0e+001.0e+001.0e+001.0e+003.1e-05 NA NA NA NA NA
G-PSOLS-201.0e+001.0e+001.0e+001.0e+001.2e-111.5e-08 NA NA NA NA
H-EPUSLS1.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00 NA NA NA
I-RLS1.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00 NA NA
J-ISL1.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00 NA
Z-IPSO1.5e-151.1e-161.1e-161.5e-151.1e-161.1e-161.1e-161.1e-161.1e-161.1e-16
Salomon function - 100 dimensions
Fully-connected topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.0e+00 NA NA NA NA NA NA NA NA NA
C-PSO-10001.0e+001.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.0e+001.1e-141.1e-14 NA NA NA NA NA NA NA
E-PSOLS-51.0e+001.0e+001.0e+001.0e+00 NA NA NA NA NA NA
F-PSOLS-101.0e+001.0e+001.0e+001.0e+005.6e-08 NA NA NA NA NA
G-PSOLS-201.0e+001.0e+001.0e+001.0e+002.6e-128.1e-09 NA NA NA NA
H-EPUSLS1.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00 NA NA NA
I-RLS1.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00 NA NA
J-ISL1.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00 NA
Z-IPSO8.8e-101.1e-161.1e-165.3e-161.1e-161.1e-161.1e-161.1e-161.1e-161.1e-16
Ring topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.0e+00 NA NA NA NA NA NA NA NA NA
C-PSO-10001.0e+001.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.0e+001.6e-141.6e-14 NA NA NA NA NA NA NA
E-PSOLS-51.0e+001.0e+001.0e+001.0e+00 NA NA NA NA NA NA
F-PSOLS-101.0e+001.0e+001.0e+001.0e+005.6e-08 NA NA NA NA NA
G-PSOLS-201.0e+001.0e+001.0e+001.0e+002.6e-128.1e-09 NA NA NA NA
H-EPUSLS1.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00 NA NA NA
I-RLS1.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00 NA NA
J-ISL1.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00 NA
Z-IPSO9.8e-141.1e-161.1e-164.3e-151.1e-161.1e-161.1e-161.1e-161.1e-161.1e-16
Schaffer function - 100 dimensions
Fully-connected topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.0e+00 NA NA NA NA NA NA NA NA NA
C-PSO-10001.0e+001.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.0e+001.0e+001.0e+00 NA NA NA NA NA NA NA
E-PSOLS-51.0e+001.0e+001.0e+001.0e+00 NA NA NA NA NA NA
F-PSOLS-101.0e+001.0e+001.0e+001.0e+002.0e-06 NA NA NA NA NA
G-PSOLS-201.0e+001.0e+001.0e+001.0e+002.3e-091.4e-04 NA NA NA NA
H-EPUSLS1.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00 NA NA NA
I-RLS1.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00 NA NA
J-ISL1.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00 NA
Z-IPSO1.0e+001.0e+001.0e+001.0e+001.3e-132.3e-114.2e-083.0e-168.7e-158.7e-15
Ring topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.0e+00 NA NA NA NA NA NA NA NA NA
C-PSO-10001.0e+001.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.0e+001.0e+001.0e+00 NA NA NA NA NA NA NA
E-PSOLS-51.0e+001.0e+001.0e+001.0e+00 NA NA NA NA NA NA
F-PSOLS-101.0e+001.0e+001.0e+001.0e+002.0e-06 NA NA NA NA NA
G-PSOLS-201.0e+001.0e+001.0e+001.0e+002.3e-091.4e-04 NA NA NA NA
H-EPUSLS1.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00 NA NA NA
I-RLS1.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00 NA NA
J-ISL1.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00 NA
Z-IPSO1.0e+001.0e+001.0e+001.0e+001.1e-136.6e-124.3e-088.0e-166.4e-156.4e-15
Schwefel function - 100 dimensions
Fully-connected topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.0e+00 NA NA NA NA NA NA NA NA NA
C-PSO-10001.0e+001.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.0e+001.0e+001.0e+00 NA NA NA NA NA NA NA
E-PSOLS-51.0e+001.0e+001.0e+001.0e+00 NA NA NA NA NA NA
F-PSOLS-101.0e+001.0e+001.0e+001.0e+008.7e-02 NA NA NA NA NA
G-PSOLS-201.0e+001.0e+001.0e+001.5e-012.4e-064.8e-03 NA NA NA NA
H-EPUSLS1.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00 NA NA NA
I-RLS1.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00 NA NA
J-ISL1.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00 NA
Z-IPSO1.0e+002.7e-072.7e-074.8e-154.1e-159.6e-151.3e-132.3e-151.4e-151.4e-15
Ring topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.0e+00 NA NA NA NA NA NA NA NA NA
C-PSO-10001.0e+001.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.0e+001.0e+001.0e+00 NA NA NA NA NA NA NA
E-PSOLS-51.0e+001.0e+001.0e+001.0e+00 NA NA NA NA NA NA
F-PSOLS-101.0e+001.0e+001.0e+001.0e+008.5e-02 NA NA NA NA NA
G-PSOLS-201.0e+001.0e+001.0e+002.2e-022.6e-065.0e-03 NA NA NA NA
H-EPUSLS1.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00 NA NA NA
I-RLS1.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00 NA NA
J-ISL1.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00 NA
Z-IPSO1.0e+001.4e-021.4e-022.5e-149.1e-142.7e-131.3e-121.2e-138.9e-158.9e-15
Sphere function - 100 dimensions
Fully-connected topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.0e+00 NA NA NA NA NA NA NA NA NA
C-PSO-10001.0e+001.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.0e+001.7e-151.7e-15 NA NA NA NA NA NA NA
E-PSOLS-51.0e+001.0e+001.0e+001.0e+00 NA NA NA NA NA NA
F-PSOLS-101.0e+001.0e+001.0e+001.0e+001.7e-03 NA NA NA NA NA
G-PSOLS-201.0e+001.0e+001.0e+001.0e+002.2e-054.0e-02 NA NA NA NA
H-EPUSLS1.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00 NA NA NA
I-RLS1.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00 NA NA
J-ISL1.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00 NA
Z-IPSO2.7e-091.1e-161.1e-162.8e-141.1e-161.1e-161.1e-161.1e-161.1e-161.1e-16
Ring topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.0e+00 NA NA NA NA NA NA NA NA NA
C-PSO-10001.0e+001.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.0e+002.8e-152.8e-15 NA NA NA NA NA NA NA
E-PSOLS-51.0e+001.0e+001.0e+001.0e+00 NA NA NA NA NA NA
F-PSOLS-101.0e+001.0e+001.0e+001.0e+001.7e-03 NA NA NA NA NA
G-PSOLS-201.0e+001.0e+001.0e+001.0e+002.2e-054.0e-02 NA NA NA NA
H-EPUSLS1.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00 NA NA NA
I-RLS1.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00 NA NA
J-ISL1.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00 NA
Z-IPSO6.5e-131.1e-161.1e-169.7e-151.1e-161.1e-161.1e-161.1e-161.1e-161.1e-16
Step function - 100 dimensions
Fully-connected topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.0e+00 NA NA NA NA NA NA NA NA NA
C-PSO-10001.0e+001.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.0e+001.0e+001.0e+00 NA NA NA NA NA NA NA
E-PSOLS-51.0e+001.0e+001.0e+001.0e+00 NA NA NA NA NA NA
F-PSOLS-101.0e+001.0e+001.0e+005.9e-011.2e-03 NA NA NA NA NA
G-PSOLS-201.0e+001.0e+001.0e+004.5e-061.4e-081.0e-05 NA NA NA NA
H-EPUSLS1.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00 NA NA NA
I-RLS1.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00 NA NA
J-ISL1.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00 NA
Z-IPSO1.0e+001.1e-161.1e-161.1e-161.1e-161.1e-161.1e-161.1e-161.1e-161.1e-16
Ring topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.0e+00 NA NA NA NA NA NA NA NA NA
C-PSO-10001.0e+001.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.0e+001.0e+001.0e+00 NA NA NA NA NA NA NA
E-PSOLS-51.0e+001.0e+001.0e+001.0e+00 NA NA NA NA NA NA
F-PSOLS-101.0e+001.0e+001.0e+007.9e-011.2e-03 NA NA NA NA NA
G-PSOLS-201.0e+001.0e+001.0e+004.8e-061.4e-081.0e-05 NA NA NA NA
H-EPUSLS1.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00 NA NA NA
I-RLS1.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00 NA NA
J-ISL1.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00 NA
Z-IPSO1.0e+002.6e-162.6e-161.1e-161.1e-161.1e-161.2e-161.1e-161.1e-161.1e-16
Weierstrass function - 100 dimensions
Fully-connected topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.0e+00 NA NA NA NA NA NA NA NA NA
C-PSO-10001.0e+001.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.0e+001.0e+001.0e+00 NA NA NA NA NA NA NA
E-PSOLS-51.0e+001.0e+001.0e+001.0e+00 NA NA NA NA NA NA
F-PSOLS-101.0e+001.0e+001.0e+001.0e+001.0e+00 NA NA NA NA NA
G-PSOLS-201.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00 NA NA NA NA
H-EPUSLS1.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00 NA NA NA
I-RLS1.0e+001.0e+001.0e+001.0e+008.9e-011.0e+001.0e+001.0e+00 NA NA
J-ISL1.0e+001.0e+001.0e+001.0e+008.9e-011.0e+001.0e+001.0e+001.0e+00 NA
Z-IPSO7.3e-037.6e-157.6e-152.9e-151.3e-147.3e-155.1e-151.2e-159.9e-159.9e-15
Ring topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.0e+00 NA NA NA NA NA NA NA NA NA
C-PSO-10001.0e+001.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.0e+001.0e+001.0e+00 NA NA NA NA NA NA NA
E-PSOLS-51.0e+001.0e+001.0e+001.0e+00 NA NA NA NA NA NA
F-PSOLS-101.0e+001.0e+001.0e+001.0e+001.0e+00 NA NA NA NA NA
G-PSOLS-201.0e+001.0e+001.0e+004.0e-011.0e+001.0e+00 NA NA NA NA
H-EPUSLS1.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00 NA NA NA
I-RLS1.0e+001.0e+001.0e+001.0e+008.9e-011.0e+001.0e+001.0e+00 NA NA
J-ISL1.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00 NA
Z-IPSO1.0e+005.8e-085.8e-083.4e-137.2e-113.1e-112.2e-117.0e-126.3e-114.7e-12

Differences after 1000 function evaluations

Ackley function - 100 dimensions
Fully-connected topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.0e+00 NA NA NA NA NA NA NA NA NA
C-PSO-10001.0e+001.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.0e+001.0e+001.6e-11 NA NA NA NA NA NA NA
E-PSOLS-51.1e-161.1e-161.1e-161.1e-16 NA NA NA NA NA NA
F-PSOLS-101.1e-161.1e-161.1e-161.1e-161.0e+00 NA NA NA NA NA
G-PSOLS-201.1e-161.1e-161.1e-161.1e-161.0e+001.0e+00 NA NA NA NA
H-EPUSLS1.1e-161.1e-161.1e-161.1e-161.0e+001.0e+001.0e+00 NA NA NA
I-RLS1.1e-161.1e-161.1e-161.1e-169.3e-103.6e-141.3e-161.0e+00 NA NA
J-ISL1.1e-161.1e-161.1e-161.1e-169.3e-103.6e-141.3e-161.0e+001.0e+00 NA
Z-IPSO9.1e-037.5e-051.1e-163.5e-111.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00
Ring topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.0e+00 NA NA NA NA NA NA NA NA NA
C-PSO-10001.0e+001.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.0e+001.0e+007.9e-12 NA NA NA NA NA NA NA
E-PSOLS-58.4e-161.1e-161.1e-161.1e-16 NA NA NA NA NA NA
F-PSOLS-108.4e-161.1e-161.1e-161.1e-161.0e+00 NA NA NA NA NA
G-PSOLS-209.0e-161.1e-161.1e-161.1e-161.0e+001.0e+00 NA NA NA NA
H-EPUSLS9.8e-161.1e-161.1e-161.1e-161.0e+001.0e+001.0e+00 NA NA NA
I-RLS8.4e-161.1e-161.1e-161.1e-168.9e-103.3e-141.5e-161.0e+00 NA NA
J-ISL8.4e-161.1e-161.1e-161.1e-168.9e-103.3e-141.5e-161.0e+001.0e+00 NA
Z-IPSO4.9e-011.2e-161.1e-162.4e-161.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00
Griewank function - 100 dimensions
Fully-connected topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.0e+00 NA NA NA NA NA NA NA NA NA
C-PSO-10001.0e+001.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.0e+004.9e-111.1e-16 NA NA NA NA NA NA NA
E-PSOLS-51.1e-161.1e-161.1e-161.1e-16 NA NA NA NA NA NA
F-PSOLS-101.1e-161.1e-161.1e-161.1e-161.0e+00 NA NA NA NA NA
G-PSOLS-201.1e-161.1e-161.1e-161.1e-161.0e+001.0e+00 NA NA NA NA
H-EPUSLS1.1e-161.1e-161.1e-161.1e-161.0e+001.0e+001.0e+00 NA NA NA
I-RLS1.1e-161.1e-161.1e-161.1e-161.0e+001.0e+001.0e+001.0e+00 NA NA
J-ISL1.1e-161.1e-161.1e-161.1e-161.0e+001.0e+001.0e+001.0e+001.0e+00 NA
Z-IPSO1.0e+001.1e-161.1e-161.4e-141.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00
Ring topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.0e+00 NA NA NA NA NA NA NA NA NA
C-PSO-10001.0e+001.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.0e+001.1e-161.1e-16 NA NA NA NA NA NA NA
E-PSOLS-51.1e-161.1e-161.1e-161.1e-16 NA NA NA NA NA NA
F-PSOLS-101.1e-161.1e-161.1e-161.1e-161.0e+00 NA NA NA NA NA
G-PSOLS-201.1e-161.1e-161.1e-161.1e-161.0e+001.0e+00 NA NA NA NA
H-EPUSLS1.1e-161.1e-161.1e-161.1e-161.0e+001.0e+001.0e+00 NA NA NA
I-RLS1.1e-161.1e-161.1e-161.1e-161.0e+001.0e+001.0e+001.0e+00 NA NA
J-ISL1.1e-161.1e-161.1e-161.1e-161.0e+001.0e+001.0e+001.0e+001.0e+00 NA
Z-IPSO1.0e+001.1e-161.1e-161.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00
Rastrigin function - 100 dimensions
Fully-connected topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.0e+00 NA NA NA NA NA NA NA NA NA
C-PSO-10001.0e+001.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.0e+002.5e-041.1e-16 NA NA NA NA NA NA NA
E-PSOLS-51.1e-161.1e-161.1e-161.1e-16 NA NA NA NA NA NA
F-PSOLS-101.1e-161.1e-161.1e-161.1e-161.0e+00 NA NA NA NA NA
G-PSOLS-201.1e-161.1e-161.1e-161.1e-161.0e+001.0e+00 NA NA NA NA
H-EPUSLS1.1e-161.1e-161.1e-161.1e-162.2e-012.1e-022.9e-04 NA NA NA
I-RLS1.1e-161.1e-161.1e-161.1e-166.5e-132.4e-161.1e-161.0e+00 NA NA
J-ISL1.1e-161.1e-161.1e-161.1e-166.5e-132.4e-161.1e-161.0e+001.0e+00 NA
Z-IPSO1.0e+001.6e-141.1e-161.6e-031.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00
Ring topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.0e+00 NA NA NA NA NA NA NA NA NA
C-PSO-10001.0e+001.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.0e+001.6e-141.1e-16 NA NA NA NA NA NA NA
E-PSOLS-51.1e-161.1e-161.1e-161.1e-16 NA NA NA NA NA NA
F-PSOLS-101.1e-161.1e-161.1e-161.1e-161.0e+00 NA NA NA NA NA
G-PSOLS-201.1e-161.1e-161.1e-161.1e-161.0e+001.0e+00 NA NA NA NA
H-EPUSLS1.1e-161.1e-161.1e-161.1e-162.2e-012.1e-022.8e-04 NA NA NA
I-RLS1.1e-161.1e-161.1e-161.1e-166.2e-132.4e-161.1e-161.0e+00 NA NA
J-ISL1.1e-161.1e-161.1e-161.1e-166.2e-132.4e-161.1e-161.0e+001.0e+00 NA
Z-IPSO1.0e+001.1e-161.1e-162.8e-101.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00
Rosenbrock function - 100 dimensions
Fully-connected topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.0e+00 NA NA NA NA NA NA NA NA NA
C-PSO-10001.0e+001.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.0e+002.0e-141.1e-16 NA NA NA NA NA NA NA
E-PSOLS-51.0e+001.0e+001.1e-161.0e+00 NA NA NA NA NA NA
F-PSOLS-101.0e+001.0e+001.1e-161.0e+001.0e+00 NA NA NA NA NA
G-PSOLS-201.0e+001.0e+001.1e-161.0e+001.0e+001.0e+00 NA NA NA NA
H-EPUSLS1.0e+001.0e+001.1e-161.0e+002.4e-018.6e-021.7e-02 NA NA NA
I-RLS1.0e+001.0e+001.1e-161.0e+007.0e-151.1e-161.1e-161.0e+00 NA NA
J-ISL1.0e+001.0e+001.1e-161.0e+007.0e-151.1e-161.1e-161.0e+001.0e+00 NA
Z-IPSO1.0e+001.1e-161.1e-161.1e-137.8e-166.5e-162.2e-163.5e-141.1e-151.1e-15
Ring topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.0e+00 NA NA NA NA NA NA NA NA NA
C-PSO-10001.0e+001.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.0e+001.1e-161.1e-16 NA NA NA NA NA NA NA
E-PSOLS-51.0e+009.8e-131.1e-161.0e+00 NA NA NA NA NA NA
F-PSOLS-101.0e+003.0e-121.1e-161.0e+001.0e+00 NA NA NA NA NA
G-PSOLS-201.0e+004.0e-111.1e-161.0e+001.0e+001.0e+00 NA NA NA NA
H-EPUSLS1.0e+003.1e-151.1e-161.0e+002.0e-017.2e-021.4e-02 NA NA NA
I-RLS1.0e+006.1e-131.1e-161.0e+007.6e-151.1e-161.1e-161.0e+00 NA NA
J-ISL1.0e+006.1e-131.1e-161.0e+007.6e-151.1e-161.1e-161.0e+001.0e+00 NA
Z-IPSO1.0e+001.1e-161.1e-161.0e+008.9e-071.5e-077.1e-091.1e-022.5e-062.5e-06
Salomon function - 100 dimensions
Fully-connected topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.0e+00 NA NA NA NA NA NA NA NA NA
C-PSO-10001.0e+001.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.0e+001.0e+001.3e-16 NA NA NA NA NA NA NA
E-PSOLS-51.0e+001.0e+001.0e+001.0e+00 NA NA NA NA NA NA
F-PSOLS-101.0e+001.0e+001.0e+001.0e+008.3e-06 NA NA NA NA NA
G-PSOLS-201.0e+001.0e+001.0e+001.0e+002.8e-106.3e-07 NA NA NA NA
H-EPUSLS1.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00 NA NA NA
I-RLS1.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00 NA NA
J-ISL1.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00 NA
Z-IPSO1.0e+001.1e-161.1e-161.5e-161.1e-161.1e-161.1e-161.1e-161.1e-161.1e-16
Ring topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.0e+00 NA NA NA NA NA NA NA NA NA
C-PSO-10001.0e+001.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.0e+001.4e-161.1e-16 NA NA NA NA NA NA NA
E-PSOLS-51.0e+001.0e+001.0e+001.0e+00 NA NA NA NA NA NA
F-PSOLS-101.0e+001.0e+001.0e+001.0e+008.3e-06 NA NA NA NA NA
G-PSOLS-201.0e+001.0e+001.0e+001.0e+002.8e-106.3e-07 NA NA NA NA
H-EPUSLS1.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00 NA NA NA
I-RLS1.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00 NA NA
J-ISL1.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00 NA
Z-IPSO1.0e+001.1e-161.1e-161.9e-021.1e-161.1e-161.1e-161.1e-161.1e-161.1e-16
Schaffer function - 100 dimensions
Fully-connected topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.0e+00 NA NA NA NA NA NA NA NA NA
C-PSO-10001.0e+001.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.0e+001.0e+001.0e+00 NA NA NA NA NA NA NA
E-PSOLS-51.4e-143.1e-151.8e-151.9e-15 NA NA NA NA NA NA
F-PSOLS-101.4e-143.2e-151.9e-151.9e-151.0e+00 NA NA NA NA NA
G-PSOLS-202.0e-145.3e-152.3e-152.1e-151.0e+001.0e+00 NA NA NA NA
H-EPUSLS5.3e-152.1e-154.4e-161.7e-161.0e+001.0e+001.0e+00 NA NA NA
I-RLS1.0e-142.3e-151.5e-151.5e-154.9e-087.8e-135.3e-151.0e+00 NA NA
J-ISL1.0e-142.3e-151.5e-151.5e-154.9e-087.8e-135.3e-151.0e+001.0e+00 NA
Z-IPSO1.0e+001.0e+006.4e-032.2e-021.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00
Ring topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.0e+00 NA NA NA NA NA NA NA NA NA
C-PSO-10001.0e+001.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.0e+001.0e+001.0e+00 NA NA NA NA NA NA NA
E-PSOLS-51.9e-141.2e-151.5e-159.2e-16 NA NA NA NA NA NA
F-PSOLS-101.9e-141.2e-151.5e-159.3e-161.0e+00 NA NA NA NA NA
G-PSOLS-202.9e-141.4e-152.1e-151.2e-151.0e+001.0e+00 NA NA NA NA
H-EPUSLS8.7e-154.8e-164.4e-161.8e-161.0e+001.0e+001.0e+00 NA NA NA
I-RLS1.4e-141.0e-151.3e-157.6e-164.9e-087.8e-135.1e-151.0e+00 NA NA
J-ISL1.4e-141.0e-151.3e-157.6e-164.9e-087.8e-135.1e-151.0e+001.0e+00 NA
Z-IPSO1.0e+003.2e-046.3e-035.5e-041.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00
Schwefel function - 100 dimensions
Fully-connected topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.0e+00 NA NA NA NA NA NA NA NA NA
C-PSO-10001.0e+001.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.0e+001.0e+001.0e+00 NA NA NA NA NA NA NA
E-PSOLS-51.1e-161.1e-161.1e-161.1e-16 NA NA NA NA NA NA
F-PSOLS-101.1e-161.1e-161.1e-161.1e-161.0e+00 NA NA NA NA NA
G-PSOLS-201.1e-161.1e-161.1e-161.1e-161.0e+001.0e+00 NA NA NA NA
H-EPUSLS1.1e-161.1e-161.1e-161.1e-161.0e+001.0e+001.0e+00 NA NA NA
I-RLS1.1e-161.1e-161.1e-161.1e-162.9e-091.1e-151.1e-161.0e+00 NA NA
J-ISL1.1e-161.1e-161.1e-161.1e-162.9e-091.1e-151.1e-161.0e+001.0e+00 NA
Z-IPSO1.0e+001.1e-161.1e-161.9e-161.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00
Ring topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.0e+00 NA NA NA NA NA NA NA NA NA
C-PSO-10001.0e+001.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.0e+001.0e+001.0e+00 NA NA NA NA NA NA NA
E-PSOLS-51.1e-161.1e-161.1e-161.1e-16 NA NA NA NA NA NA
F-PSOLS-101.1e-161.1e-161.1e-161.1e-161.0e+00 NA NA NA NA NA
G-PSOLS-201.1e-161.1e-161.1e-161.1e-161.0e+001.0e+00 NA NA NA NA
H-EPUSLS1.1e-161.1e-161.1e-161.1e-161.0e+001.0e+001.0e+00 NA NA NA
I-RLS1.1e-161.1e-161.1e-161.1e-162.9e-091.1e-151.1e-161.0e+00 NA NA
J-ISL1.1e-161.1e-161.1e-161.1e-162.9e-091.1e-151.1e-161.0e+001.0e+00 NA
Z-IPSO1.0e+001.8e-161.1e-162.1e-161.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00
Sphere function - 100 dimensions
Fully-connected topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.0e+00 NA NA NA NA NA NA NA NA NA
C-PSO-10001.0e+001.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.0e+001.5e-121.1e-16 NA NA NA NA NA NA NA
E-PSOLS-51.1e-161.1e-161.1e-161.1e-16 NA NA NA NA NA NA
F-PSOLS-101.1e-161.1e-161.1e-161.1e-161.0e+00 NA NA NA NA NA
G-PSOLS-201.1e-161.1e-161.1e-161.1e-161.0e+001.0e+00 NA NA NA NA
H-EPUSLS1.1e-161.1e-161.1e-161.1e-161.0e+001.0e+001.0e+00 NA NA NA
I-RLS1.1e-161.1e-161.1e-161.1e-161.0e+001.0e+001.0e+001.0e+00 NA NA
J-ISL1.1e-161.1e-161.1e-161.1e-161.0e+001.0e+001.0e+001.0e+001.0e+00 NA
Z-IPSO1.0e+001.1e-161.1e-162.7e-121.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00
Ring topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.0e+00 NA NA NA NA NA NA NA NA NA
C-PSO-10001.0e+001.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.0e+001.1e-161.1e-16 NA NA NA NA NA NA NA
E-PSOLS-51.1e-161.1e-161.1e-161.1e-16 NA NA NA NA NA NA
F-PSOLS-101.1e-161.1e-161.1e-161.1e-161.0e+00 NA NA NA NA NA
G-PSOLS-201.1e-161.1e-161.1e-161.1e-161.0e+001.0e+00 NA NA NA NA
H-EPUSLS1.1e-161.1e-161.1e-161.1e-161.0e+001.0e+001.0e+00 NA NA NA
I-RLS1.1e-161.1e-161.1e-161.1e-161.0e+001.0e+001.0e+001.0e+00 NA NA
J-ISL1.1e-161.1e-161.1e-161.1e-161.0e+001.0e+001.0e+001.0e+001.0e+00 NA
Z-IPSO1.0e+001.1e-161.1e-161.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00
Step function - 100 dimensions
Fully-connected topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.0e+00 NA NA NA NA NA NA NA NA NA
C-PSO-10001.0e+001.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.0e+001.0e+001.0e+00 NA NA NA NA NA NA NA
E-PSOLS-51.0e+007.4e-011.1e-161.1e-16 NA NA NA NA NA NA
F-PSOLS-101.0e+001.0e+001.1e-161.1e-161.0e+00 NA NA NA NA NA
G-PSOLS-201.0e+001.0e+001.1e-161.1e-161.0e+001.0e+00 NA NA NA NA
H-EPUSLS1.0e+001.2e-011.1e-161.1e-161.0e+001.0e+002.3e-01 NA NA NA
I-RLS1.0e+003.7e-011.1e-161.1e-162.4e-061.6e-102.8e-131.0e+00 NA NA
J-ISL1.0e+003.7e-011.1e-161.1e-162.4e-061.6e-102.8e-131.0e+001.0e+00 NA
Z-IPSO1.0e+009.6e-161.1e-161.1e-165.5e-144.0e-142.1e-142.9e-138.5e-148.5e-14
Ring topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.0e+00 NA NA NA NA NA NA NA NA NA
C-PSO-10001.0e+001.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.0e+001.0e+001.0e+00 NA NA NA NA NA NA NA
E-PSOLS-51.0e+001.1e-161.1e-161.1e-16 NA NA NA NA NA NA
F-PSOLS-101.0e+001.1e-161.1e-161.1e-161.0e+00 NA NA NA NA NA
G-PSOLS-201.0e+001.1e-161.1e-161.1e-161.0e+001.0e+00 NA NA NA NA
H-EPUSLS1.0e+001.1e-161.1e-161.1e-161.0e+001.0e+002.4e-01 NA NA NA
I-RLS1.0e+001.1e-161.1e-161.1e-162.4e-061.6e-102.7e-131.0e+00 NA NA
J-ISL1.0e+001.1e-161.1e-161.1e-162.4e-061.6e-102.7e-131.0e+001.0e+00 NA
Z-IPSO1.0e+001.1e-161.1e-161.1e-161.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00
Weierstrass function - 100 dimensions
Fully-connected topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.0e+00 NA NA NA NA NA NA NA NA NA
C-PSO-10001.0e+001.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.0e+002.2e-034.5e-10 NA NA NA NA NA NA NA
E-PSOLS-51.1e-161.1e-161.1e-161.1e-16 NA NA NA NA NA NA
F-PSOLS-101.1e-161.1e-161.1e-161.1e-161.0e+00 NA NA NA NA NA
G-PSOLS-201.1e-161.1e-161.1e-161.1e-161.0e+001.0e+00 NA NA NA NA
H-EPUSLS1.1e-161.1e-161.1e-161.1e-161.0e+001.2e-015.3e-06 NA NA NA
I-RLS1.1e-161.1e-161.1e-161.1e-166.9e-151.1e-161.1e-161.0e+00 NA NA
J-ISL1.1e-161.1e-161.1e-161.1e-166.9e-151.1e-161.1e-161.0e+001.0e+00 NA
Z-IPSO1.0e+001.1e-161.1e-161.8e-081.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00
Ring topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.0e+00 NA NA NA NA NA NA NA NA NA
C-PSO-10001.0e+001.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.0e+001.0e+001.8e-05 NA NA NA NA NA NA NA
E-PSOLS-51.1e-161.1e-161.1e-161.1e-16 NA NA NA NA NA NA
F-PSOLS-101.1e-161.1e-161.1e-161.1e-161.0e+00 NA NA NA NA NA
G-PSOLS-201.1e-161.1e-161.1e-161.1e-161.0e+001.0e+00 NA NA NA NA
H-EPUSLS1.1e-161.1e-161.1e-161.1e-161.0e+001.4e-016.3e-06 NA NA NA
I-RLS1.1e-161.1e-161.1e-161.1e-167.8e-151.1e-161.1e-161.0e+00 NA NA
J-ISL1.1e-161.1e-161.1e-161.1e-161.0e+001.0e+001.0e+001.0e+001.0e+00 NA
Z-IPSO1.0e+002.0e-101.1e-162.0e-111.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00

Differences after 10,000 function evaluations

Ackley function - 100 dimensions
Fully-connected topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1007.8e-11 NA NA NA NA NA NA NA NA NA
C-PSO-10001.0e+001.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.0e+001.0e+001.5e-06 NA NA NA NA NA NA NA
E-PSOLS-55.4e-121.0e+001.1e-161.1e-16 NA NA NA NA NA NA
F-PSOLS-105.4e-121.0e+001.1e-161.1e-161.0e+00 NA NA NA NA NA
G-PSOLS-205.4e-121.0e+001.1e-161.1e-161.0e+001.0e+00 NA NA NA NA
H-EPUSLS4.1e-101.0e+001.1e-161.1e-161.0e+001.0e+001.0e+00 NA NA NA
I-RLS8.3e-121.0e+001.1e-161.1e-161.0e+001.0e+001.0e+001.0e+00 NA NA
J-ISL5.1e-163.9e-071.1e-161.1e-162.4e-112.4e-112.3e-119.1e-094.3e-11 NA
Z-IPSO6.1e-041.0e+001.4e-141.5e-061.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00
Ring topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.0e+00 NA NA NA NA NA NA NA NA NA
C-PSO-10001.0e+001.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.0e+001.0e+001.1e-15 NA NA NA NA NA NA NA
E-PSOLS-56.4e-028.2e-161.1e-163.7e-16 NA NA NA NA NA NA
F-PSOLS-106.4e-028.2e-161.1e-163.7e-161.0e+00 NA NA NA NA NA
G-PSOLS-206.4e-028.2e-161.1e-163.7e-161.0e+001.0e+00 NA NA NA NA
H-EPUSLS6.5e-021.1e-151.1e-163.7e-141.0e+001.0e+001.0e+00 NA NA NA
I-RLS7.2e-037.7e-161.1e-163.0e-151.0e+001.0e+001.0e+001.0e+00 NA NA
J-ISL4.4e-121.1e-161.1e-161.1e-162.1e-112.1e-112.0e-118.2e-093.6e-11 NA
Z-IPSO9.7e-011.1e-151.1e-161.5e-151.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00
Griewank function - 100 dimensions
Fully-connected topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.5e-13 NA NA NA NA NA NA NA NA NA
C-PSO-10001.0e+001.0e+00 NA NA NA NA NA NA NA NA
D-EPUS8.1e-105.0e-072.3e-13 NA NA NA NA NA NA NA
E-PSOLS-51.1e-161.1e-161.1e-161.1e-16 NA NA NA NA NA NA
F-PSOLS-101.1e-161.1e-161.1e-161.1e-161.0e+00 NA NA NA NA NA
G-PSOLS-201.1e-161.1e-161.1e-161.1e-161.0e+001.0e+00 NA NA NA NA
H-EPUSLS1.1e-161.1e-161.1e-161.1e-161.0e+001.0e+001.0e+00 NA NA NA
I-RLS1.1e-161.1e-161.1e-161.1e-161.0e+001.0e+001.0e+001.0e+00 NA NA
J-ISL1.1e-161.1e-161.1e-161.1e-161.0e+001.0e+001.0e+001.0e+001.0e+00 NA
Z-IPSO1.1e-162.1e-161.1e-161.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00
Ring topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.0e+00 NA NA NA NA NA NA NA NA NA
C-PSO-10001.0e+001.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.0e+001.1e-161.1e-16 NA NA NA NA NA NA NA
E-PSOLS-51.1e-161.1e-161.1e-161.1e-16 NA NA NA NA NA NA
F-PSOLS-101.1e-161.1e-161.1e-161.1e-161.0e+00 NA NA NA NA NA
G-PSOLS-201.1e-161.1e-161.1e-161.1e-161.0e+001.0e+00 NA NA NA NA
H-EPUSLS1.1e-161.1e-161.1e-161.1e-161.0e+001.0e+001.0e+00 NA NA NA
I-RLS1.1e-161.1e-161.1e-161.1e-161.0e+001.0e+001.0e+001.0e+00 NA NA
J-ISL1.1e-161.1e-161.1e-161.1e-161.0e+001.0e+001.0e+001.0e+001.0e+00 NA
Z-IPSO1.0e+001.1e-161.1e-161.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00
Rastrigin function - 100 dimensions
Fully-connected topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.0e+00 NA NA NA NA NA NA NA NA NA
C-PSO-10001.0e+001.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.0e+001.0e+001.1e-14 NA NA NA NA NA NA NA
E-PSOLS-51.1e-161.1e-161.1e-161.1e-16 NA NA NA NA NA NA
F-PSOLS-101.1e-161.1e-161.1e-161.1e-161.0e+00 NA NA NA NA NA
G-PSOLS-201.1e-161.1e-161.1e-161.1e-161.0e+001.0e+00 NA NA NA NA
H-EPUSLS1.1e-161.1e-161.1e-161.1e-161.0e+001.0e+001.0e+00 NA NA NA
I-RLS1.1e-161.1e-161.1e-161.1e-161.0e+001.0e+001.0e+001.0e+00 NA NA
J-ISL1.1e-161.1e-161.1e-161.1e-168.0e-098.0e-098.0e-094.7e-084.9e-08 NA
Z-IPSO1.0e+001.0e+001.1e-161.2e-041.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00
Ring topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.0e+00 NA NA NA NA NA NA NA NA NA
C-PSO-10001.0e+001.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.0e+007.8e-091.1e-16 NA NA NA NA NA NA NA
E-PSOLS-51.1e-161.1e-161.1e-161.1e-16 NA NA NA NA NA NA
F-PSOLS-101.1e-161.1e-161.1e-161.1e-161.0e+00 NA NA NA NA NA
G-PSOLS-201.1e-161.1e-161.1e-161.1e-161.0e+001.0e+00 NA NA NA NA
H-EPUSLS1.1e-161.1e-161.1e-161.1e-161.0e+001.0e+001.0e+00 NA NA NA
I-RLS1.1e-161.1e-161.1e-161.1e-161.0e+001.0e+001.0e+001.0e+00 NA NA
J-ISL1.1e-161.1e-161.1e-161.1e-167.7e-097.7e-097.7e-094.3e-084.5e-08 NA
Z-IPSO1.0e+003.4e-091.1e-161.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00
Rosenbrock function - 100 dimensions
Fully-connected topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.8e-09 NA NA NA NA NA NA NA NA NA
C-PSO-10001.0e+001.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.1e-161.1e-161.1e-16 NA NA NA NA NA NA NA
E-PSOLS-51.1e-161.1e-161.1e-161.1e-16 NA NA NA NA NA NA
F-PSOLS-101.1e-161.1e-161.1e-161.1e-161.0e+00 NA NA NA NA NA
G-PSOLS-201.1e-161.1e-161.1e-161.1e-161.0e+001.0e+00 NA NA NA NA
H-EPUSLS1.1e-161.1e-161.1e-161.1e-162.9e-012.9e-012.9e-01 NA NA NA
I-RLS1.1e-161.1e-161.1e-161.1e-162.5e-078.9e-119.9e-131.0e+00 NA NA
J-ISL1.1e-161.1e-161.1e-161.1e-162.5e-078.9e-119.9e-131.0e+001.0e+00 NA
Z-IPSO1.1e-161.1e-161.1e-161.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00
Ring topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.0e+00 NA NA NA NA NA NA NA NA NA
C-PSO-10001.0e+001.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.0e+001.1e-161.1e-16 NA NA NA NA NA NA NA
E-PSOLS-51.1e-161.1e-161.1e-161.1e-16 NA NA NA NA NA NA
F-PSOLS-101.1e-161.1e-161.1e-161.1e-161.0e+00 NA NA NA NA NA
G-PSOLS-201.1e-161.1e-161.1e-161.1e-161.0e+001.0e+00 NA NA NA NA
H-EPUSLS1.1e-161.1e-161.1e-161.1e-163.4e-013.4e-013.4e-01 NA NA NA
I-RLS1.1e-161.1e-161.1e-161.1e-162.9e-079.7e-111.1e-121.0e+00 NA NA
J-ISL1.1e-161.1e-161.1e-161.1e-162.9e-079.7e-111.1e-121.0e+001.0e+00 NA
Z-IPSO1.0e+002.2e-161.1e-161.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00
Salomon function - 100 dimensions
Fully-connected topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.2e-16 NA NA NA NA NA NA NA NA NA
C-PSO-10001.0e+001.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.0e+001.0e+003.0e-14 NA NA NA NA NA NA NA
E-PSOLS-51.0e+001.0e+001.0e+001.0e+00 NA NA NA NA NA NA
F-PSOLS-101.0e+001.0e+001.0e+001.0e+001.0e+00 NA NA NA NA NA
G-PSOLS-201.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00 NA NA NA NA
H-EPUSLS1.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00 NA NA NA
I-RLS1.0e+001.0e+001.0e+001.0e+001.2e-041.7e-067.8e-081.0e+00 NA NA
J-ISL1.0e+001.0e+001.0e+001.0e+001.2e-041.7e-067.8e-081.0e+001.0e+00 NA
Z-IPSO1.1e-165.5e-131.1e-161.1e-161.1e-161.1e-161.1e-161.1e-161.1e-161.1e-16
Ring topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.0e+00 NA NA NA NA NA NA NA NA NA
C-PSO-10001.0e+001.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.0e+001.1e-141.1e-16 NA NA NA NA NA NA NA
E-PSOLS-51.0e+001.0e+001.1e-161.0e+00 NA NA NA NA NA NA
F-PSOLS-101.0e+001.0e+001.1e-161.0e+001.0e+00 NA NA NA NA NA
G-PSOLS-201.0e+001.0e+001.1e-161.0e+001.0e+001.0e+00 NA NA NA NA
H-EPUSLS1.0e+001.0e+001.1e-161.0e+001.0e+001.0e+001.0e+00 NA NA NA
I-RLS1.0e+001.0e+001.1e-161.0e+001.0e-041.5e-067.1e-081.0e+00 NA NA
J-ISL1.0e+001.0e+001.1e-161.0e+001.0e-041.5e-067.1e-081.0e+001.0e+00 NA
Z-IPSO1.0e+001.9e-161.1e-161.0e+001.1e-161.1e-161.1e-161.1e-161.1e-161.1e-16
Schaffer function - 100 dimensions
Fully-connected topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.0e+00 NA NA NA NA NA NA NA NA NA
C-PSO-10001.0e+001.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.0e+001.0e+001.0e+00 NA NA NA NA NA NA NA
E-PSOLS-51.1e-161.1e-161.1e-161.1e-16 NA NA NA NA NA NA
F-PSOLS-101.1e-161.1e-161.1e-161.1e-161.0e+00 NA NA NA NA NA
G-PSOLS-201.1e-161.1e-161.1e-161.1e-161.0e+001.0e+00 NA NA NA NA
H-EPUSLS1.1e-161.1e-161.1e-161.1e-161.0e+001.0e+001.0e+00 NA NA NA
I-RLS1.1e-161.1e-161.1e-161.1e-163.5e-062.4e-101.3e-151.0e+00 NA NA
J-ISL1.1e-161.1e-161.1e-161.1e-163.5e-062.4e-101.3e-151.0e+001.0e+00 NA
Z-IPSO1.0e+001.0e+001.3e-035.0e-011.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00
Ring topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.0e+00 NA NA NA NA NA NA NA NA NA
C-PSO-10001.0e+001.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.0e+001.0e+006.5e-11 NA NA NA NA NA NA NA
E-PSOLS-51.1e-161.1e-161.1e-161.1e-16 NA NA NA NA NA NA
F-PSOLS-101.1e-161.1e-161.1e-161.1e-161.0e+00 NA NA NA NA NA
G-PSOLS-201.1e-161.1e-161.1e-161.1e-161.0e+001.0e+00 NA NA NA NA
H-EPUSLS1.1e-161.1e-161.1e-161.1e-161.0e+001.0e+001.0e+00 NA NA NA
I-RLS1.1e-161.1e-161.1e-161.1e-163.2e-062.3e-101.2e-151.0e+00 NA NA
J-ISL1.1e-161.1e-161.1e-161.1e-163.2e-062.3e-101.2e-151.0e+001.0e+00 NA
Z-IPSO1.0e+001.0e+003.1e-169.2e-041.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00
Schwefel function - 100 dimensions
Fully-connected topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.0e+00 NA NA NA NA NA NA NA NA NA
C-PSO-10001.0e+001.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.0e+001.0e+009.5e-10 NA NA NA NA NA NA NA
E-PSOLS-51.1e-161.1e-161.1e-161.1e-16 NA NA NA NA NA NA
F-PSOLS-101.1e-161.1e-161.1e-161.1e-161.0e+00 NA NA NA NA NA
G-PSOLS-201.1e-161.1e-161.1e-161.1e-161.0e+001.0e+00 NA NA NA NA
H-EPUSLS1.1e-161.1e-161.1e-161.1e-161.0e+001.0e+001.0e+00 NA NA NA
I-RLS1.1e-161.1e-161.1e-161.1e-161.0e+001.0e+001.0e+001.0e+00 NA NA
J-ISL1.1e-161.1e-161.1e-161.1e-164.9e-054.9e-054.9e-053.7e-049.5e-05 NA
Z-IPSO1.0e+001.0e+001.1e-161.6e-131.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00
Ring topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.0e+00 NA NA NA NA NA NA NA NA NA
C-PSO-10001.0e+001.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.0e+001.0e+003.3e-16 NA NA NA NA NA NA NA
E-PSOLS-51.1e-161.1e-161.1e-161.1e-16 NA NA NA NA NA NA
F-PSOLS-101.1e-161.1e-161.1e-161.1e-161.0e+00 NA NA NA NA NA
G-PSOLS-201.1e-161.1e-161.1e-161.1e-161.0e+001.0e+00 NA NA NA NA
H-EPUSLS1.1e-161.1e-161.1e-161.1e-161.0e+001.0e+001.0e+00 NA NA NA
I-RLS1.1e-161.1e-161.1e-161.1e-161.0e+001.0e+001.0e+001.0e+00 NA NA
J-ISL1.1e-161.1e-161.1e-161.1e-164.9e-054.9e-054.9e-053.7e-049.5e-05 NA
Z-IPSO1.0e+001.3e-031.1e-163.4e-051.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00
Sphere function - 100 dimensions
Fully-connected topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.3e-13 NA NA NA NA NA NA NA NA NA
C-PSO-10001.0e+001.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.7e-141.3e-131.7e-14 NA NA NA NA NA NA NA
E-PSOLS-51.1e-161.1e-161.1e-161.1e-16 NA NA NA NA NA NA
F-PSOLS-101.1e-161.1e-161.1e-161.1e-161.0e+00 NA NA NA NA NA
G-PSOLS-201.1e-161.1e-161.1e-161.1e-161.0e+001.0e+00 NA NA NA NA
H-EPUSLS1.1e-161.1e-161.1e-161.1e-161.0e+001.0e+001.0e+00 NA NA NA
I-RLS1.1e-161.1e-161.1e-161.1e-161.0e+001.0e+001.0e+001.1e-16 NA NA
J-ISL1.1e-161.1e-161.1e-161.1e-161.0e+001.0e+001.0e+001.1e-161.0e+00 NA
Z-IPSO1.1e-161.9e-161.1e-161.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00
Ring topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.0e+00 NA NA NA NA NA NA NA NA NA
C-PSO-10001.0e+001.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.0e+001.1e-161.1e-16 NA NA NA NA NA NA NA
E-PSOLS-51.1e-161.1e-161.1e-161.1e-16 NA NA NA NA NA NA
F-PSOLS-101.1e-161.1e-161.1e-161.1e-161.0e+00 NA NA NA NA NA
G-PSOLS-201.1e-161.1e-161.1e-161.1e-161.0e+001.0e+00 NA NA NA NA
H-EPUSLS1.1e-161.1e-161.1e-161.1e-161.0e+001.0e+001.0e+00 NA NA NA
I-RLS1.1e-161.1e-161.1e-161.1e-161.0e+001.0e+001.0e+001.1e-16 NA NA
J-ISL1.1e-161.1e-161.1e-161.1e-161.0e+001.0e+001.0e+001.1e-161.0e+00 NA
Z-IPSO1.0e+001.1e-161.1e-161.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00
Step function - 100 dimensions
Fully-connected topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.1e-16 NA NA NA NA NA NA NA NA NA
C-PSO-10003.9e-011.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.0e+001.0e+001.0e+00 NA NA NA NA NA NA NA
E-PSOLS-51.1e-164.0e-031.1e-161.1e-16 NA NA NA NA NA NA
F-PSOLS-101.1e-164.0e-031.1e-161.1e-161.0e+00 NA NA NA NA NA
G-PSOLS-201.1e-164.0e-031.1e-161.1e-161.0e+001.0e+00 NA NA NA NA
H-EPUSLS1.1e-162.2e-031.1e-161.1e-161.0e+001.0e+001.0e+00 NA NA NA
I-RLS1.1e-164.0e-031.1e-161.1e-161.0e+001.0e+001.0e+001.0e+00 NA NA
J-ISL1.1e-161.0e-051.1e-161.1e-164.3e-034.3e-034.3e-036.9e-014.3e-03 NA
Z-IPSO1.9e-161.0e+001.1e-161.1e-161.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00
Ring topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.1e-16 NA NA NA NA NA NA NA NA NA
C-PSO-10001.0e+001.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.0e+001.0e+001.0e+00 NA NA NA NA NA NA NA
E-PSOLS-51.8e-151.0e+001.1e-161.1e-16 NA NA NA NA NA NA
F-PSOLS-101.8e-151.0e+001.1e-161.1e-161.0e+00 NA NA NA NA NA
G-PSOLS-201.8e-151.0e+001.1e-161.1e-161.0e+001.0e+00 NA NA NA NA
H-EPUSLS1.2e-151.0e+001.1e-161.1e-161.0e+001.0e+001.0e+00 NA NA NA
I-RLS1.8e-151.0e+001.1e-161.1e-161.0e+001.0e+001.0e+001.0e+00 NA NA
J-ISL6.4e-161.0e+001.1e-161.1e-164.3e-034.3e-034.3e-036.9e-014.3e-03 NA
Z-IPSO1.1e-162.4e-011.1e-161.1e-161.1e-161.1e-161.1e-161.1e-161.1e-161.8e-16
Weierstrass function - 100 dimensions
Fully-connected topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.0e+00 NA NA NA NA NA NA NA NA NA
C-PSO-10001.0e+001.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.0e+002.0e-024.0e-16 NA NA NA NA NA NA NA
E-PSOLS-51.1e-161.1e-161.1e-161.1e-16 NA NA NA NA NA NA
F-PSOLS-101.1e-161.1e-161.1e-161.1e-161.0e+00 NA NA NA NA NA
G-PSOLS-201.1e-161.1e-161.1e-161.1e-161.0e+001.0e+00 NA NA NA NA
H-EPUSLS1.1e-161.1e-161.1e-161.1e-161.0e+001.0e+001.0e+00 NA NA NA
I-RLS1.1e-161.1e-161.1e-161.1e-162.7e-021.1e-035.3e-061.0e+00 NA NA
J-ISL1.1e-161.1e-161.1e-161.1e-162.5e-011.6e-036.3e-051.0e+001.0e+00 NA
Z-IPSO2.0e-041.9e-161.1e-161.9e-041.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00
Ring topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.0e+00 NA NA NA NA NA NA NA NA NA
C-PSO-10001.0e+001.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.0e+002.1e-131.1e-16 NA NA NA NA NA NA NA
E-PSOLS-51.1e-161.1e-161.1e-161.1e-16 NA NA NA NA NA NA
F-PSOLS-101.1e-161.1e-161.1e-161.1e-161.0e+00 NA NA NA NA NA
G-PSOLS-201.1e-161.1e-161.1e-161.1e-161.0e+001.0e+00 NA NA NA NA
H-EPUSLS1.1e-161.1e-161.1e-161.1e-161.0e+001.0e+001.0e+00 NA NA NA
I-RLS1.1e-161.1e-161.1e-161.1e-163.2e-021.2e-035.2e-061.0e+00 NA NA
J-ISL1.1e-161.1e-161.1e-161.1e-161.0e+001.0e+001.0e+001.0e+001.0e+00 NA
Z-IPSO1.0e+001.5e-161.1e-161.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00

Differences after 100,000 function evaluations

Ackley function - 100 dimensions
Fully-connected topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1006.2e-16 NA NA NA NA NA NA NA NA NA
C-PSO-10003.8e-161.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.0e+001.0e+001.0e+00 NA NA NA NA NA NA NA
E-PSOLS-54.1e-011.0e+001.0e+001.0e+00 NA NA NA NA NA NA
F-PSOLS-101.6e-061.0e+001.0e+002.4e-031.5e-10 NA NA NA NA NA
G-PSOLS-204.1e-121.0e+001.0e+002.7e-122.3e-141.5e-09 NA NA NA NA
H-EPUSLS5.5e-041.0e+001.0e+004.3e-052.0e-021.0e+001.0e+00 NA NA NA
I-RLS1.7e-142.9e-022.1e-011.7e-142.7e-121.2e-061.0e+001.6e-05 NA NA
J-ISL1.1e-161.1e-161.1e-161.1e-163.1e-168.0e-151.9e-122.3e-148.4e-16 NA
Z-IPSO2.3e-141.0e+001.0e+004.5e-142.9e-064.7e-011.0e+001.0e+001.0e+001.0e+00
Ring topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.1e-16 NA NA NA NA NA NA NA NA NA
C-PSO-10001.0e+001.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.0e+001.0e+003.0e-03 NA NA NA NA NA NA NA
E-PSOLS-51.0e+001.0e+001.4e-031.0e+00 NA NA NA NA NA NA
F-PSOLS-101.0e+001.0e+007.8e-083.0e-034.7e-10 NA NA NA NA NA
G-PSOLS-201.1e-051.0e+004.6e-141.2e-102.7e-144.0e-09 NA NA NA NA
H-EPUSLS1.0e+001.0e+001.5e-098.6e-051.4e-021.0e+001.0e+00 NA NA NA
I-RLS1.2e-101.0e+007.1e-162.6e-122.2e-129.0e-071.0e+001.2e-05 NA NA
J-ISL1.1e-161.1e-161.1e-161.1e-161.7e-161.7e-151.5e-142.6e-145.8e-16 NA
Z-IPSO1.3e-161.0e+001.1e-164.2e-131.7e-101.0e-041.0e+009.0e-041.0e+001.0e+00
Griewank function - 100 dimensions
Fully-connected topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.1e-16 NA NA NA NA NA NA NA NA NA
C-PSO-10002.2e-151.0e+00 NA NA NA NA NA NA NA NA
D-EPUS9.0e-088.5e-078.5e-07 NA NA NA NA NA NA NA
E-PSOLS-51.1e-161.1e-161.1e-165.1e-16 NA NA NA NA NA NA
F-PSOLS-101.1e-161.1e-161.1e-161.9e-167.8e-01 NA NA NA NA NA
G-PSOLS-201.1e-161.1e-161.1e-161.1e-166.8e-011.0e+00 NA NA NA NA
H-EPUSLS1.1e-161.9e-161.1e-161.0e+001.0e+001.0e+001.0e+00 NA NA NA
I-RLS1.1e-161.1e-161.1e-168.0e-161.0e+001.0e+001.0e+002.1e-16 NA NA
J-ISL1.1e-161.1e-161.1e-161.1e-166.8e-011.0e+001.0e+001.1e-161.0e+00 NA
Z-IPSO1.1e-161.0e+001.1e-161.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00
Ring topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1002.5e-04 NA NA NA NA NA NA NA NA NA
C-PSO-10001.0e+001.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.9e-121.8e-141.1e-16 NA NA NA NA NA NA NA
E-PSOLS-51.1e-161.1e-161.1e-161.1e-16 NA NA NA NA NA NA
F-PSOLS-101.1e-161.1e-161.1e-161.1e-167.1e-01 NA NA NA NA NA
G-PSOLS-201.1e-161.1e-161.1e-161.1e-167.1e-011.0e+00 NA NA NA NA
H-EPUSLS2.0e-161.1e-161.1e-167.3e-111.0e+001.0e+001.0e+00 NA NA NA
I-RLS1.1e-161.1e-161.1e-161.1e-161.0e+001.0e+001.0e+002.0e-16 NA NA
J-ISL1.1e-161.1e-161.1e-161.1e-167.1e-011.0e+001.0e+001.1e-161.0e+00 NA
Z-IPSO1.0e+001.0e+001.1e-161.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00
Rastrigin function - 100 dimensions
Fully-connected topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.1e-16 NA NA NA NA NA NA NA NA NA
C-PSO-10007.6e-131.0e+00 NA NA NA NA NA NA NA NA
D-EPUS6.7e-021.0e+001.0e+00 NA NA NA NA NA NA NA
E-PSOLS-51.1e-161.1e-161.1e-161.1e-16 NA NA NA NA NA NA
F-PSOLS-101.1e-161.1e-161.1e-161.1e-164.8e-09 NA NA NA NA NA
G-PSOLS-201.1e-161.1e-161.1e-161.1e-165.6e-123.2e-07 NA NA NA NA
H-EPUSLS1.1e-161.3e-161.1e-161.1e-161.0e+001.0e+001.0e+00 NA NA NA
I-RLS1.1e-161.1e-161.1e-161.1e-162.0e-107.4e-055.5e-011.4e-15 NA NA
J-ISL1.1e-161.1e-161.1e-161.1e-161.1e-161.1e-161.1e-161.1e-161.1e-16 NA
Z-IPSO1.1e-161.0e+005.2e-118.9e-161.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00
Ring topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.5e-10 NA NA NA NA NA NA NA NA NA
C-PSO-10001.0e+001.0e+00 NA NA NA NA NA NA NA NA
D-EPUS4.6e-095.6e-011.1e-16 NA NA NA NA NA NA NA
E-PSOLS-51.1e-161.1e-161.1e-161.1e-16 NA NA NA NA NA NA
F-PSOLS-101.1e-161.1e-161.1e-161.1e-163.6e-09 NA NA NA NA NA
G-PSOLS-201.1e-161.1e-161.1e-161.1e-166.1e-125.2e-07 NA NA NA NA
H-EPUSLS1.1e-161.1e-161.1e-161.1e-161.0e+001.0e+001.0e+00 NA NA NA
I-RLS1.1e-161.1e-161.1e-161.1e-162.2e-109.3e-055.9e-019.8e-16 NA NA
J-ISL1.1e-161.1e-161.1e-161.1e-161.1e-161.1e-161.1e-161.1e-161.1e-16 NA
Z-IPSO1.0e+001.0e+001.1e-161.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00
Rosenbrock function - 100 dimensions
Fully-connected topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.1e-16 NA NA NA NA NA NA NA NA NA
C-PSO-10002.7e-141.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.1e-163.5e-141.1e-16 NA NA NA NA NA NA NA
E-PSOLS-51.1e-161.1e-161.1e-161.1e-16 NA NA NA NA NA NA
F-PSOLS-101.1e-161.1e-161.1e-161.1e-161.0e+00 NA NA NA NA NA
G-PSOLS-201.1e-161.1e-161.1e-161.1e-161.0e+001.0e+00 NA NA NA NA
H-EPUSLS1.1e-161.1e-161.1e-161.1e-161.5e-019.5e-079.5e-07 NA NA NA
I-RLS1.1e-161.1e-161.1e-161.1e-161.0e+001.0e+001.0e+001.0e+00 NA NA
J-ISL1.1e-161.1e-161.1e-161.1e-164.1e-038.5e-138.5e-131.0e+001.2e-12 NA
Z-IPSO1.1e-161.0e+001.1e-161.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00
Ring topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.5e-01 NA NA NA NA NA NA NA NA NA
C-PSO-10001.0e+001.0e+00 NA NA NA NA NA NA NA NA
D-EPUS8.3e-072.0e-161.1e-16 NA NA NA NA NA NA NA
E-PSOLS-51.1e-161.1e-161.1e-161.1e-16 NA NA NA NA NA NA
F-PSOLS-101.1e-161.1e-161.1e-161.1e-161.0e+00 NA NA NA NA NA
G-PSOLS-201.1e-161.1e-161.1e-161.1e-161.0e+001.0e+00 NA NA NA NA
H-EPUSLS1.1e-161.1e-161.1e-161.1e-161.6e-011.1e-061.1e-06 NA NA NA
I-RLS1.1e-161.1e-161.1e-161.1e-161.0e+001.0e+001.0e+001.0e+00 NA NA
J-ISL1.1e-161.1e-161.1e-161.1e-164.7e-039.9e-139.9e-131.0e+001.5e-12 NA
Z-IPSO1.0e+001.0e+001.1e-161.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00
Salomon function - 100 dimensions
Fully-connected topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.1e-16 NA NA NA NA NA NA NA NA NA
C-PSO-10001.1e-161.0e+00 NA NA NA NA NA NA NA NA
D-EPUS2.0e-141.0e+001.0e+00 NA NA NA NA NA NA NA
E-PSOLS-51.1e-161.0e+003.2e-021.0e+00 NA NA NA NA NA NA
F-PSOLS-107.5e-121.0e+001.0e+001.0e+001.0e+00 NA NA NA NA NA
G-PSOLS-207.5e-121.0e+001.0e+001.0e+001.0e+001.0e+00 NA NA NA NA
H-EPUSLS1.1e-161.0e+001.1e-161.3e-074.0e-141.1e-161.1e-16 NA NA NA
I-RLS8.6e-121.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00 NA NA
J-ISL1.1e-161.0e+001.1e-168.1e-101.1e-161.1e-161.1e-162.8e-031.1e-16 NA
Z-IPSO1.1e-162.0e-061.1e-161.1e-161.1e-161.1e-161.1e-161.1e-161.1e-161.1e-16
Ring topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1005.5e-14 NA NA NA NA NA NA NA NA NA
C-PSO-10001.0e+001.0e+00 NA NA NA NA NA NA NA NA
D-EPUS2.1e-091.0e+001.1e-16 NA NA NA NA NA NA NA
E-PSOLS-51.0e+001.0e+001.1e-161.0e+00 NA NA NA NA NA NA
F-PSOLS-101.0e+001.0e+001.1e-161.0e+001.0e+00 NA NA NA NA NA
G-PSOLS-201.0e+001.0e+001.1e-161.0e+001.0e+001.0e+00 NA NA NA NA
H-EPUSLS1.6e-091.0e+001.1e-161.0e+003.3e-131.1e-161.1e-16 NA NA NA
I-RLS1.0e+001.0e+001.1e-161.0e+001.0e+001.0e+001.0e+001.0e+00 NA NA
J-ISL5.5e-131.0e+001.1e-166.5e-031.1e-161.1e-161.1e-161.6e-031.1e-16 NA
Z-IPSO1.0e+001.0e+001.1e-161.0e+001.0e+001.1e-161.1e-161.0e+001.1e-161.0e+00
Schaffer function - 100 dimensions
Fully-connected topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.0e+00 NA NA NA NA NA NA NA NA NA
C-PSO-10001.0e+001.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.0e+001.0e+004.2e-04 NA NA NA NA NA NA NA
E-PSOLS-51.1e-161.1e-161.1e-161.1e-16 NA NA NA NA NA NA
F-PSOLS-101.1e-161.1e-161.1e-161.1e-161.0e+00 NA NA NA NA NA
G-PSOLS-201.1e-161.1e-161.1e-161.1e-161.0e+001.0e+00 NA NA NA NA
H-EPUSLS1.1e-161.1e-161.1e-161.1e-163.9e-161.1e-161.1e-16 NA NA NA
I-RLS1.1e-161.1e-161.1e-161.1e-161.0e+001.0e+001.0e+001.0e+00 NA NA
J-ISL1.1e-161.1e-161.1e-161.1e-161.1e-161.1e-161.1e-161.0e+001.1e-16 NA
Z-IPSO1.0e+001.0e+002.0e-061.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00
Ring topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.0e+00 NA NA NA NA NA NA NA NA NA
C-PSO-10001.0e+001.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.0e+001.0e+004.8e-10 NA NA NA NA NA NA NA
E-PSOLS-51.1e-161.1e-161.1e-161.1e-16 NA NA NA NA NA NA
F-PSOLS-101.1e-161.1e-161.1e-161.1e-161.0e+00 NA NA NA NA NA
G-PSOLS-201.1e-161.1e-161.1e-161.1e-161.0e+001.0e+00 NA NA NA NA
H-EPUSLS1.1e-161.1e-161.1e-161.1e-163.9e-161.1e-161.1e-16 NA NA NA
I-RLS1.1e-161.1e-161.1e-161.1e-161.0e+001.0e+001.0e+001.0e+00 NA NA
J-ISL1.1e-161.1e-161.1e-161.1e-161.1e-161.1e-161.1e-161.0e+001.1e-16 NA
Z-IPSO1.0e+001.0e+002.0e-138.6e-011.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00
Schwefel function - 100 dimensions
Fully-connected topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.1e-16 NA NA NA NA NA NA NA NA NA
C-PSO-10003.1e-121.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.0e+001.0e+001.0e+00 NA NA NA NA NA NA NA
E-PSOLS-51.1e-161.1e-161.1e-161.1e-16 NA NA NA NA NA NA
F-PSOLS-101.1e-161.1e-161.1e-161.1e-161.2e-07 NA NA NA NA NA
G-PSOLS-201.1e-161.1e-161.1e-161.1e-161.5e-118.2e-04 NA NA NA NA
H-EPUSLS1.1e-161.1e-161.1e-161.1e-161.0e+001.0e+001.0e+00 NA NA NA
I-RLS1.1e-161.1e-161.1e-161.1e-161.2e-101.7e-051.0e+009.6e-16 NA NA
J-ISL1.1e-161.1e-161.1e-161.1e-161.1e-161.1e-161.1e-161.1e-161.1e-16 NA
Z-IPSO8.8e-131.0e+003.9e-012.1e-131.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00
Ring topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.4e-02 NA NA NA NA NA NA NA NA NA
C-PSO-10001.0e+001.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.2e-041.2e-014.6e-16 NA NA NA NA NA NA NA
E-PSOLS-51.1e-161.1e-161.1e-161.1e-16 NA NA NA NA NA NA
F-PSOLS-101.1e-161.1e-161.1e-161.1e-165.8e-07 NA NA NA NA NA
G-PSOLS-201.1e-161.1e-161.1e-161.1e-161.6e-118.9e-04 NA NA NA NA
H-EPUSLS1.1e-161.1e-161.1e-161.1e-161.0e+001.0e+001.0e+00 NA NA NA
I-RLS1.1e-161.1e-161.1e-161.1e-161.3e-101.6e-051.0e+009.2e-16 NA NA
J-ISL1.1e-161.1e-161.1e-161.1e-161.1e-161.1e-161.1e-161.1e-161.1e-16 NA
Z-IPSO1.0e+001.0e+001.1e-161.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00
Sphere function - 100 dimensions
Fully-connected topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.1e-16 NA NA NA NA NA NA NA NA NA
C-PSO-10001.6e-151.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.6e-145.6e-121.6e-14 NA NA NA NA NA NA NA
E-PSOLS-51.1e-161.1e-161.1e-161.1e-16 NA NA NA NA NA NA
F-PSOLS-101.1e-161.1e-161.1e-161.1e-161.0e+00 NA NA NA NA NA
G-PSOLS-201.1e-161.1e-161.1e-161.1e-161.0e+001.0e+00 NA NA NA NA
H-EPUSLS1.1e-161.1e-161.1e-161.1e-161.0e+001.0e+001.0e+00 NA NA NA
I-RLS1.1e-161.1e-161.1e-161.1e-161.0e+001.0e+001.0e+001.1e-16 NA NA
J-ISL1.1e-161.1e-161.1e-161.1e-161.0e+001.0e+001.0e+001.1e-161.0e+00 NA
Z-IPSO1.1e-164.8e-011.1e-161.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00
Ring topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1005.8e-05 NA NA NA NA NA NA NA NA NA
C-PSO-10001.0e+001.0e+00 NA NA NA NA NA NA NA NA
D-EPUS3.0e-121.7e-141.1e-16 NA NA NA NA NA NA NA
E-PSOLS-51.1e-161.1e-161.1e-161.1e-16 NA NA NA NA NA NA
F-PSOLS-101.1e-161.1e-161.1e-161.1e-161.0e+00 NA NA NA NA NA
G-PSOLS-201.1e-161.1e-161.1e-161.1e-161.0e+001.0e+00 NA NA NA NA
H-EPUSLS1.1e-161.1e-161.1e-161.1e-161.0e+001.0e+001.0e+00 NA NA NA
I-RLS1.1e-161.1e-161.1e-161.1e-161.0e+001.0e+001.0e+001.1e-16 NA NA
J-ISL1.1e-161.1e-161.1e-161.1e-161.0e+001.0e+001.0e+001.1e-161.0e+00 NA
Z-IPSO1.0e+001.0e+001.1e-161.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00
Step function - 100 dimensions
Fully-connected topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.0e-16 NA NA NA NA NA NA NA NA NA
C-PSO-10001.0e-162.5e-14 NA NA NA NA NA NA NA NA
D-EPUS1.0e+001.0e+001.0e+00 NA NA NA NA NA NA NA
E-PSOLS-51.0e-161.0e-168.0e-151.0e-16 NA NA NA NA NA NA
F-PSOLS-101.0e-161.2e-071.0e+001.0e-161.0e+00 NA NA NA NA NA
G-PSOLS-201.0e-161.2e-071.0e+001.0e-161.0e+001.0e+00 NA NA NA NA
H-EPUSLS1.0e-164.5e-051.0e+001.0e-161.0e+001.0e+001.0e+00 NA NA NA
I-RLS1.0e-161.2e-071.0e+001.0e-161.0e+001.0e+001.0e+003.5e-11 NA NA
J-ISL1.0e-161.0e-161.0e-161.0e-161.0e-161.0e-161.0e-161.0e-161.0e-16 NA
Z-IPSO1.0e-161.0e-161.6e-141.0e-162.3e-061.0e-161.0e-161.0e-161.0e-161.0e+00
Ring topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1009.2e-17 NA NA NA NA NA NA NA NA NA
C-PSO-10009.2e-171.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.0e+001.0e+001.0e+00 NA NA NA NA NA NA NA
E-PSOLS-59.2e-171.0e+001.0e+009.2e-17 NA NA NA NA NA NA
F-PSOLS-103.0e-161.0e+001.0e+009.2e-171.0e+00 NA NA NA NA NA
G-PSOLS-203.0e-161.0e+001.0e+009.2e-171.0e+001.0e+00 NA NA NA NA
H-EPUSLS6.9e-161.0e+001.0e+009.2e-171.0e+001.0e+001.0e+00 NA NA NA
I-RLS3.3e-161.0e+001.0e+009.2e-171.0e+001.0e+001.0e+004.1e-11 NA NA
J-ISL9.2e-171.0e+003.7e-029.2e-179.2e-179.2e-179.2e-179.2e-179.2e-17 NA
Z-IPSO9.2e-171.0e+009.2e-179.2e-179.2e-179.1e-179.1e-179.2e-179.1e-179.2e-17
Weierstrass function - 100 dimensions
Fully-connected topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.1e-16 NA NA NA NA NA NA NA NA NA
C-PSO-10008.4e-161.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.6e-111.0e+001.3e-01 NA NA NA NA NA NA NA
E-PSOLS-51.1e-161.1e-161.1e-161.1e-16 NA NA NA NA NA NA
F-PSOLS-101.1e-161.1e-161.1e-161.1e-162.5e-01 NA NA NA NA NA
G-PSOLS-201.1e-161.1e-161.1e-161.1e-162.5e-011.0e+00 NA NA NA NA
H-EPUSLS1.1e-161.1e-161.1e-161.1e-161.0e+001.0e+001.0e+00 NA NA NA
I-RLS1.1e-161.1e-161.1e-161.1e-161.4e-031.0e+001.0e+001.6e-11 NA NA
J-ISL1.1e-161.1e-161.1e-161.1e-165.2e-021.0e+001.0e+006.0e-081.0e+00 NA
Z-IPSO1.1e-161.1e-011.1e-161.1e-161.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00
Ring topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.7e-11 NA NA NA NA NA NA NA NA NA
C-PSO-10001.0e+001.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.1e-161.1e-161.1e-16 NA NA NA NA NA NA NA
E-PSOLS-51.1e-161.1e-161.1e-161.1e-16 NA NA NA NA NA NA
F-PSOLS-101.1e-161.1e-161.1e-161.1e-162.4e-01 NA NA NA NA NA
G-PSOLS-201.1e-161.1e-161.1e-161.1e-162.4e-011.0e+00 NA NA NA NA
H-EPUSLS1.1e-161.1e-161.1e-161.1e-161.0e+001.0e+001.0e+00 NA NA NA
I-RLS1.1e-161.1e-161.1e-161.1e-161.5e-031.0e+001.0e+001.7e-11 NA NA
J-ISL1.1e-161.1e-161.1e-161.1e-161.0e+001.0e+001.0e+001.0e+001.0e+00 NA
Z-IPSO9.6e-111.0e+001.1e-161.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00

Differences after 1,000,000 function evaluations

Ackley function - 100 dimensions
Fully-connected topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1004.8e-16 NA NA NA NA NA NA NA NA NA
C-PSO-10001.5e-162.3e-11 NA NA NA NA NA NA NA NA
D-EPUS1.8e-011.0e+001.0e+00 NA NA NA NA NA NA NA
E-PSOLS-53.3e-011.0e+001.0e+001.0e+00 NA NA NA NA NA NA
F-PSOLS-101.3e-061.0e+001.0e+002.6e-023.4e-11 NA NA NA NA NA
G-PSOLS-203.8e-121.0e+001.0e+001.4e-112.2e-153.7e-12 NA NA NA NA
H-EPUSLS2.9e-142.6e-064.7e-011.9e-135.3e-111.5e-063.3e-01 NA NA NA
I-RLS1.1e-161.1e-167.2e-161.1e-169.2e-162.2e-128.2e-051.0e+00 NA NA
J-ISL1.1e-161.1e-161.1e-161.1e-161.5e-164.2e-153.8e-091.1e-032.8e-16 NA
Z-IPSO1.2e-151.0e+001.0e+001.3e-154.5e-123.7e-061.0e+001.0e+001.0e+001.0e+00
Ring topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.1e-16 NA NA NA NA NA NA NA NA NA
C-PSO-10001.1e-161.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.0e+001.0e+001.0e+00 NA NA NA NA NA NA NA
E-PSOLS-51.0e+001.0e+001.0e+001.0e+00 NA NA NA NA NA NA
F-PSOLS-101.0e+001.0e+001.0e+001.0e+001.5e-10 NA NA NA NA NA
G-PSOLS-202.7e-051.0e+001.0e+003.1e-031.2e-141.0e-10 NA NA NA NA
H-EPUSLS2.8e-121.0e+001.0e+001.3e-061.0e-108.7e-072.5e-02 NA NA NA
I-RLS1.1e-161.5e-131.1e-161.1e-166.5e-164.3e-141.0e-101.0e+00 NA NA
J-ISL1.1e-161.2e-151.1e-161.1e-161.1e-162.8e-161.8e-151.2e-073.7e-16 NA
Z-IPSO1.1e-161.0e+001.1e-161.0e-102.7e-151.1e-112.1e-041.0e+001.0e+001.0e+00
Griewank function - 100 dimensions
Fully-connected topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.1e-16 NA NA NA NA NA NA NA NA NA
C-PSO-10001.1e-163.7e-06 NA NA NA NA NA NA NA NA
D-EPUS9.4e-084.1e-051.0e+00 NA NA NA NA NA NA NA
E-PSOLS-51.1e-162.0e-163.4e-155.4e-16 NA NA NA NA NA NA
F-PSOLS-101.1e-161.1e-161.1e-162.0e-161.0e+00 NA NA NA NA NA
G-PSOLS-201.1e-161.1e-161.1e-161.1e-161.0e+001.0e+00 NA NA NA NA
H-EPUSLS1.1e-162.0e-101.0e+001.0e+001.0e+001.0e+001.0e+00 NA NA NA
I-RLS1.1e-161.1e-161.1e-161.1e-161.0e+001.0e+001.0e+001.1e-16 NA NA
J-ISL1.1e-161.1e-161.1e-161.1e-161.0e+001.0e+001.0e+001.1e-161.0e+00 NA
Z-IPSO1.1e-167.5e-132.8e-041.2e-021.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00
Ring topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1009.9e-17 NA NA NA NA NA NA NA NA NA
C-PSO-10009.0e-051.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.1e-161.0e+009.9e-17 NA NA NA NA NA NA NA
E-PSOLS-59.9e-178.6e-179.9e-172.2e-13 NA NA NA NA NA NA
F-PSOLS-109.9e-173.2e-209.9e-171.0e-151.0e+00 NA NA NA NA NA
G-PSOLS-209.9e-174.3e-229.9e-179.9e-171.0e+001.0e+00 NA NA NA NA
H-EPUSLS1.2e-161.0e+009.9e-171.0e+001.0e+001.0e+001.0e+00 NA NA NA
I-RLS9.9e-174.3e-229.9e-179.9e-171.0e+001.0e+001.0e+009.9e-17 NA NA
J-ISL9.9e-174.3e-229.9e-179.9e-171.0e+001.0e+001.0e+009.9e-171.0e+00 NA
Z-IPSO1.0e-121.0e+009.9e-171.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00
Rastrigin function - 100 dimensions
Fully-connected topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.1e-16 NA NA NA NA NA NA NA NA NA
C-PSO-10001.1e-164.6e-15 NA NA NA NA NA NA NA NA
D-EPUS2.5e-101.0e+001.0e+00 NA NA NA NA NA NA NA
E-PSOLS-51.1e-161.1e-163.6e-011.1e-16 NA NA NA NA NA NA
F-PSOLS-101.1e-161.1e-163.9e-041.1e-164.8e-09 NA NA NA NA NA
G-PSOLS-201.1e-161.1e-161.4e-071.1e-163.6e-123.1e-08 NA NA NA NA
H-EPUSLS1.1e-161.1e-161.0e+001.1e-161.0e+001.0e+001.0e+00 NA NA NA
I-RLS1.1e-161.1e-167.6e-161.1e-161.1e-162.2e-163.2e-151.1e-16 NA NA
J-ISL1.1e-161.1e-161.1e-161.1e-161.1e-161.1e-161.1e-161.1e-161.1e-16 NA
Z-IPSO1.1e-161.1e-165.9e-031.1e-168.1e-011.0e+001.0e+002.7e-031.0e+001.0e+00
Ring topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.1e-16 NA NA NA NA NA NA NA NA NA
C-PSO-10001.1e-161.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.2e-168.6e-011.8e-03 NA NA NA NA NA NA NA
E-PSOLS-51.1e-161.1e-161.1e-161.3e-16 NA NA NA NA NA NA
F-PSOLS-101.1e-161.1e-161.1e-161.1e-163.1e-09 NA NA NA NA NA
G-PSOLS-201.1e-161.1e-161.1e-161.1e-162.2e-122.7e-08 NA NA NA NA
H-EPUSLS1.1e-161.1e-161.1e-163.6e-161.0e+001.0e+001.0e+00 NA NA NA
I-RLS1.1e-161.1e-161.1e-161.1e-161.1e-161.9e-162.8e-151.1e-16 NA NA
J-ISL1.1e-161.1e-161.1e-161.1e-161.1e-161.1e-161.1e-161.1e-161.1e-16 NA
Z-IPSO1.1e-167.0e-021.2e-088.6e-011.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00
Rosenbrock function - 100 dimensions
Fully-connected topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.1e-16 NA NA NA NA NA NA NA NA NA
C-PSO-10001.1e-161.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.1e-161.5e-082.2e-09 NA NA NA NA NA NA NA
E-PSOLS-51.1e-161.1e-161.1e-161.4e-08 NA NA NA NA NA NA
F-PSOLS-101.1e-161.1e-161.1e-167.6e-121.1e-07 NA NA NA NA NA
G-PSOLS-201.1e-161.1e-161.1e-164.0e-162.9e-101.1e-05 NA NA NA NA
H-EPUSLS1.1e-161.1e-161.1e-161.4e-161.1e-115.4e-099.7e-08 NA NA NA
I-RLS1.1e-161.1e-161.1e-162.2e-051.0e+001.0e+001.0e+001.0e+00 NA NA
J-ISL1.1e-161.1e-161.1e-161.1e-168.1e-125.5e-071.5e-021.0e+001.1e-16 NA
Z-IPSO1.1e-161.0e+008.6e-021.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00
Ring topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1002.9e-14 NA NA NA NA NA NA NA NA NA
C-PSO-10008.8e-031.0e+00 NA NA NA NA NA NA NA NA
D-EPUS4.7e-141.0e+001.1e-16 NA NA NA NA NA NA NA
E-PSOLS-51.1e-161.1e-161.1e-161.1e-16 NA NA NA NA NA NA
F-PSOLS-101.1e-161.1e-161.1e-161.1e-166.0e-08 NA NA NA NA NA
G-PSOLS-201.1e-161.1e-161.1e-161.1e-163.6e-101.8e-06 NA NA NA NA
H-EPUSLS1.1e-161.1e-161.1e-161.1e-162.1e-113.0e-083.5e-05 NA NA NA
I-RLS1.1e-161.1e-161.1e-161.1e-161.0e+001.0e+001.0e+001.0e+00 NA NA
J-ISL1.1e-161.1e-161.1e-161.1e-161.9e-121.9e-071.9e-021.0e+001.1e-16 NA
Z-IPSO9.2e-071.0e+001.1e-161.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00
Salomon function - 100 dimensions
Fully-connected topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.1e-16 NA NA NA NA NA NA NA NA NA
C-PSO-10001.1e-167.6e-14 NA NA NA NA NA NA NA NA
D-EPUS1.1e-143.1e-041.0e+00 NA NA NA NA NA NA NA
E-PSOLS-51.1e-161.0e+001.0e+001.0e+00 NA NA NA NA NA NA
F-PSOLS-101.1e-164.3e-071.0e+001.0e+004.3e-16 NA NA NA NA NA
G-PSOLS-201.1e-161.0e+001.0e+001.0e+001.0e+001.0e+00 NA NA NA NA
H-EPUSLS1.1e-161.7e-021.0e+001.0e+005.0e-051.0e+001.3e-15 NA NA NA
I-RLS2.2e-161.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00 NA NA
J-ISL1.1e-161.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.1e-16 NA
Z-IPSO1.1e-161.1e-161.0e-101.5e-081.1e-161.1e-161.1e-161.1e-161.1e-161.1e-16
Ring topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.1e-16 NA NA NA NA NA NA NA NA NA
C-PSO-10007.3e-151.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.1e-161.0e+001.1e-16 NA NA NA NA NA NA NA
E-PSOLS-51.2e-161.0e+001.1e-161.0e+00 NA NA NA NA NA NA
F-PSOLS-101.1e-161.0e+001.1e-161.0e+008.0e-10 NA NA NA NA NA
G-PSOLS-201.7e-161.0e+001.1e-161.0e+001.0e+001.0e+00 NA NA NA NA
H-EPUSLS1.2e-161.0e+001.1e-161.0e+001.0e+001.0e+008.3e-13 NA NA NA
I-RLS1.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00 NA NA
J-ISL7.0e-161.0e+002.9e-141.0e+001.0e+001.0e+001.0e+001.0e+001.1e-16 NA
Z-IPSO1.1e-161.0e+001.1e-161.0e+001.0e+001.0e+001.1e-161.0e+001.1e-161.1e-16
Schaffer function - 100 dimensions
Fully-connected topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.4e-16 NA NA NA NA NA NA NA NA NA
C-PSO-10009.9e-091.0e+00 NA NA NA NA NA NA NA NA
D-EPUS6.6e-051.0e+001.0e+00 NA NA NA NA NA NA NA
E-PSOLS-51.1e-161.1e-161.1e-161.1e-16 NA NA NA NA NA NA
F-PSOLS-101.1e-161.1e-161.1e-161.1e-162.4e-04 NA NA NA NA NA
G-PSOLS-201.1e-161.1e-161.1e-161.1e-163.0e-051.0e+00 NA NA NA NA
H-EPUSLS1.1e-161.1e-161.1e-161.1e-163.4e-051.0e+001.0e+00 NA NA NA
I-RLS1.1e-161.1e-161.1e-161.1e-161.0e+001.0e+001.0e+001.0e+00 NA NA
J-ISL1.1e-161.1e-161.1e-161.1e-161.2e-081.3e-031.2e-022.3e-031.1e-16 NA
Z-IPSO3.1e-081.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00
Ring topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.0e+00 NA NA NA NA NA NA NA NA NA
C-PSO-10001.0e+001.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.0e+001.0e+005.2e-07 NA NA NA NA NA NA NA
E-PSOLS-51.1e-161.1e-161.1e-161.1e-16 NA NA NA NA NA NA
F-PSOLS-101.1e-161.1e-161.1e-161.1e-165.6e-08 NA NA NA NA NA
G-PSOLS-201.1e-161.1e-161.1e-161.1e-164.4e-061.0e+00 NA NA NA NA
H-EPUSLS1.1e-161.1e-161.1e-161.1e-166.2e-071.0e+001.0e+00 NA NA NA
I-RLS1.1e-161.1e-161.1e-161.1e-161.0e+001.0e+001.0e+001.0e+00 NA NA
J-ISL1.1e-161.1e-161.1e-161.1e-162.9e-071.0e+001.0e+001.0e+001.1e-16 NA
Z-IPSO1.0e+001.0e+001.3e-081.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00
Schwefel function - 100 dimensions
Fully-connected topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.1e-16 NA NA NA NA NA NA NA NA NA
C-PSO-10001.1e-161.9e-16 NA NA NA NA NA NA NA NA
D-EPUS1.3e-041.0e+001.0e+00 NA NA NA NA NA NA NA
E-PSOLS-51.1e-161.1e-161.1e-161.1e-16 NA NA NA NA NA NA
F-PSOLS-101.1e-161.1e-161.1e-161.1e-167.3e-08 NA NA NA NA NA
G-PSOLS-201.1e-161.1e-161.1e-161.1e-161.1e-143.7e-11 NA NA NA NA
H-EPUSLS1.1e-161.1e-161.1e-161.1e-161.0e+001.0e+001.0e+00 NA NA NA
I-RLS1.1e-161.1e-161.1e-161.1e-161.1e-161.3e-162.6e-151.1e-16 NA NA
J-ISL1.1e-161.1e-161.1e-161.1e-161.1e-161.1e-161.1e-161.1e-161.1e-16 NA
Z-IPSO1.1e-161.7e-161.0e+001.1e-161.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00
Ring topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1006.0e-15 NA NA NA NA NA NA NA NA NA
C-PSO-10008.3e-151.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.7e-151.0e-146.8e-15 NA NA NA NA NA NA NA
E-PSOLS-51.1e-161.1e-161.1e-161.1e-16 NA NA NA NA NA NA
F-PSOLS-101.1e-161.1e-161.1e-161.1e-161.5e-08 NA NA NA NA NA
G-PSOLS-201.1e-161.1e-161.1e-161.1e-162.6e-145.1e-11 NA NA NA NA
H-EPUSLS1.1e-161.1e-161.1e-161.1e-161.0e+001.0e+001.0e+00 NA NA NA
I-RLS1.1e-161.1e-161.1e-161.1e-161.1e-161.5e-163.2e-151.1e-16 NA NA
J-ISL1.1e-161.1e-161.1e-161.1e-161.1e-161.1e-161.1e-161.1e-161.1e-16 NA
Z-IPSO1.7e-164.2e-068.6e-091.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00
Sphere function - 100 dimensions
Fully-connected topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1009.9e-17 NA NA NA NA NA NA NA NA NA
C-PSO-10009.9e-171.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.6e-149.6e-101.6e-08 NA NA NA NA NA NA NA
E-PSOLS-59.9e-176.9e-189.9e-179.9e-17 NA NA NA NA NA NA
F-PSOLS-109.9e-176.9e-189.9e-179.9e-171.0e+00 NA NA NA NA NA
G-PSOLS-209.9e-176.9e-189.9e-179.9e-171.0e+001.0e+00 NA NA NA NA
H-EPUSLS9.9e-179.9e-179.9e-179.9e-171.0e+001.0e+001.0e+00 NA NA NA
I-RLS9.9e-176.9e-189.9e-179.9e-171.0e+001.0e+001.0e+009.9e-17 NA NA
J-ISL9.9e-176.9e-189.9e-179.9e-171.0e+001.0e+001.0e+009.9e-171.0e+00 NA
Z-IPSO9.9e-171.0e+009.9e-171.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00
Ring topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.1e-14 NA NA NA NA NA NA NA NA NA
C-PSO-10001.4e-041.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.1e-163.9e-049.6e-17 NA NA NA NA NA NA NA
E-PSOLS-59.6e-174.3e-229.6e-179.6e-17 NA NA NA NA NA NA
F-PSOLS-109.6e-174.3e-229.6e-179.6e-171.0e+00 NA NA NA NA NA
G-PSOLS-209.6e-174.3e-229.6e-179.6e-171.0e+001.0e+00 NA NA NA NA
H-EPUSLS9.6e-179.6e-179.6e-179.6e-171.0e+001.0e+001.0e+00 NA NA NA
I-RLS9.6e-174.3e-229.6e-179.6e-171.0e+001.0e+001.0e+009.6e-17 NA NA
J-ISL9.6e-174.3e-229.6e-179.6e-171.0e+001.0e+001.0e+009.6e-171.0e+00 NA
Z-IPSO1.3e-121.0e+009.6e-171.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00
Step function - 100 dimensions
Fully-connected topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1008.8e-17 NA NA NA NA NA NA NA NA NA
C-PSO-10008.8e-172.5e-14 NA NA NA NA NA NA NA NA
D-EPUS1.0e+001.0e+001.0e+00 NA NA NA NA NA NA NA
E-PSOLS-58.8e-178.8e-178.6e-178.8e-17 NA NA NA NA NA NA
F-PSOLS-108.8e-178.8e-178.6e-178.8e-171.0e+00 NA NA NA NA NA
G-PSOLS-208.8e-178.8e-178.8e-178.8e-171.0e+001.0e+00 NA NA NA NA
H-EPUSLS8.8e-172.8e-121.0e+008.8e-171.0e+001.0e+001.0e+00 NA NA NA
I-RLS8.8e-175.3e-111.0e+008.8e-171.0e+001.0e+001.0e+001.0e+00 NA NA
J-ISL8.8e-178.8e-178.6e-178.8e-174.6e-031.3e-015.6e-168.8e-178.2e-17 NA
Z-IPSO8.8e-178.8e-178.6e-178.8e-179.2e-011.0e+001.1e-118.8e-178.3e-171.0e+00
Ring topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1009.7e-17 NA NA NA NA NA NA NA NA NA
C-PSO-10009.7e-171.0e+00 NA NA NA NA NA NA NA NA
D-EPUS1.0e+001.0e+001.0e+00 NA NA NA NA NA NA NA
E-PSOLS-59.7e-171.0e+001.0e+009.7e-17 NA NA NA NA NA NA
F-PSOLS-109.7e-171.0e+001.0e+009.7e-171.0e+00 NA NA NA NA NA
G-PSOLS-209.7e-171.0e+001.0e+009.7e-171.0e+001.0e+00 NA NA NA NA
H-EPUSLS2.3e-161.0e+001.0e+009.7e-171.0e+001.0e+001.0e+00 NA NA NA
I-RLS2.0e-161.0e+001.0e+009.7e-171.0e+001.0e+001.0e+001.8e-03 NA NA
J-ISL9.7e-171.0e+001.0e+009.7e-171.0e+001.0e+001.2e-149.6e-178.3e-17 NA
Z-IPSO9.7e-171.0e+001.0e+009.7e-171.7e-025.2e-025.9e-159.6e-178.3e-177.1e-02
Weierstrass function - 100 dimensions
Fully-connected topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.1e-16 NA NA NA NA NA NA NA NA NA
C-PSO-10001.1e-161.1e-16 NA NA NA NA NA NA NA NA
D-EPUS5.7e-141.0e+001.0e+00 NA NA NA NA NA NA NA
E-PSOLS-51.1e-161.1e-161.1e-161.1e-16 NA NA NA NA NA NA
F-PSOLS-101.1e-161.1e-161.1e-161.1e-162.6e-10 NA NA NA NA NA
G-PSOLS-201.1e-161.1e-161.1e-161.1e-162.0e-152.0e-08 NA NA NA NA
H-EPUSLS1.1e-161.1e-161.1e-161.1e-161.0e+001.0e+001.0e+00 NA NA NA
I-RLS1.1e-161.1e-161.1e-161.1e-161.4e-169.1e-142.0e-081.6e-16 NA NA
J-ISL1.1e-161.1e-161.1e-161.1e-161.1e-163.0e-156.9e-101.7e-162.4e-01 NA
Z-IPSO1.1e-161.1e-161.4e-041.1e-161.0e+001.0e+001.0e+001.0e+001.0e+001.0e+00
Ring topology
A-PSO-10B-PSO-100C-PSO-1000D-EPUSE-PSOLS-5F-PSOLS-10G-PSOLS-20H-EPUSLSI-RLSJ-ISL
B-PSO-1001.6e-14 NA NA NA NA NA NA NA NA NA
C-PSO-10001.6e-165.8e-06 NA NA NA NA NA NA NA NA
D-EPUS1.1e-161.1e-161.1e-16 NA NA NA NA NA NA NA
E-PSOLS-51.1e-161.1e-161.1e-161.1e-16 NA NA NA NA NA NA
F-PSOLS-101.1e-161.1e-161.1e-161.1e-161.5e-10 NA NA NA NA NA
G-PSOLS-201.1e-161.1e-161.1e-161.1e-166.1e-163.0e-09 NA NA NA NA
H-EPUSLS1.1e-161.1e-161.1e-161.1e-161.0e+001.0e+001.0e+00 NA NA NA
I-RLS1.1e-161.1e-161.1e-161.1e-161.6e-161.1e-131.4e-072.2e-16 NA NA
J-ISL1.1e-161.1e-161.1e-161.1e-161.0e+001.0e+001.0e+001.0e+001.0e+00 NA
Z-IPSO1.1e-161.1e-161.1e-161.0e+001.0e+001.0e+001.0e+001.0e+001.0e+001.0e+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 topologyRing topology
FC Ring
IPSOLS
Fully-connected topologyRing topology
FC Ring

Results after 1,000 function evaluations

IPSO
Fully-connected topologyRing topology
FC Ring
IPSOLS
Fully-connected topologyRing topology
FC Ring

Results after 10,000 function evaluations

IPSO
Fully-connected topologyRing topology
FC Ring
IPSOLS
Fully-connected topologyRing topology
FC Ring

Results after 100,000 function evaluations

IPSO
Fully-connected topologyRing topology
FC Ring
IPSOLS
Fully-connected topologyRing topology
FC Ring

Results after 1,000,000 function evaluations

IPSO
Fully-connected topologyRing topology
FC Ring
IPSOLS
Fully-connected topologyRing topology
FC Ring

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 topologyRing topology
Ackley - FC Ackley - Ring
Griewank function - 100 dimensions
Fully-connected topologyRing topology
Griewank - FC Griewank - Ring
Rastrigin function - 100 dimensions
Fully-connected topologyRing topology
Rastrigin - FC Rastrigin - Ring
Rosenbrock function - 100 dimensions
Fully-connected topologyRing topology
Rosenbrock - FC Rosenbrock - Ring
Salomon function - 100 dimensions
Fully-connected topologyRing topology
Salomon - FC Salomon - Ring
Schaffer function - 100 dimensions
Fully-connected topologyRing topology
Schaffer - FC Schaffer - Ring
Schwefel function - 100 dimensions
Fully-connected topologyRing topology
Schwefel - FC Schwefel - Ring
Sphere function - 100 dimensions
Fully-connected topologyRing topology
Sphere - FC Sphere - Ring
Step function - 100 dimensions
Fully-connected topologyRing topology
Step - FC Step - Ring
Weierstrass function - 100 dimensions
Fully-connected topologyRing topology
Weierstrass - FC Weierstrass - Ring

Results after 1,000 function evaluations

Ackley function - 100 dimensions
Fully-connected topologyRing topology
Ackley - FC Ackley - Ring
Griewank function - 100 dimensions
Fully-connected topologyRing topology
Griewank - FC Griewank - Ring
Rastrigin function - 100 dimensions
Fully-connected topologyRing topology
Rastrigin - FC Rastrigin - Ring
Rosenbrock function - 100 dimensions
Fully-connected topologyRing topology
Rosenbrock - FC Rosenbrock - Ring
Salomon function - 100 dimensions
Fully-connected topologyRing topology
Salomon - FC Salomon - Ring
Schaffer function - 100 dimensions
Fully-connected topologyRing topology
Schaffer - FC Schaffer - Ring
Schwefel function - 100 dimensions
Fully-connected topologyRing topology
Schwefel - FC Schwefel - Ring
Sphere function - 100 dimensions
Fully-connected topologyRing topology
Sphere - FC Sphere - Ring
Step function - 100 dimensions
Fully-connected topologyRing topology
Step - FC Step - Ring
Weierstrass function - 100 dimensions
Fully-connected topologyRing topology
Weierstrass - FC Weierstrass - Ring

Results after 10,000 function evaluations

Ackley function - 100 dimensions
Fully-connected topologyRing topology
Ackley - FC Ackley - Ring
Griewank function - 100 dimensions
Fully-connected topologyRing topology
Griewank - FC Griewank - Ring
Rastrigin function - 100 dimensions
Fully-connected topologyRing topology
Rastrigin - FC Rastrigin - Ring
Rosenbrock function - 100 dimensions
Fully-connected topologyRing topology
Rosenbrock - FC Rosenbrock - Ring
Salomon function - 100 dimensions
Fully-connected topologyRing topology
Salomon - FC Salomon - Ring
Schaffer function - 100 dimensions
Fully-connected topologyRing topology
Schaffer - FC Schaffer - Ring
Schwefel function - 100 dimensions
Fully-connected topologyRing topology
Schwefel - FC Schwefel - Ring
Sphere function - 100 dimensions
Fully-connected topologyRing topology
Sphere - FC Sphere - Ring
Step function - 100 dimensions
Fully-connected topologyRing topology
Step - FC Step - Ring
Weierstrass function - 100 dimensions
Fully-connected topologyRing topology
Weierstrass - FC Weierstrass - Ring

Results after 100,000 function evaluations

Ackley function - 100 dimensions
Fully-connected topologyRing topology
Ackley - FC Ackley - Ring
Griewank function - 100 dimensions
Fully-connected topologyRing topology
Griewank - FC Griewank - Ring
Rastrigin function - 100 dimensions
Fully-connected topologyRing topology
Rastrigin - FC Rastrigin - Ring
Rosenbrock function - 100 dimensions
Fully-connected topologyRing topology
Rosenbrock - FC Rosenbrock - Ring
Salomon function - 100 dimensions
Fully-connected topologyRing topology
Salomon - FC Salomon - Ring
Schaffer function - 100 dimensions
Fully-connected topologyRing topology
Schaffer - FC Schaffer - Ring
Schwefel function - 100 dimensions
Fully-connected topologyRing topology
Schwefel - FC Schwefel - Ring
Sphere function - 100 dimensions
Fully-connected topologyRing topology
Sphere - FC Sphere - Ring
Step function - 100 dimensions
Fully-connected topologyRing topology
Step - FC Step - Ring
Weierstrass function - 100 dimensions
Fully-connected topologyRing topology
Weierstrass - FC Weierstrass - Ring

Results after 1,000,000 function evaluations

Ackley function - 100 dimensions
Fully-connected topologyRing topology
Ackley - FC Ackley - Ring
Griewank function - 100 dimensions
Fully-connected topologyRing topology
Griewank - FC Griewank - Ring
Rastrigin function - 100 dimensions
Fully-connected topologyRing topology
Rastrigin - FC Rastrigin - Ring
Rosenbrock function - 100 dimensions
Fully-connected topologyRing topology
Rosenbrock - FC Rosenbrock - Ring
Salomon function - 100 dimensions
Fully-connected topologyRing topology
Salomon - FC Salomon - Ring
Schaffer function - 100 dimensions
Fully-connected topologyRing topology
Schaffer - FC Schaffer - Ring
Schwefel function - 100 dimensions
Fully-connected topologyRing topology
Schwefel - FC Schwefel - Ring
Sphere function - 100 dimensions
Fully-connected topologyRing topology
Sphere - FC Sphere - Ring
Step function - 100 dimensions
Fully-connected topologyRing topology
Step - FC Step - Ring
Weierstrass function - 100 dimensions
Fully-connected topologyRing topology
Weierstrass - FC Weierstrass - Ring