Function | Algorithm | Literature | Our implementation | Settings | Reference | ||||||||||||||||||||||||
Sphere | Canonical-PSO | 6.86e-24 (--) | 4.73991e-09 (2.87181e-09) | Dimensions: 30 Topology: Square Initialization: asymmetrical No. of particles: 20 No. of runs: 50 No. of iterations: 3000 | (Kennedy, 2004) | ||||||||||||||||||||||||
Time-Increasing Inertia Weight PSO | 1.3128e-9 (--) | 1.05764e-06 (3.0892e-06) | Dimensions: 30 Topology: Fully connected Initialization: asymmetrical No. of particles: 20 No. of runs: 20 No. of iterations: 2000 | (Zheng et al., 2003) | |||||||||||||||||||||||||
Time-Decreasing Inertia Weight PSO | 0.0000 (--) | 6.21681e-08 ( 1.15432e-07) | Dimensions: 30 Topology: Fully connected Initialization: asymmetrical No. of particles: 20 No. of runs: 50 No. of iterations: 2000 | (Kennedy et al., 2001) | |||||||||||||||||||||||||
Stochastic Inertia Weight PSO | 0.01 (--) | 5.48384e-09 ( 2.79073e-09) | Dimensions: 30 Topology: Fully connected Initialization: asymmetrical No. of particles: 40 No. of runs: 50 No. of iterations: 3000 | (Ratnaweera et al., 2004) | |||||||||||||||||||||||||
Fully Informed Particle Swarm | 3.13e-39 (8.25e-39) | 5.23306e-09 (3.28642e-09) | Dimensions: 30 Topology: Square Initialization: asymmetrical No. of particles: 20 No. of runs: 50 No. of iterations: 3000 | (Kennedy,2003) | |||||||||||||||||||||||||
Self-Organizing Hierarchical Particle Swarm Optimizer with Time-varying Acceleration Coefficients | 0.01 (-) | 5.73233e-09 (2.74801e-09) | Dimensions: 30 Topology: Fully connected Initialization: asymmetrical No. of particles: 40 No. of runs: 50 No. of iterations: 3000 | (Ratnaweera et al., 2004) | |||||||||||||||||||||||||
Adaptive Hierarchical Particle Swarm Optimizer | 1e-48 (aprox)* (--) | 5.89199e-09 (2.8147e-09) | Dimensions: 30 Topology: -- Initialization: symmetrical No. of particles: 40 No. of runs: 100 No. of iterations: 3000 | (Janson and Middendorf, 2005) | |||||||||||||||||||||||||
Rosenbrock | Canonical-PSO | 39.5256 (--) | 96.04 (101.04) | Dimensions: 30 Topology: Square Initialization: asymmetrical No. of particles: 20 No. of runs: 50 No. of iterations: 3000 | (Kennedy, 2004) | ||||||||||||||||||||||||
Time-Increasing Inertia Weight PSO | 37.4257 (--) | 2.52679e+09 ( 1.94479e+09) | Dimensions: 30 Topology: Fully connected Initialization: asymmetrical No. of particles: 20 No. of runs: 20 No. of iterations: 2000 | (Zheng et al., 2003) | |||||||||||||||||||||||||
Time-Decreasing Inertia Weight PSO | 316.4468 (--) | 231.258 (286.765) | Dimensions: 30 Topology: Fully connected Initialization: asymmetrical No. of particles: 20 No. of runs: 50 No. of iterations: 2000 | (Kennedy et al., 2001) | |||||||||||||||||||||||||
Stochastic Inertia Weight PSO | 35.277 (55.751) | 24.5597 (35.0822) | Dimensions: 30 Topology: Fully connected Initialization: asymmetrical No. of particles: 40 No. of runs: 50 No. of iterations: 5000 | (Ratnaweera et al., 2004) | |||||||||||||||||||||||||
Fully Informed Particle Swarm | 67.03906 (57.48949) | 389.118 (909.047) | Dimensions: 30 Topology: Square Initialization: asymmetrical No. of particles: 20 No. of runs: 50 No. of iterations: 3000 | (Kennedy, 2003) | |||||||||||||||||||||||||
Self-Organizing Hierarchical Particle Swarm Optimizer with Time-varying Acceleration Coefficients | 13.666 (11.006) | 67.0844 (46.3846) | Dimensions: 30 Topology: Fully connected Initialization: asymmetrical No. of particles: 40 No. of runs: 50 No. of iterations: 5000 | (Ratnaweera et al., 2004) | |||||||||||||||||||||||||
Adaptive Hierarchical Particle Swarm Optimizer | 19 (aprox)* (--) | 46.6737 (57.1728) | Dimensions: 30 Topology: -- Initialization: symmetrical No. of particles: 40 No. of runs: 100 No. of iterations: 3000 | (Janson and Middendorf, 2005) | |||||||||||||||||||||||||
Griewank | Canonical-PSO | 0.0106 (--) | 0.0117472 (0.017055) | Dimensions: 30 Topology: Square Initialization: asymmetrical No. of particles: 20 No. of runs: 50 No. of iterations: 3000 | (Kennedy, 2004) | ||||||||||||||||||||||||
Time-Increasing Inertia Weight PSO | 18.1028 (--) | 0.0216872 (0.0235111) | Dimensions: 30 Topology: Fully connected Initialization: asymmetrical No. of particles: 20 No. of runs: 20 No. of iterations: 2000 | (Zheng et al., 2003) | |||||||||||||||||||||||||
Time-Decreasing Inertia Weight PSO | 0.0182 (--) | 0.0141078 (0.0176244) | Dimensions: 30 Topology: Fully connected Initialization: asymmetrical No. of particles: 20 No. of runs: 50 No. of iterations: 2000 | (Kennedy et al., 2001) | |||||||||||||||||||||||||
Stochastic Inertia Weight PSO | 0.0175 (0.018) | 0.0207172 (0.0202154) | Dimensions: 30 Topology: Fully connected Initialization: asymmetrical No. of particles: 40 No. of runs: 50 No. of iterations: 5000 | (Ratnaweera et al., 2004) | |||||||||||||||||||||||||
Fully Informed Particle Swarm | 0.003534 (0.009502) | 8.26762 (7.53187) | Dimensions: 30 Topology: Square Initialization: asymmetrical No. of particles: 20 No. of runs: 50 No. of iterations: 3000 | (Kennedy, 2003) | |||||||||||||||||||||||||
Self-Organizing Hierarchical Particle Swarm Optimizer with Time-varying Acceleration Coefficients | 0.01 (0.0035) | 0.00256344 (0.00413481) | Dimensions: 30 Topology: Fully connected Initialization: asymmetrical No. of particles: 40 No. of runs: 50 No. of iterations: 5000 | (Ratnaweera et al., 2004) | |||||||||||||||||||||||||
Adaptive Hierarchical Particle Swarm Optimizer | 0.004 (aprox)* (--) | 0.0060568 (0.00820175) | Dimensions: 30 Topology: -- Initialization: symmetrical No. of particles: 40 No. of runs: 100 No. of iterations: 3000 | (Janson and Middendorf, 2005) | |||||||||||||||||||||||||
Rastrigin | Canonical-PSO | 95.0581 (--) | 68.7913 (21.8641) | Dimensions: 30 Topology: Square Initialization: asymmetrical No. of particles: 20 No. of runs: 50 No. of iterations: 3000 | (Kennedy, 2004) | ||||||||||||||||||||||||
Time-Increasing Inertia Weight PSO | 123.3182 (--) | 74.174 (20.0151) | Dimensions: 30 Topology: Fully connected Initialization: asymmetrical No. of particles: 20 No. of runs: 20 No. of iterations: 2000 | (Zheng et al., 2003) | |||||||||||||||||||||||||
Time-Decreasing Inertia Weight PSO | 47.2941 (--) | 43.0845 (10.2529) | Dimensions: 30 Topology: Fully connected Initialization: asymmetrical No. of particles: 20 No. of runs: 50 No. of iterations: 2000 | (Kennedy et al., 2001) | |||||||||||||||||||||||||
Stochastic Inertia Weight PSO | 69.7266 (20.7) | 60.3939 (15.3708) | Dimensions: 30 Topology: Fully connected Initialization: asymmetrical No. of particles: 40 No. of runs: 50 No. of iterations: 5000 | (Ratnaweera et al., 2004) | |||||||||||||||||||||||||
Fully Informed Particle Swarm | 57.8667 (16.66862) | 77.0502 (19.4693) | Dimensions: 30 Topology: Square Initialization: asymmetrical No. of particles: 20 No. of runs: 50 No. of iterations: 3000 | (Kennedy, 2003) | |||||||||||||||||||||||||
Self-Organizing Hierarchical Particle Swarm Optimizer with Time-varying Acceleration Coefficients | 0.044 (0.196) | 12.8561 ( 6.43465) | Dimensions: 30 Topology: Fully connected Initialization: asymmetrical No. of particles: 40 No. of runs: 50 No. of iterations: 5000 | (Ratnaweera et al., 2004) | |||||||||||||||||||||||||
Adaptive Hierarchical Particle Swarm Optimizer | 30 (aprox)* (--) | 42.7036 (13.21) | Dimensions: 30 Topology: -- Initialization: symmetrical No. of particles: 40 No. of runs: 100 No. of iterations: 3000 | (Janson and Middendorf, 2005) | |||||||||||||||||||||||||
Schaffer's F6 | Canonical-PSO | 0.0006 (--) | 0.00038864 ( 0.00192325) | Dimensions: 2 Topology: Square Initialization: asymmetrical No. of particles: 20 No. of runs: 50 No. of iterations: 3000 | (Kennedy, 2004) | ||||||||||||||||||||||||
Time-Increasing Inertia Weight PSO | -- (--) | 0.00437216 (0.00495917) | Dimensions: 2 Topology: Fully connected Initialization: asymmetrical No. of particles: 20 No. of runs: 20 No. of iterations: 2000 Not tested in reference (Zheng et al., 2003)
| Time-Decreasing Inertia Weight PSO
| -- | (--) 0.00116591 | (0.00318935) Dimensions: 2 | Topology: Fully connected Initialization: asymmetrical No. of particles: 20 No. of runs: 50 No. of iterations: 2000 Not tested in reference (Kennedy et al., 2001)
| Stochastic Inertia Weight PSO
| 0.0029 | (0.004) 0.00233182 | (0.00419163) Dimensions: 2 | Topology: Fully connected Initialization: asymmetrical No. of particles: 40 No. of runs: 50 No. of iterations: 1000 (Ratnaweera et al., 2004)
| Fully Informed Particle Swarm
| 0.001675 | (0.003485) 0.00296635 | (0.00427008) Dimensions: 2 | Topology: Square Initialization: asymmetrical No. of particles: 20 No. of runs: 50 No. of iterations: 3000 (Kennedy, 2003)
| Self-Organizing Hierarchical Particle | Swarm Optimizer with Time-varying Acceleration Coefficients 0.01 | (0.007) 0.00446932 | (0.00489155) Dimensions: 2 | Topology: Fully connected Initialization: asymmetrical No. of particles: 40 No. of runs: 50 No. of iterations: 1000 (Ratnaweera et al., 2004)
| Adaptive Hierarchical Particle Swarm | Optimizer << 0.0001 (aprox)* | (--) 3.90043e-09 | (3.10343e-09) Dimensions: 30 | Topology: -- Initialization: symmetrical No. of particles: 40 No. of runs: 100 No. of iterations: 3000 (Janson and Middendorf, 2005)
| |
Function | Fully Connected Topology | Ring Topology |
Griewank | ||
Rastrigin | ||
Rosenbrock | ||
Schaffer's F6 | ||
Sphere |
Function | Fully Connected Topology | Ring Topology |
Griewank 0.01% | ||
Rastrigin 30.0% | ||
Rosenbrock 10.0% | ||
Schaffer's F6 0.0001% | ||
Sphere 0.01% |
S. Janson and M. Middendorf. A Hierarchical Particle Swarm Optimizer and Its Adaptive Variant. IEEE Transactions on Systems, Man and Cybernetics--Part B Vol. 35 (6). pp 1272--1282. 2005. |
J. Kennedy, R. Eberhart with Y.Shi. Swarm Intelligence. Morgan Kaufmann. 2001 |
J. Kennedy. Probability and Dynamics in the Particle Swarm. Proc. of the 2004 IEEE Congress on Evolutionary Computation. pp. 340--347. 2004 |
A. Ratnaweera, S. K. Halgamuge and H. C. Watson. Self-Organizing Hierarchical Particle Swarm Optimizer With Time-Varying Acceleration Coefficients. IEEE Transactions on Evolutionary Computation Vol. 8 (3). pp 240--255. 2004. |
Y. Zheng, L. Ma, L. Zhang and J. Qian. Empirical Study of Particle Swarm Optimizer with an Increasing Inertia Weight. Proc. of the 2003 IEEE Congress on Evolutionary Computation. pp. 221--226. 2003 |