Fusion Global-Local-Topology Particle Swarm Optimization for Global Optimization Problems

Table 3

Minimization results for the rotated and shifted unimodal and multimodal functions (maximum iteration = 5000 and 𝑛=10).

Function		FGLT-PSO	PSO	LPSO	QIPSO
𝐹10	Avg. best solution	7.056e − 208	4.585e − 059	2.358e − 021	1.127e − 058
	SD	0.000e + 000	8.736e − 059	7.425e − 021	5.346e − 058
	Median best solution	1.930e − 209	7.785e − 060	3.417e − 022	1.023e − 060
	Avg. iteration for finding the best solution	4741	4999	4997	4999
𝐹11	Avg. best solution	−6.602e + 001	−6.645e + 001	−6.616e + 001	−6.613e + 001
	SD	1.736e + 000	1.175e + 000	9.989e − 001	1.720e + 000
	Median best solution	−6.606e + 001	−6.614e + 001	−6.607e + 001	−6.588e + 001
	Avg. iteration for finding the best solution	3408	2930	3099	3185
𝐹12	Avg. best solution	1.604e + 001	2.352e + 001	2.319e + 001	2.278e + 001
	SD	2.974e + 000	3.762e + 000	4.012e + 000	4.387e + 000
	Median best solution	1.589e + 001	2.358e + 001	2.351e + 001	2.240e + 001
	Avg. iteration for finding the best solution	2394	3656	3786	3660
𝐹13	Avg. best solution	0.000e + 000	1.351e + 000	7.438e − 008	7.957e − 001
	SD	0.000e + 000	3.079e + 000	4.072e − 007	2.428e + 000
	Median best solution	0.000e + 000	0.000e + 000	0.000e + 000	0.000e + 000
	Avg. iteration for finding the best solution	448	3192	4877	3446
𝐹14	Avg. best solution	1.165e − 001	1.032e − 001	9.987e − 002	1.132e − 001
	SD	3.790e − 002	1.826e − 002	0.000e + 000	3.457e − 002
	Median best solution	9.987e − 002	9.987e − 002	9.987e − 002	9.987e − 002
	Avg. iteration for finding the best solution	1998	2916	3268	2795
𝐹15	Avg. best solution	−4.500e + 002	−4.396e + 002	−4.480e + 002	−4.406e + 002
	SD	8.039e − 014	7.334e + 000	2.470e + 000	7.991e + 000
	Median best solution	−4.500e + 002	−4.450e + 002	−4.500e + 002	−4.450e + 002
	Avg. iteration for finding the best solution	1324	757	3561	1213
𝐹16	Avg. best solution	−1.798e + 002	−1.745e + 002	−1.793e + 002	−1.766e + 002
	SD	3.789e − 001	8.186e + 000	5.222e − 001	3.309e + 000
	Median best solution	−1.800e + 002	−1.780e + 002	−1.789e + 002	−1.780e + 002
	Avg. iteration for finding the best solution	2922	2592	3398	2711
𝐹17	Avg. best solution	3.915e + 002	9.048e + 006	6.752e + 004	6.596e + 006
	SD	6.315e + 000	1.678e + 007	3.676e + 005	1.638e + 007
	Median best solution	3.900e + 002	2.014e + 006	3.933e + 002	4.867e + 002
	Avg. iteration for finding the best solution	4831	3983	4884	4090
𝐹18	Avg. best solution	−3.287e + 002	−3.215e + 002	−3.247e + 002	−3.233e + 002
	SD	1.113e + 000	5.979e + 000	3.144e + 000	4.822e + 000
	Median best solution	−3.290e + 002	−3.225e + 002	−3.250e + 002	−3.225e + 002
	Avg. iteration for finding the best solution	4809	3193	4509	3331
𝐹19	Avg. best solution	−119.744	−119.745	−119.804	−119.746
	SD	5.750e − 002	7.142e − 002	5.558e − 002	6.911e − 002
	Median best solution	−119.731	−119.748	−119.804	−119.73
	Avg. iteration for finding the best solution	1849	2240	2072	2414
𝐹20	Avg. best solution	−3.196e + 002	−3.091e + 002	−3.137e + 002	−3.078e + 002
	SD	4.236e + 000	7.174e + 000	5.338e + 000	7.995e + 000
	Median best solution	−3.196e + 002	−3.102e + 002	−3.130e + 002	−3.079e + 002
	Avg. iteration for finding the best solution	3252	3315	4721	3479
Avg. rank		1.8	3.2	2.1	2.9
Final rank		1	4	2	3
Algorithms		FGLT-PSO	PSO	LPSO	QIPSO