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

Table 9

Comparison of FGLT-PSO with PSO, LPSO, and QIPSO for the rotated and shifted unimodal and multimodal functions using Wilcoxon’s rank sum test (𝑛=30).

Function	Wilcoxon’s rank sum test	PSO	LPSO	QIPSO
𝐹10	𝑃 value	3.2922e − 010	1.4041e − 010	3.1451e − 009
	ℎ-value	1	1	1
	𝑧-value	−6.28435	−6.41545	−5.92384
𝐹11	𝑃 value	1.0233e − 001	3.0418e − 001	4.4642e − 001
	ℎ-value	0	0	0
	𝑧-value	1.63368	−1.02752	0.761398
𝐹12	𝑃 value	1.0937e − 010	1.4643e − 010	3.0199e − 011
	ℎ-value	1	1	1
	𝑧-value	−6.4534	−6.40905	−6.6456
𝐹13	𝑃 value	1.4288e − 008	1.3281e − 010	1.1736e − 003
	ℎ-value	1	1	1
	𝑧-value	−5.66991	−6.42392	−3.24523
𝐹14	𝑃 value	1.3470e − 003	6.7707e − 003	3.5527e − 003
	ℎ-value	−1	−1	−1
	𝑧-value	3.20578	2.70792	2.91537
𝐹15	𝑃 value	2.8840e − 010	4.7657e − 005	2.8252e − 011
	ℎ-value	1	1	−1
	𝑧-value	−6.30489	−4.06683	6.65541
𝐹16	𝑃 value	2.9543e − 011	5.3712e − 011	2.9543e − 011
	ℎ-value	1	1	1
	𝑧-value	−6.64883	−6.56027	−6.64883
𝐹17	𝑃 value	3.0199e − 11	3.0199e − 11	3.0199e − 11
	ℎ-value	1	1	1
	𝑧-value	−6.6456	−6.6456	−6.6456
𝐹18	𝑃 value	1.0937e − 010	1.2870e − 009	1.4643e − 010
	ℎ-value	1	1	1
	𝑧-value	−6.4534	−6.06901	−6.40905
𝐹19	𝑃 value	8.7663e − 001	4.0595e − 002	7.7312e − 001
	ℎ-value	0	1	0
	𝑧-value	0.155236	2.04764	0.288296
𝐹20	𝑃 value	3.0199e − 011	7.3891e − 011	4.9752e − 011
	ℎ-value	1	1	1
	𝑧-value	−6.6456	−6.51254	−6.57168
1 (better)		8	9	7
0 (same)		2	1	2
−1 (worse)		1	1	2