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

Table 5

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=10).

Function	Wilcoxon’s rank sum test	PSO	LPSO	QIPSO
𝐹10	𝑃 value	3.0199e − 011	3.0199e − 011	3.0199e − 011
	ℎ-value	1	1	1
	𝑧-value	−6.6456	−6.6456	−6.6456
𝐹11	𝑃 value	4.1191e − 001	7.3940e − 001	8.4180e − 001
	ℎ-value	0	0	0
	𝑧-value	0.820536	0.33265	0.19959
𝐹12	𝑃 value	1.8567e − 009	1.8500e − 008	5.5329e − 008
	ℎ-value	1	1	1
	𝑧-value	−6.00987	−5.62547	−5.43328
𝐹13	𝑃 value	2.1577e − 002	2.1577e − 002	8.1523e − 002
	ℎ-value	1	1	0
	𝑧-value	−2.29773	−2.29773	−1.74192
𝐹14	𝑃 value	1.1439e − 001	1.4425e − 004	7.7181e − 001
	ℎ-value	0	−1	0
	𝑧-value	1.57878	3.80076	0.290007
𝐹15	𝑃 value	1.5553e − 011	1.2883e − 011	1.7966e − 008
	ℎ-value	1	1	1
	𝑧-value	−6.74264	−6.76995	−5.63053
𝐹16	𝑃 value	1.2755e − 010	1.9667e − 003	5.5338e − 010
	ℎ-value	1	1	1
	𝑧-value	−6.43006	−3.09521	−6.20317
𝐹17	𝑃 value	7.3270e − 011	3.6443e − 008	5.0030e − 010
	ℎ-value	1	1	1
	𝑧-value	−6.51381	−5.50727	−6.21901
𝐹18	𝑃 value	5.7512e − 006	3.5043e − 007	4.0269e − 005
	ℎ-value	1	1	1
	𝑧-value	−4.53533	−5.09408	−4.10593
𝐹19	𝑃 value	9.2344e − 001	2.3885e − 004	8.6499e − 001
	ℎ-value	0	−1	0
	𝑧-value	0.0960988	3.67393	0.170021
𝐹20	𝑃 value	5.2991e − 008	9.2051e − 005	4.6756e − 008
	ℎ-value	1	1	1
	𝑧-value	−5.44097	−3.91064	−5.46322
1 (better)		8	8	7
0 (same)		3	1	4
−1 (worse)		0	2	0