Human Behavior-Based Particle Swarm Optimization

Table 6

Comparison results of eight PSO algorithms [22] with HPSO on 10 functions (𝑁=20, 𝐷=30, and FEs=2×10⁵).

Function	GPSO	LPSO	VPSO	FIPS	HPSO-TVAC	DMS-PSO	CLPSO	APSO	HPSO
𝐹1
Mean	1.98𝑒−53	4.77𝑒−29	5.11𝑒−38	3.21𝑒−30	3.38𝑒−41	3.85𝑒−54	1.89𝑒−19	1.45𝑒−150	0
SD	7.08𝑒−53	1.13𝑒−28	1.91𝑒−37	3.60𝑒−30	8.50𝑒−41	1.75𝑒−53	1.49𝑒−19	5.73𝑒−150	0
Rank	4	8	6	7	5	3	9	2	1
𝐹2
Mean	2.51𝑒−34	2.03𝑒−20	6.29𝑒−27	1.32𝑒−17	6.9𝑒−23	2.61𝑒−29	1.01𝑒−13	5.15𝑒−84	0
SD	5.84𝑒−34	2.89𝑒−20	8.68𝑒−27	7.86𝑒−18	6.89𝑒−23	6.6𝑒−29	6.51𝑒−14	1.44𝑒−83	0
Rank	3	7	5	8	6	4	9	2	1
𝐹3
Mean	6.45𝑒−2	18.60	1.44	0.77	2.89𝑒−7	47.5	395	𝟏.𝟎𝐞−𝟏𝟎	167
SD	9.45𝑒−2	30.71	1.55	0.86	2.97𝑒−7	56.4	142	𝟐.𝟏𝟑𝐞−𝟏𝟎	913
Rank	3	6	5	4	2	7	9	1	8
𝐹5
Mean	0	0	0	0	0	0	0	0	0
SD	0	0	0	0	0	0	0	0	0
Rank	1	1	1	1	1	1	1	1	1
𝐹6
Mean	7.77𝑒−3	1.49𝑒−2	1.08𝑒−2	2.55𝑒−3	5.54𝑒−2	1.1𝑒−2	3.92𝑒−3	4.66𝑒−3	𝟏.𝟎𝟑𝐞−𝟎𝟒
SD	2.42𝑒−3	5.66𝑒−3	3.24𝑒−3	6.25𝑒−4	2.08𝑒−2	3.94𝑒−3	1.14𝑒−3	1.7𝑒−3	𝟖.𝟗𝟗𝐞−𝟎𝟓
Rank	5	8	6	2	9	7	3	4	1
𝐹9
Mean	30.7	34.90	34.09	29.98	2.39	28.1	2.57𝑒−11	5.8𝑒−15	0
SD	8.68	7.25	8.07	10.92	3.71	6.42	6.64𝑒−11	1.01𝑒−14	0
Rank	7	9	8	6	4	5	3	2	1
𝐹10
Mean	15.5	30.40	21.33	35.91	1.83	32.8	0.167	4.14𝑒−16	0
SD	7.4	9.23	9.46	9.49	2.65	6.49	0.379	1.45𝑒−15	0
Rank	5	7	6	9	4	8	3	2	1
𝐹11
Mean	1.15𝑒−14	1.85𝑒−14	1.4𝑒−14	7.69𝑒−15	2.06𝑒−10	8.52𝑒−15	2.01𝑒−12	1.11𝑒−14	𝟖.𝟖𝟖𝐞−𝟏𝟔
SD	2.27𝑒−15	4.80𝑒−15	3.48𝑒−15	9.33𝑒−16	9.45𝑒−10	1.79𝑒−15	9.22𝑒−13	3.55𝑒−15	0
Rank	5	7	6	2	9	3	8	4	1
𝐹12
Mean	2.37𝑒−2	1.10𝑒−2	1.31𝑒−2	9.04𝑒−4	1.07𝑒−2	1.31𝑒−2	6.45𝑒−13	1.67𝑒−2	0
SD	2.57𝑒−2	1.60𝑒−2	1.35𝑒−2	2.78𝑒−3	1.14𝑒−2	1.73𝑒−2	2.07𝑒−12	2.41𝑒−2	0
Rank	9	5	6	3	4	7	2	8	1
𝐹14
Mean	1.04𝑒−2	2.18𝑒−30	3.46𝑒−3	1.22𝑒−31	7.07𝑒−30	𝟐.𝟎𝟓𝐞−𝟑𝟐	1.59𝑒−21	3.76𝑒−31	1.70𝑒−2
SD	3.16𝑒−2	5.14𝑒−30	1.89𝑒−2	4.85𝑒−32	4.05𝑒−30	𝟖.𝟏𝟐𝐞−𝟑𝟑	1.93𝑒−21	1.2𝑒−30	1.42𝑒−2
Rank	8	4	7	2	5	1	6	3	9
Average rank	5	6.2	5.6	4.4	4.9	4.6	5.3	2.9	2.5
Final rank	6	9	8	3	5	4	7	2	1