Particle Swarm Algorithms to Solve Engineering Problems: A Comparison of Performance

Table 3

Results for E01: welded beam design.

Algorithm	FEs	Runs	Best	Mean	St. Dev.	Worst
(𝜇+𝜆)-ES1	30000	30	1.724852	1.777692	8.8𝐸−2	2.074562
𝜖PSO2	5000	NA	1.7258	1.8073	1.2𝐸−1	2.1427
HPSACO3	NA	30	1.724849	1.727564	8.3𝐸−3	1.759522
NM-PSO4	80000	30	1.724717	1.726373	3.5𝐸−3	1.733393
HEA-ACT5	200000	30	2.380957	2.380971	1.3𝐸−5	2.381021
PSOLVER6	297	30	1.724717	1.724717	1.6𝐸−11	1.724717
CPSOSA7	2450	30	1.724852	1.724853	1.7𝐸−5	1.724861
GABC8	30000	30	1.724	1.763	3.3𝐸−2	NA
PSO9	30000	30	1.724897	1.730813	1.0281𝐸−2	1.767000
GDA10	20000	20	1.724852	1.724852	0	1.724852
SiCPSO	30000	50	1.724852	1.9590	2.557𝐸−1	2.6175
MCEPSO	30000	50	1.724852	1.7333	1.78𝐸−2	1.8043

NA stands for not available.
1[8], 2[9], 3[10], 4[11], 5[12], 6[13], 7[14], 8[15], 9[16], and 10[17].