Improved Particle Swarm Optimization with a Collective Local Unimodal Search for Continuous Optimization Problems

Table 2

Benchmark problems.

Number	Problem	Dimensions	Optimal value	Success threshold
1	Ackley	10, 20, 30	0	10^−5
2	Booth	2	0	10^−5
3	Easom	2	−1	−1
4	Griewank	10, 20, 30	0	10^−5
5	Dixon-Price	10, 20, 30	0	10^−5
6	Levy	10, 20, 30	0	10^−5
7	Michalewicz	5	−4.687	−4.687
8	Noisy Quartic	10, 20, 30	0	10^−5
9	Noncontinous Rastrigin	10, 20, 30	0	20
10	Rastrigin	10, 20, 30	0	20
11	Rosenbrock	10, 20, 30	0	20
12	Rotated Ellipsoid	10, 20, 30	0	10^−5
13	Salomon	5	0	10^−5
14	Schaffer's f6	2	0	10^−5
15	Schwefel	10, 20, 30
16	Schwefel P2.22	10, 20, 30	0	10^−5
17	Shubert	2	−186.7309	−186.7309
18	Sphere	10, 20, 30	0	10^−5
19	Step	10, 20, 30	0	10^−5
20	Sum Squares	10, 20, 30	0	10^−5
21	Trid	6	−50	−50