Opposition-Based Barebones Particle Swarm for Constrained Nonlinear Optimization Problems

Table 1

Summary of main characteristics of benchmark problems, where 𝐹 means the feasible region, 𝑆 is the whole search region, NE represents nonlinear equality, NI indicates nonlinear inequality, LI means linear inequality, and 𝛼 is the number of active constraints at optimum.

Problems	𝐷	Type	|𝐹|/|𝑆|	LI	NE	NI	𝛼
𝐺01	13	Quadratic	0.011%	9	0	0	6
𝐺02	20	Nonlinear	99.990%	1	0	1	1
𝐺03	10	Polynomial	0.002%	0	1	0	1
𝐺04	5	Quadratic	52.123%	0	0	6	2
𝐺05	4	Cubic	0.000%	2	3	0	3
𝐺06	2	Cubic	0.006%	0	0	2	2
𝐺07	10	Quadratic	0.000%	3	0	5	6
𝐺08	2	Nonlinear	0.856%	0	0	2	0
𝐺09	7	Polynomial	0.512%	0	0	4	2
𝐺10	8	Linear	0.001%	3	0	3	3
𝐺11	2	Quadratic	0.000%	0	1	0	1
𝐺12	3	Quadratic	4.779%	0	0	9^3	0
𝐺13	5	Exponential	0.000%	0	3	0	3