Particle Swarm Optimization with Double Learning Patterns

Table 1

Benchmark functions used in this paper.

Number	Description and expression	Search space
Group 1: conventional problems
	Sphere	[−100, 100	10^−6	0
	Schwefel’s function 1.2	[−100, 100	10^−6	0
	Noise quadric	[−1.28, 1.28	10^−2	0
	Rosenbrock	[−10, 10	10^−2	0
	Ackley	[−32.768, 32.768	10^−6	0
	Griewank	[−600, 600	10^−6	0
	Rastrigin	[−5.12, 5.12	10^−6	0
	Noncontinuous Rastrigin	[−5.12, 5.12	10^−6	0
	Expanded Schaffer	[−100, 100	10^−6	0
Group 2: rotated problems
	Rotated Rosenbrock , , is an orthogonal matrix	[−10, 10	10	0
	Rotated Ackley ,	[−32.768, 32.768	10	0
	Rotated Griewank ,	[−600, 600	10	0
	Rotated Rastrigin ,	[−5.12, 5.12	10	0
	Rotated noncontinuous Rastrigin ,	[−5.12, 5.12	10	0
Group 3: shifted problems
	Shifted Sphere , ,	[−100, 100	10^−6	−450
	Shifted Rosenbrock , ,	[−10, 10	10^−6	390
	Shifted Rastrigin , ,	[−5.12, 5.12	10^−6	−330
	Shifted non-Rastrigin , ,	[−5.12, 5.12	10^−6	−330
	Shifted rotated Ackley’s function with global optimum on bounds	[−32.76, 32.76	10^−6	−140
	Shifted rotated Rastrigin’s function	[−5.12, 5.12	10^−6	−330