ResearchArticle

An Adaptive Particle Swarm Optimization Algorithm for Unconstrained Optimization

Table 4

Summary of test functions in the CEC 2005 benchmark.

FunctionDomainType and

F1 (Shifted Sphere Function)U, −450
F2 (Shifted Schwefel’s Problem 1.2)U, −450
F3 (Shifted Rotated High-Conditioned Elliptic Function)U, −450
F4 (Shifted Schwefel’s Problem 1.2 with Noise in Fitness)U, −450
F5 (Schwefel’s Problem 2.6 with Global Optimum on Bounds)U, −310
F6 (Shifted Rosenbrock’s Function)M, 390
F7 (Shifted Rotated Griewank’s Function without Bounds)M, −180
F8 (Shifted Rotated Ackley’s Function with Global Optimum on Bounds)M, −140
F9 (Shifted Rastrigin’s Function)M, −330
F10 (Shifted Rotated Rastrigin’s Function)M, −330
F11 (Shifted Rotated Weierstrass Function)M, 90
F12 (Schwefel’s Problem 2.13)M, −460
F13 (Expanded Extended Griewank’s plus Rosenbrock’s Function (F8F2))E, −130
F14 (Expanded Rotated Extended Scaffe’s F6)E, −300
F15 (Hybrid Composition Function 1)HC, 120
F16 (Rotated Hybrid Composition Function 1)HC, 120
F17 (Rotated Hybrid Composition Function 1 with Noise in Fitness)HC, 120
F18 (Rotated Hybrid Composition Function 2)HC, 10
F19 (Rotated Hybrid Composition Function 2 with a Narrow Basin for the Global Optimum)HC, 10
F20 (Rotated Hybrid Composition Function 2 with the Global Optimum on the Bounds)HC, 10
F21 (Rotated Hybrid Composition Function 3)HC, 360
F22 (Rotated Hybrid Composition Function 3 with High Condition Number Matrix)HC, 360
F23 (Noncontinuous Rotated Hybrid Composition Function 3)HC, 360
F24 (Rotated Hybrid Composition Function 4)HC, 260
F25 (Rotated Hybrid Composition Function 4 without Bounds)HC, 260

U means unimodal function, M means multimodal function, E means extended function, and HC means hybrid composition function.