Cellular Harmony Search for Optimization Problems

Table 1

CEC’2005 functions.

Abb.	Function name	Search range	𝑥^∗	𝑓(𝑥^∗)
𝑓1	Shifted sphere function	[−100,100]	𝐨=(𝑜1,𝑜2,𝑜𝐷)	−450
𝑓2	Shifted Schwefel's problem 1.2	[−100,100]	𝐨=(𝑜1,𝑜2,…,𝑜𝐷)	−450
𝑓3	Shifted rotated high conditioned elliptic function	[−100,100]	𝐨=(𝑜1,𝑜2,𝑜𝐷)	−450
𝑓4	Shifted Schwefel's problem 1.2 with noise in fitness	[−100,100]	𝐨=(𝑜1,𝑜2,𝑜𝐷)	−450
𝑓5	Schwefel's problem 2.6 with global optimum on bounds	[−100,100]	𝐨=(𝑜1,𝑜2,𝑜𝐷)	−310
𝑓6	Shifted Rosenbrock's function	[−100,100]	𝐨=(𝑜1,𝑜2,𝑜𝐷)	390
𝑓7	Shifted rotated Griewank's function without bounds	[0,600]	𝐨=(𝑜1,𝑜2,𝑜𝐷)	−180
𝑓8	Shifted rotated Ackley's function with global optimum on bounds	[−32,32]	𝐨=(𝑜1,𝑜2,𝑜𝐷)	−140
𝑓9	Shifted rastrigin's function	[−5,5]	𝐨=(𝑜1,𝑜2,𝑜𝐷)	−330
𝑓10	Shifted rotated Rastrigin's function	[−5,5]	𝐨=(𝑜1,𝑜2,𝑜𝐷)	−330
𝑓11	Shifted rotated Weierstrass function	[−0.5,0.5]	𝐨=(𝑜1,𝑜2,𝑜𝐷)	90
𝑓12	Schwefel's problem 2.13	[−𝜋,𝜋]	𝛼	−460
𝑓13	Expanded extended Griewank's plus Rosenbrock's function (F8F2)	[−5,5]	𝐨=(𝑜1,𝑜2,𝑜𝐷)	−130
𝑓14	Shifted rotated expanded Scaffer's F6	[−100,100]	𝐨=(𝑜1,𝑜2,𝑜𝐷)	−300
𝑓15	Hybrid composition function	[−5,5]	𝐨1	120
𝑓16	Rotated hybrid composition function	[−5,5]	𝐨1	120
𝑓17	Rotated hybrid composition function with noise in fitness	[−5,5]	𝐨1	120
𝑓18	Rotated hybrid composition function	[−5,5]	𝐨1	10
𝑓19	Rotated hybrid composition function with a narrow basin for the global optimum	[−5,5]	𝐨1	10
𝑓20	Rotated hybrid composition function with the global optimum on the bounds	[−5,5]	𝐨1	10
𝑓21	Rotated hybrid composition function	[−5,5]	𝐨1	360
𝑓22	Rotated hybrid composition function with high condition number matrix	[−5,5]	𝐨1	360
𝑓23	Noncontinuous rotated hybrid composition function	[−5,5]	𝐨1	360
𝑓24	Rotated hybrid composition function	[−5,5]	𝐨1	260
𝑓25	Rotated hybrid composition function without bounds	[2,5]	𝐨1	260