Design of Fixed and Ladder Mutation Factor-Based Clonal Selection Algorithm for Solving Unimodal and Multimodal Functions

Table 1

Benchmark test functions of dimension 𝐷. Test functions each of them has a global minimum value of 0.

	Test function	Domain range
𝑓1	∑^𝐷𝑇=1𝑥^21	[−100–100]^D
𝑓2	∑^𝐷𝑇=1|𝑥1|+∏^𝐷𝑡=1|𝑥1|	[−10–10]^D
𝑓3	∑^𝐷𝑇=1(∑^𝑡𝑗𝑥𝑗)^2	[−100–100]^D
𝑓4	10^4𝑥^21+∑^𝐷𝑡=2𝑥^21	[−100–100]^D
𝑓5	∑^𝐷−1𝑡=1[100(𝑥𝑖+1−𝑥^21)^2+(𝑥1−1)^2]	[−30–30]^D
𝑓6	∑^𝐷𝑡=1[𝑥𝑖+0.5]^2	[−100–100]^D
𝑓7	∑^𝐷𝑡=1𝑖𝑥^4𝑡+rand[0.1)	[−1.28–1.28]^D
𝑓8	∑^𝐷𝑡=1[𝑥^21−10cos(2𝜋𝑥1)+10]	[−5.12–5.12]^D
𝑓9	−20exp((−0.2(1/𝐷)∑^𝐷𝑡=1𝑥^21)−exp((1/𝐷)∑^𝐷𝑡=1cos(2𝜋𝑥1)+20+𝑒	[−32–32]^D
𝑓10	Σ^𝐷𝑡=1[−𝑥𝑖sin|𝑥1|+D.418.98288727433]	[−500–500]^D
𝑓11	(1/4000)∑^𝐷𝑡=1𝑥^21−∏^𝐷𝑡=1cos(𝑥𝑖/√𝑡)+1	[−600–600]^D
𝑓12	∑^𝑁𝑡=1𝑥^2𝑡+(∑^𝑁𝑡=10.5𝑡⋅𝑥^21)+(∑^𝑁𝑡=10.5𝑡⋅𝑥^41)	[−10–10]^D