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

Table 2

Statistical means and standard deviations of the solutions of twelve Benchmark test functions, listed in Table 1 for the CLONALG, FMCSA, and the LMCSA.

Functions	Expressions	Basic CLONALG; Mean ± StD	FMCSA; Mean ± StD	LMCSA; Mean ± StD
Sphere	𝑓1	1.0463𝑒−002±1.023𝑒−004	1.103𝑒−003±1.836𝑒−005	7.804𝑒−005±1.8025𝑒−007
Schwefel’s Problem 2.22	𝑓2	2.3359±1.45602	6945𝑒−001±4.5602𝑒−001	2.359𝑒−001±1.9721−002
Schwefel’s Problem 1.2	𝑓3	2.277±3.49	7.514𝑒−001±1.61	9.1𝑒−002±7.11𝑒−001
Tablet	𝑓4	6.85𝑒+002±13.1𝑒+002	3.17𝑒+001±9.7𝑒+001	1.089±3.58
Generalized Rosenbrock	𝑓5	2.409𝑒+003±1.31𝑒+003	1.17𝑒+002±9.25𝑒+001	8.9±1.14𝑒+001
Step	𝑓6	2.217𝑒−001±2.99𝑒−001	8.709𝑒−002±2.46𝑒−004	2.076𝑒−002±3.40𝑒−003
Quartic Noisy	𝑓7	1.762𝑒−001±1.07𝑒−001	4.031𝑒−002±3.71𝑒−002	3.408𝑒−004±4.39𝑒−003
Generalized Rastrigin	𝑓8	3.89757±6.201	2.4420±3.15	2.390𝑒−001±2.1604
Ackley	𝑓9	2.6739±1.1735	1.5230𝑒−003±2.78𝑒−002	9.7821𝑒−003±3.657𝑒−003
Generalized Schwefel’s Problem 2.26	𝑓10	3.66𝑒+002±9.61𝑒+001	1.8𝑒+001±3.1𝑒+001	9.12𝑒−001±1.21𝑒−001
Griewank	𝑓11	1.178𝑒−004±3.4𝑒−008	6.159𝑒−007±2.3𝑒−010	1.3912𝑒−011±2.4𝑒−012
Zakharov	𝑓12	3.72𝑒+001±6.9975	1.23𝑒−001±2.71	9.141𝑒−04±1.21𝑒−002