Stability and iterative convergence of water cycle algorithm for computationally expensive and combinatorial Internet shopping optimisation problems

Abstract

ABSTRACTWater cycle algorithm (WCA) is a population-based metaheuristic algorithm, inspired by the water cycle process and movement of rivers and streams towards sea. The WCA shows good performance in both exploration and exploitation phases. Further, the relationship between improvised exploitation and each parameter under asymmetric interval is derived and an iterative convergence of WCA is proved theoretically. In this paper, CEC’15 computationally expensive benchmark problems (i.e., 15 problems) have been considered for efficiency measurement of WCA accompanied with other optimisers. Also, a new discretisation strategy for the WCA has been proposed and applied along with other optimisers for solving combinatorial Internet shopping optimisation problem. By applying complexity analysis, it shows that using the WCA intricacy from dimension 10–30 is increased for almost three times. Proposing a unique discretisation approach along with providing iterative convergence proof can be considered as novelty of this research. By observing the attained numerical results, the WCA could find the minimum average error of CEC’15 in 12 and 8 out of 15 cases for dimensions 10 and 30, respectively. Experimental optimisation results for a wide range computationally expensive problems reveal the effectiveness and advantage of WCA for solving both continuous and discrete optimisation problems.