Island-based Cuckoo Search with Elite Opposition-based Learning and Multiple Mutation Methods for Solving Discrete and Continuous Optimization Problems

Abstract

The Island Cuckoo Search ( i CSPM) algorithm is a new variation of Cuckoo Search (CS) that uses the island model and the Highly Disruptive Polynomial (HDP) mutation for solving a broad range of optimization problems. This article introduces an improved i CSPM algorithm called i CSPM with elite opposition-based learning and multiple mutation methods ( i CSPM2). i CSPM2 has three main characteristics. Firstly, it separates candidate solutions into a number of islands (sub-populations) and then divides the islands equally among four improved versions of CS: CS via Le'vy fights (CS1) [1], CS with HDPM mutation (CS10) [2], CS with Jaya mutation (CSJ) and CS with pitch adjustment mutation (CS11) [2]. Secondly, it uses Elite Opposition-based Learning (EOBL) to improve its convergence rate and exploration ability. Finally, it uses the Smallest Position Value (SPV) with scheduling problems to convert continuous candidate solutions into discrete ones. A set of 15 popular benchmark functions was used to compare the performance of iCSPM2 to the performance of the original i CSPM algorithm based on different experimental scenarios. Results indicate that i CSPM2 exhibits improved performance over i CSPM. However, the sensitivity analysis of i CSPM and i CSPM2 to their parameters indicates that their convergence behavior is sensitive to the island model parameters. Further, the single-objective IEEE CEC 2014 functions were used to evaluate and compare the performance of iCSPM2 to four well-known swarm optimization algorithms: DGWO [3], L-SHADE [4], MHDA [5] and FWA-DM [6]. The overall experimental and statistical results suggest that i CSPM2 has better performance than the four well-known swarm optimization algorithms. i CSPM2's performance was also compared to two powerful discrete optimization algorithms (GAIbH [7] and MASC [8]) using a set of Taillard's benchmark instances for the permutation flow shop scheduling problem. The results indicate that i CSPM2 performs better than GAIbH and MASC. The source code of i CSPM2 is publicly available at https://github.com/bilalh2021/iCSPM2