An improved sexual genetic algorithm for solving 0/1 multidimensional knapsack problem

Abstract

The purpose of this paper is to provide an improved genetic algorithm to solve 0/1 multidimensional knapsack problem (0/1 MKP), by proposing new selection and crossover operators that cooperate to explore the search space.,The authors first present a new sexual selection strategy that significantly improves the one proposed by (Varnamkhasti and Lee, 2012), while working in phenotype space. Then they propose two variants of the two-stage recombination operator of (Aghezzaf and Naimi, 2009), while they adapt the latter in the context of 0/1 MKP. The authors evaluate the efficiency of both proposed operators on a large set of 0/1 MKP benchmark instances. The obtained results are compared against that of conventional selection and crossover operators, in terms of solution quality and computing time.,The paper shows that the proposed selection respects the two major factors of any metaheuristic: exploration and exploitation aspects. Furthermore, the first variant of the two-stage recombination operator pushes the search space towards exploitation, while the second variant increases the genetic diversity. The paper then demonstrates that the improved genetic algorithm combining the two proposed operators is a competitive method for solving the 0/1 MKP.,Although only 0/1 MKP standard instances were tested in the empirical experiments in this paper, the improved genetic algorithm can be used as a powerful tool to solve many real-world applications of 0/1 MKP, as the latter models several industrial and investment issues. Moreover, the proposed selection and crossover operators can be incorporated into other bio-inspired algorithms to improve their performance. Furthermore, the two proposed operators can be adapted to solve other binary combinatorial optimization problems.,This research study provides an effective solution for a well-known non-deterministic polynomial-time (NP)-hard combinatorial optimization problem; that is 0/1 MKP, by tackling it with an improved genetic algorithm. The proposed evolutionary mechanism is based on two new genetic operators. The first proposed operator is a new and deeply different variant of the so-called sexual selection that has been rarely addressed in the literature. The second proposed operator is an adaptation of the two-stage recombination operator in the 0/1 MKP context. This adaptation results in two variants of the two-stage recombination operator that aim to improve the quality of encountered solutions, while taking advantage of the sexual selection criteria to prevent the classical issue of genetic algorithm that is premature convergence.