Solving multiobjective knapsack problem using scalarizing function based local search

Abstract

Multiobjective optimization has grown to become an active research area since almost all real-world problems have multiple, usually conflicting, objectives. In this paper, we focus on the multiobjective knapsack problem, we solve instances with two, three and four objectives from the literature. We define an iterated local search algorithm in which a Tchebycheff function is used as a selection process to generate a good approximation of the efficient set. The proposed algorithm, Min-Max TLS, designs an efficient neighborhood function based on a permutation process. Min-Max TLS is compared with state-of-the-art approaches such as 2PPLS and MOTGA. Results show that our algorithm can achieve a good balance between exploitation and exploration during the search process.