Ant-Antlion Optimizer with Similarity Information for Multidimensional Knapsack Problem

Abstract

The Multidimensional Knapsack Problem (MKP) is one kind of classical mathematical model that has been extensively studied by researchers. Due to its NP-hard nature, finding an exact solution for MKP in polynomial time is not feasible, and the methods based on evolutionary algorithms have been widely explored and proven successful in solving the MKP. To effectively tackle MKP, we propose a novel method called the ant-antlion optimizer with similarity information. It incorporates the similarity concept throughout the evolution process. A new evaluation measure that combines individual’s fitness and the similarity degree between the elite individual and other solutions is developed. This measure is utilized to enhance its searching capability. In addition, it employs both fitness values and similarity information of the population to implement a self-adaptive mutation strategy to improve its diversity performance. To evaluate our method, a comprehensive experiment consisting of forty-eight testing instances and six well-known algorithms is carried out. The results demonstrate that our proposed approach effectively solves MKP, and the inclusion of similarity information significantly enhances its performance.