Modified Artificial Bee Colony Algorithm for Multiple-Choice Multidimensional Knapsack Problem

Abstract

The multiple-choice multidimensional knapsack problem (MMKP) is a well-known NP-hard problem that has many real-time applications. However, owing to its complexity, finding computationally efficient solutions for the MMKP remains a challenging task. In this study, we propose a Modified Artificial Bee Colony algorithm (MABC) to solve the MMKP. The MABC employs surrogate relaxation, Hamming distance, and a tabu list to enhance the local search process and exploit neighborhood information. We evaluated the performance of the MABC on standard benchmark instances and compared it with several state-of-the-art algorithms, including RLS, ALMMKP, ACO, PEGF-PERC, TIKS-TIKS2 and D-QPSO. The experimental results reveal that MABC produces highly competitive solutions in terms of the best solutions found, achieving approximately 2% of the optimal solutions with trivial (milliseconds) CPU time. The Kruskal-Wallis test revealed that there was no statistically significant difference in the objective function values between the MABC algorithm and other state-of-the-art algorithms (H = 0.31506, p = 0.98882). However, for CPU efficiency, the test showed a statistically significant difference (H = 84.90850, p = 0), indicating that the MABC algorithm exhibited significantly better CPU efficiency (with shorter execution times) than the other algorithms did. Along with these findings, the ease of implementation of the algorithm and the small number of control parameters make our approach highly adaptive for large-scale real-time systems.

Keywords

• Artificial bee colony algorithm
• multiple-choice multidimensional knapsack problem
• hamming distance
• surrogate relaxation