Multiswarm Binary Butterfly Optimization Algorithm for Solving the Multidimensional Knapsack Problem

The multidimensional knapsack problem (MKP) is a well-known NP-hard combinatorial optimization problem which can be employed to model many practical engineering problems. Metaheuristic methods are proven efficient in solving NP-hard problems in a reasonable amount of time where exact methods face limitations. In the past decades, many heuristic methods have been developed to solve the MKP. Butterfly Optimization Algorithm (BOA) is a recently developed metaheuristic method that has attracted the attention of various researchers due to its simplicity and potential as an optimization technique for global optimization problems in various applications. In this paper, the Multiswarm Binary BOA (MBBOA) is introduced to solve the 0–1 MKP. MBBOA employs a parallel search strategy to reach the optimum values in a reduced amount of time. To prove the efficiency of the proposed method, two experiments are conducted on 11 medium-scale and large-scale benchmark problems. Obtained results show that MBBOA is able to solve the MKP in a remarkably less amount of time compared with the sequential binary BOA algorithm.