A Hybrid Mutation Scheme-Based Discrete Differential Evolution Algorithm for Multidimensional Knapsack Problem

This paper presents a discrete differential evolution algorithm with hybrid mutation strategy (HMDE) to solve the multidimensional knapsack problem (MKP). The standard differential evolution is continuous algorithm, while MKP is one of the most difficult discrete problems. The proposed algorithm works in continuous domain and the individuals with real value will be converted to 0-1 binary by modified sigmoid function. Moreover, we adapt hybrid mutation scheme, where DE/rand/1 and DE/best/1 run concurrently. Greedy strategy is adopted to repair infeasible solutions and select better trail individuals. The proposed algorithm is tested on benchmarks with different dimensions and search space sizes of MKP. Experimental results illustrate that the HMDE algorithm proposed in this paper is very effective and can get more optimized results when compared to the existing methods.