A self-adaptive harmony search combined with a stochastic local search for the 0-1 multidimensional knapsack problem

This paper presents a new hybrid self-adaptive harmony search combined with a stochastic local search algorithm SAHS-SLS to solve the 0-1 multidimensional knapsack problem MKP. The proposed SAHS-SLS uses SAHS to create harmonies that will be improved with SLS. We propose a dynamic adjustment of the walk probability wp in SLS and a technique to compute the bandwidth bw and the pitch adjusting rate PAR in SAHS. The overall method SAHS-SLS is implemented and evaluated on benchmarks in order to measure its performance in solving the MKP. It is compared to other approaches to show its effectiveness. The numerical results are encouraging and demonstrate the benefit of the proposed approach.