A hybrid grey wolf optimizer for solving the product knapsack problem

The product knapsack problem (PKP) is a new variation of the knapsack problem which arises in social choice computation. Although some deterministic algorithms have been reported to handle small-scale problems, the solution to the middle and large-scale problems is still lack of progress. For efficiently solving this problem, a new ideal of solving PKP by evolutionary algorithms is proposed in the paper. Firstly, an accelerated binary grey wolf optimizer (ABGWO) is proposed by modifying the transfer function, in which the original sigmoid function is replaced by a step function to reduce the computation and accelerate convergence. Secondly, a two-phase repair and optimize algorithm based on greedy strategy is proposed, which is used to handle the infeasible solutions when using evolutionary algorithm to solve PKP. In order to validate the performance of ABGWO, we use it to solve four kinds of PKP instances and compare with the performance of genetic algorithms, discrete particle swarm optimization, discrete differential evolution, and two existed binary grey wolf optimizers. Comparison results show that ABGWO is superior to others in terms of solution quality, robustness and convergence speed, and it is most suitable for solving PKP.