Combinatorial optimization and local search: A case study of the discount knapsack problem

Many problems in real life can be transformed into combinatorial optimization problems. As an important heuristic, the local search algorithm has achieved outstanding performance in many classical combinatorial optimization problems. In this study, an efficient local search algorithm named KPLS is developed for a variant of the knapsack problem. Two novel ideas are proposed to help the KPLS algorithm achieve excellent performance. First, three scoring functions are designed to help the algorithm search the neighborhood space of the current solution accurately. Second, the hybrid perturbation strategy achieves a balance between greediness and randomness, which effectively facilitates the algorithm to escape from the local optimum. Eighty classic benchmark instances are adopted to evaluate the KPLS algorithm. The experimental results show that the KPLS algorithm outperforms the state-of-the-art algorithms in both the optimal solution and the average solution for most benchmark instances.