A hybrid heuristic for the 0-1 Knapsack Sharing Problem

A new hybrid method based on ILPH and QPSO is proposed and validated on the KSP.The proposed approach can be easily adapted to other variants of knapsack problems.New valid constraints are used to speed up the reduced problems solved inside ILPH.A local search is incorporated in ILPH as an intensification process.QPSO starts with the best solutions provided by ILPH where infeasibility is allowed. The Knapsack Sharing Problem (KSP) is a variant of the well-known NP-hard knapsack problem that has received a lot of attention from the researches as it appears into several real-world problems such as allocating resources, reliability engineering, cloud computing, etc. In this paper, we propose a hybrid approach that combines an Iterative Linear Programming-based Heuristic (ILPH) and an improved Quantum Particle Swarm Optimization (QPSO) to solve the KSP. The ILPH is an algorithm conceived to solve 0-1 mixed integer programming. It solves a series of reduced problems generated by exploiting information obtained through a series of linear programming relaxations and tries to improve lower and upper bounds on the optimal value. We proposed several enhancements to strengthen the performance of the ILPH: (i) New valid constraints are introduced to speed up the resolution of reduced problems; (ii) A local search is incorporated as an intensification process to reduce the gap between the upper and the lower bounds. Finally, QPSO is launched by using the k best solutions encountered in the ILPH process as an initial population. The proposed QPSO explores feasible and infeasible solutions. Experimental results obtained on a set of problem instances of the literature and other new harder ones clearly demonstrate the good performance of the proposed hybrid approach in solving the KSP.