Lagrangian heuristic-based neighbourhood search for the multiple-choice multi-dimensional knapsack problem

摘要

This article addresses a Lagrangian heuristic-based neighbourhood search for the multiple-choice multidimensional knapsack problem, an NP-hard combinatorial optimization problem. The problem is solved by using a cooperative approach that uses a local search for exploring a series of neighbourhoods induced from the Lagrangian relaxation. Each neighbourhood is submitted to an optimization process using two alternative strategies: reducing and moving strategies. The reducing strategy serves to reduce the current search space whereas the moving strategy explores the new search space. The performance of the proposed approach is evaluated on benchmark instances taken from the literature. Its obtained results are compared with those reached by some recent methods available in the literature. New solutions have been obtained for almost 80% of the instances tested.