Fusing ant colony optimization with Lagrangian relaxation for the multiple-choice multidimensional knapsack problem

  • Authors:

  • Zhi-gang Ren;Zu-ren Feng;Ai-min Zhang

  • Affiliations:

  • Autocontrol Research Institute, Xi'an Jiaotong University, Xi'an 710049, PR China and Systems Engineering Institute, State Key Laboratory for Manufacturing Systems Engineering, Xi'an Jiaotong Univ ...;Systems Engineering Institute, State Key Laboratory for Manufacturing Systems Engineering, Xi'an Jiaotong University, Xi'an 710049, PR China;Autocontrol Research Institute, Xi'an Jiaotong University, Xi'an 710049, PR China

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2012

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Abstract

The multiple-choice multidimensional knapsack problem (MMKP) concerns a wide variety of practical problems. It is strongly constrained and NP-hard; thus searching for an efficient heuristic approach for MMKP is of great significance. In this study, we attempt to solve MMKP by fusing ant colony optimization (ACO) with Lagrangian relaxation (LR). The algorithm used here follows the algorithmic scheme of max-min ant system for its outstanding performance in solving many other combinatorial optimization problems. The Lagrangian value of the item in MMKP, obtained from LR, is used as the heuristic factor in ACO since it performs best among the six domain-based heuristic factors we define. Furthermore, a novel infeasibility index is proposed for the development of a new repair operator, which converts possibly infeasible solutions into feasible ones. The proposed algorithm was compared with four existing algorithms by applying them to three groups of instances. Computational results demonstrate that the proposed algorithm is capable of producing competitive solutions.