Integrating symmetry, dominance, and bound-and-bound in a multiple knapsack solver

Authors:
Alex S. Fukunaga
Affiliations:
Global Edge Institute, Tokyo Institute of Technology, Tokyo, Japan
Venue:
CPAIOR'08 Proceedings of the 5th international conference on Integration of AI and OR techniques in constraint programming for combinatorial optimization problems
Year:
2008

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Abstract

The multiple knapsack problem (MKP) is a classical combinatorial optimization problem. A recent algorithm for some classes of the MKP is bin-completion, a bin-oriented, branch-and-bound algorithm. In this paper, we propose path-symmetry and path-dominance, which are instances of the symmetry detection by dominance detection approach for pruning symmetric nodes in the MKP branch-and-bound search space. In addition, we integrate the "bound-and-bound" upper bound validation technique used in MKP solvers from the OR literature. We show experimentally that our new MKP solver, which integrates symmetry techniques from constraint programming and bound-and-bound techniques from operations research, significantly outperforms previous solvers on hard instances.