A branch-and-bound algorithm for hard multiple knapsack problems

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 criteria for pruning nodes in the MKP branch-and-bound search space. In addition, we integrate the “bound-and-bound” upper bound validation technique used in previous MKP solvers. We show experimentally that our new MKP solver, which successfully integrates dominance based pruning, symmetry breaking, and bound-and-bound, significantly outperforms previous solvers on some classes of hard problem instances.

• Type: Journal
• Year: 2011
• Where: ANOR
• Authors: Alex S. Fukunaga
• Keywords: ANOR 2011, MKP Branch-and-bound Search, Mkp Solver, Multiple Knapsack Problem