Exploiting Symmetry in Multiple Knapsack Problems
نویسنده
چکیده
The multiple knapsack problem (MKP) is a classical combinatorial optimization problem. A recent algorithm for some classes of the MKP is bincompletion, a bin-oriented, branch-and-bound algorithm. We investigate mechanisms for detecting and breaking symmetry in the bin-completion search space. We propose path-symmetry and pathdominance, two new symmetry relations which are more powerful generalization of previous MKP symmetry breaking techniques. Experiments show that path-symmetry and path-dominance significantly reduce the number of nodes searched by bin-completion. In particular, a variant of pathsymmetry is shown to significantly improve upon the previous state of the art for the MKP with respect to both runtime and nodes searched.
منابع مشابه
A dynamic programming approach for solving nonlinear knapsack problems
Nonlinear Knapsack Problems (NKP) are the alternative formulation for the multiple-choice knapsack problems. A powerful approach for solving NKP is dynamic programming which may obtain the global op-timal solution even in the case of discrete solution space for these problems. Despite the power of this solu-tion approach, it computationally performs very slowly when the solution space of the pr...
متن کاملA branch-and-bound algorithm for hard multiple knapsack problems
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 t...
متن کاملAPPROXIMATE ALGORITHM FOR THE MULTI-DIMENSIONAL KNAPSACK PROBLEM BY USING MULTIPLE CRITERIA DECISION MAKING
In this paper, an interesting and easy method to solve the multi-dimensional knapsack problem is presented. Although it belongs to the combinatorial optimization, but the proposed method belongs to the decision making field in mathematics. In order to, initially efficiency values for every item is calculated then items are ranked by using Multiple Criteria Decision Making (MCDA). Finally, ite...
متن کاملStatistical mechanics of the multi-constraint continuous knapsack problem
Abstract. We apply the replica analysis established by Gardner to the multiconstraint continuous knapsack problem, which is one of the linear programming problems and a most fundamental problem in the field of operations research (OR). For a large problem size, we analyse the space of solution and its volume, and estimate the optimal number of items to go into the knapsack as a function of the ...
متن کاملIntegrating Symmetry, Dominance, and Bound-and-Bound in a Multiple Knapsack Solver
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...
متن کامل