A PTAS for the multiple knapsack problem
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Cooperative Strategies for Solving the Bicriteria Sparse Multiple Knapsack Problem
Journal of Heuristics
Polynominal time approximation schemes for class-constrained packing problem
APPROX '00 Proceedings of the Third International Workshop on Approximation Algorithms for Combinatorial Optimization
General Mixed Integer Programming: Computational Issues for Branch-and-Cut Algorithms
Computational Combinatorial Optimization, Optimal or Provably Near-Optimal Solutions [based on a Spring School]
Cutting planes in integer and mixed integer programming
Discrete Applied Mathematics
Probabilistic Model of Ant Colony Optimization for Multiple Knapsack Problem
Large-Scale Scientific Computing
Branch-and-Cut-and-Price for Capacitated Connected Facility Location
Journal of Mathematical Modelling and Algorithms
Ant colony optimization for multiple knapsack problem and model bias
NAA'04 Proceedings of the Third international conference on Numerical Analysis and its Applications
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In this paper we consider the multiple knapsack problem, which is defined as follows: given a set $N$ of items with weights $f_i$, $i \in N$, a set $M$ of knapsacks with capacities $F_k$, $k \in M$, and a profit function $c_{ik}, i \in N, k \in M$, find an assignment of a subset of the set of items to the set of knapsacks that yields minimum cost. We consider the multiple knapsack problem from a polyhedral point of view. The inequalities that we describe here serve as the theoretical basis for a cutting plane algorithm. We present some of the implementation details of this algorithm, including a discussion and evaluation of different separation and primal heuristics. Our algorithm is applied to practical problem instances arising in the design of main frame computers, in the layout of electronic circuits, and in sugar cane alcohol production.