Knapsack problems: algorithms and computer implementations
Knapsack problems: algorithms and computer implementations
An efficient preprocessing procedure for the multidimensional 0–1 knapsack problem
Discrete Applied Mathematics - Special volume: viewpoints on optimization
A Genetic Algorithm for the Multidimensional Knapsack Problem
Journal of Heuristics
Core Problems in Knapsack Algorithms
Operations Research
An Exact Algorithm for the Two-Constraint 0--1 Knapsack Problem
Operations Research
The core concept for 0/1 integer programming
CATS '08 Proceedings of the fourteenth symposium on Computing: the Australasian theory - Volume 77
A hybrid approach for the 0-1 multidimensional knapsack problem
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
Kernel search: A general heuristic for the multi-dimensional knapsack problem
Computers and Operations Research
The Multidimensional Knapsack Problem: Structure and Algorithms
INFORMS Journal on Computing
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The multidimensional knapsack problem (MKP) is a well-known, strongly NP-hard problem and one of the most challenging problems in the class of the knapsack problems. In the last few years, it has been a favorite playground for metaheuristics, but very few contributions have appeared on exact methods. In this paper we introduce an exact approach based on the optimal solution of subproblems limited to a subset of variables. Each subproblem is faced through a recursive variable-fixing process that continues until the number of variables decreases below a given threshold (restricted core problem). The solution space of the restricted core problem is split into subspaces, each containing solutions of a given cardinality. Each subspace is then explored with a branch-and-bound algorithm. Pruning conditions are introduced to improve the efficiency of the branch-and-bound routine. In all the tested instances, the proposed method was shown to be, on average, more efficient than the recent branch-and-bound method proposed by Vimont et al. [Vimont, Y., S. Boussier, M. Vasquez. 2008. Reduced costs propagation in an efficient implicit enumeration for the 0-1 multidimensional knapsack problem. J. Combin. Optim.15(2) 165--178] and CPLEX 10. We were able to improve the best-known solutions for some of the largest and most difficult instances of the OR-LIBRARY data set [Chu, P. C., J. E. Beasley. 1998. A genetic algorithm for the multidimensional knapsack problem. J. Heuristics4(1) 63--86].