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
Computationally Manageable Combinatorial Auctions
Computationally Manageable Combinatorial Auctions
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
A strategy-oriented operation module for recommender systems in E-commerce
Computers and Operations Research
Journal of Intelligent Manufacturing
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The objective of the multi-dimensional knapsack problem (MKP) is to find a subset of items with maximum value that satisfies a number of knapsack constraints. Solution methods for MKP, both heuristic and exact, have been researched for several decades. This paper introduces several fast and effective heuristics for MKP that are based on solving the LP relaxation of the problem. Improving procedures are proposed to strengthen the results of these heuristics. Additionally, the heuristics are run with appropriate deterministic or randomly generated constraints imposed on the linear relaxation that allow generating a number of good solutions. All algorithms are tested experimentally on a widely used set of benchmark problem instances to show that they compare favourably with the best-performing heuristics available in the literature.