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
Generating Cuts from Surrogate Constraint Analysis for Zero-Oneand Multiple Choice Programming
Computational Optimization and Applications
Heuristic Solutions for the Multiple-Choice Multi-dimension Knapsack Problem
ICCS '01 Proceedings of the International Conference on Computational Science-Part II
Dynamic Programming and Strong Bounds for the 0-1 Knapsack Problem
Management Science
Core Problems in Knapsack Algorithms
Operations Research
On finding the exact solution of a zero-one knapsack problem
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
Quality adaptation in a multisession multimedia system: model, algorithms, and architecture
Quality adaptation in a multisession multimedia system: model, algorithms, and architecture
Probabilistic analysis of knapsack core algorithms
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
ENC '04 Proceedings of the Fifth Mexican International Conference in Computer Science
A Reactive Local Search-Based Algorithm for the Multiple-Choice Multi-Dimensional Knapsack Problem
Computational Optimization and Applications
Solving the multidimensional multiple-choice knapsack problem by constructing convex hulls
Computers and Operations Research
Enumeration Methods for Repeatedly Solving Multidimensional Knapsack Sub-Problems
IEICE - Transactions on Information and Systems
Hard multidimensional multiple choice knapsack problems, an empirical study
Computers and Operations Research
An ant colony optimization approach to the multiple-choice multidimensional knapsack problem
Proceedings of the 12th annual conference on Genetic and evolutionary computation
A New Heuristic for Solving the Multichoice Multidimensional Knapsack Problem
IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans
Approximation schemes for deal splitting and covering integer programs with multiplicity constraints
Theoretical Computer Science
Computers and Operations Research
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The multidimensional multiple-choice knapsack problem (MMKP) is an extension of the 0-1 knapsack problem. The core concept has been used to design efficient algorithms for the knapsack problem but the core has not been developed for the MMKP so far. In this paper, we develop an approximate core for the MMKP and utilize it to solve the problem exactly. Computational results show that the algorithm can solve large uncorrelated instances (up to 100 classes and 100 items in each class) and correlated instances with small number of constraints (up to 5) efficiently. In particular, it solves recently published hard instances for the MMKP in less than a second. The algorithm consumes negligible memory, and compared with the best previous exact algorithm for the MMKP performs significantly faster.