The 0–1 knapsack problem with multiple choice constraints

Nauss, Robert M.

doi:10.1016/0377-2217(78)90108-x

Cited by 75 publications

(35 citation statements)

References 4 publications

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“…A problem is formulated as a binary integer programming model with a nonlinear objective function (Ait-Kadi & Nourelfath, 2001), which is equivalent to a knapsack problem with multiple-choice constraint, so that it is the NP-hard problem (Garey & Johnson, 1979). Some algorithms for such knapsack problems with multiple-choice constraint have been suggested in the literature (Nauss, 1978;Sinha & Zoltners, 1979;Sung & Lee, 1994).…”

Section: The Reliability Allocation Problem With Component Choices (Rmentioning

confidence: 99%

A Hybrid Parallel Genetic Algorithm for Reliability Optimization

Kim¹,

Jeon²

2012

Real-World Applications of Genetic Algorithms

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Section: The Reliability Allocation Problem With Component Choices (Rmentioning

confidence: 99%

A Hybrid Parallel Genetic Algorithm for Reliability Optimization

Kim¹,

Jeon²

2012

Real-World Applications of Genetic Algorithms

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“…One of the most famous is the Multi-Dimension Knapsack Problem (MDKP) which is one kind of KP where the constraints are multidimensional (Chu and Beasley, 1998;Shih, 1979). The Multiple-Choice Knapsack Problem (MCKP) is another variant of KP where the picking criterion of items is more restrictive (Nauss, 1978;Pisinger, 1995;Sinha and Zoltners, 1979). For the MCKP variant there are one or more disjoint classes of items.…”

Section: Literature Surveymentioning

confidence: 99%

“…This problem may be considered as a generalization of the well known MultipleChoice Knapsack Problem namely MCKP by adding the multidimensionality in the capacity constraint (for more details, see Nauss (1978) and Pisinger (1995)). …”

Section: Introductionmentioning

confidence: 99%

A best first search exact algorithm for the Multiple-choice Multidimensional Knapsack Problem

Sbihi

2006

J Comb Optim

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In this paper, we propose an optimal algorithm for the Multiple-choice Multidimensional Knapsack Problem MMKP. The main principle of the approach is twofold: (i) to generate an initial feasible solution as a starting lower bound, and (ii) at different levels of the search tree to determine an intermediate upper bound obtained by solving an auxiliary problem called MMKP aux and perform the strategy of fixing items during the exploration. The approach which we develop is of best-first search strategy. The method was able to optimally solve the MMKP. The performance of the exact algorithm is evaluated on a set of small and medium instances, some of them are extracted from the literature and others are randomly generated. This algorithm is parallelizable and it is one of its important feature.

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“…For the later variant of the knapsack problem there are one or more disjoint classes of items, for more details, one can refer to Nauss. 15 Finally, the MMKP can be considered as a more generalization of the MDKP and MCKP variants of the binary knapsack problem (0-1 KP). Most algorithms for optimal solutions of knapsack problem variants are also based upon branch-and-bound procedures (see Nauss, 15 Khan 16 and Pisinger 17 ).…”

Section: Literature Surveymentioning

confidence: 99%

Heuristic algorithms for the multiple-choice multidimensional knapsack problem

Hifi

Michrafy

Sbihi

2004

Journal of the Operational Research Society

119

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In this paper, we propose several heuristics for approximately solving the multiple-choice multidimensional knapsack problem (noted MMKP), an NP-Hard combinatorial optimization problem. The first algorithm is a constructive approach used especially for constructing an initial feasible solution for the problem. The second approach is applied in order to improve the quality of the initial solution. Finally, we introduce the main algorithm, which starts by applying the first approach and tries to produce a better solution to the MMKP. The last approach can be viewed as a two-stage procedure: (i) the first stage is applied in order to penalize a chosen feasible solution and, (ii) the second stage is used in order to normalize and to improve the solution given by the firs stage. The performance of the proposed approaches has been evaluated based problem instances extracted from the literature. Encouraging results have been obtained.

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The 0–1 knapsack problem with multiple choice constraints

Cited by 75 publications

References 4 publications

A Hybrid Parallel Genetic Algorithm for Reliability Optimization

A Hybrid Parallel Genetic Algorithm for Reliability Optimization

A best first search exact algorithm for the Multiple-choice Multidimensional Knapsack Problem

Heuristic algorithms for the multiple-choice multidimensional knapsack problem

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