Construct, Merge, Solve and Adapt Versus Large Neighborhood Search for Solving the Multi-dimensional Knapsack Problem: Which One Works Better When?

Lizárraga, Evelia; Blesa, Miguel A.; Blum, Christian

doi:10.1007/978-3-319-55453-2_5

Cited by 4 publications

(4 citation statements)

References 15 publications

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“…• The increased difficulty of the instances labelled as hard (see table rows [10][11][12][13][14][15][16][17][18], produces more differences between the four approaches.…”

Section: Resultsmentioning

confidence: 99%

“…Obviously, the parameters of CMSA have to be adjusted in order for the size of the reduced sub-instances to be such that the black-box solver can solve them efficiently. CMSA has been applied to several NP-hard combinatorial optimization problems, including minimum common string partition [6,4], the repetition-free longest common subsequence problem [5], and the multi-dimensional knapsack problem [15].…”

Section: Introductionmentioning

confidence: 99%

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Generic CP-Supported CMSA for Binary Integer Linear Programs

Blum

Santos

2018

Hybrid Metaheuristics

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Construct, Merge, Solve & Adapt (CMSA) is a general hybrid metaheuristic for solving combinatorial optimization problems. At each iteration, CMSA (1) constructs feasible solutions to the tackled problem instance in a probabilistic way and (2) solves a reduced problem instance (if possible) to optimality. The construction of feasible solutions is hereby problem-specific, usually involving a fast greedy heuristic. The goal of this paper is to design a problem-agnostic CMSA variant whose exclusive input is an integer linear program (ILP). In order to reduce the complexity of this task, the current study is restricted to binary ILPs. In addition to a basic problem-agnostic CMSA variant, we also present an extended version that makes use of a constraint propagation engine for constructing solutions. The results show that our technique is able to match the upper bounds of the standalone application of CPLEX in the context of rather easy-to-solve instances, while it generally outperforms the standalone application of CPLEX in the context of hard instances. Moreover, the results indicate that the support of the constraint propagation engine is useful in the context of problems for which finding feasible solutions is rather difficult.

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“…• The increased difficulty of the instances labelled as hard (see table rows [10][11][12][13][14][15][16][17][18], produces more differences between the four approaches.…”

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Generic CP-Supported CMSA for Binary Integer Linear Programs

Blum

Santos

2018

Hybrid Metaheuristics

Self Cite

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show abstract

“…The authors of Lizárraga et al. () came up with the hypothesis that the above‐mentioned behavior is due to the fact that CMSA generates, at each iteration, solutions potentially from all over the search space, while LNS is restricted to generate solutions locally around the currently best solution. Rather small solutions cause a disadvantage of LNS, due to the resulting difficulties to perform larger jumps in the search space.…”

Section: Experimental Evaluationmentioning

confidence: 99%

Minimum common string partition: on solving large‐scale problem instances

Blum

2018

Int Trans Operational Res

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Minimum common string partition is an NP‐hard combinatorial optimization problem from the bioinformatics field. The current state‐of‐the‐art algorithm is a hybrid technique known as construct, merge, solve, and adapt (CMSA). This algorithm combines two main algorithmic components: generating solutions in a probabilistic way and solving reduced subinstances obtained from the tackled problem instances, if possible, to optimality. However, the CMSA algorithm was not intended for application to very large problem instances. Therefore, in this paper we present a technique that makes CMSA, and other available algorithms for this problem, applicable to problem instances that are about one order of magnitude larger than the largest problem instances considered so far. Moreover, a reduced variable neighborhood search (RVNS) for solving the tackled problem, based on integer programming, is introduced. The experimental results show that the modified CMSA algorithm is very strong for problem instances based on rather small alphabets. With growing alphabet size, it turns out that RVNS has a growing advantage over CMSA.

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“…First of all, we repeat the study concerning the MDKP. This is because the computational resources and the time that were available for the initial study from [34] were limited. Therefore, the parameter domains chosen for tuning were quite reduced.…”

Section: Introductionmentioning

confidence: 99%