A hybrid genetic algorithm with solution archive for the discrete $$(r|p)$$ ( r | p ) -centroid problem

Biesinger, Benjamin; Hu, Bin; Raidl, Günther R.

doi:10.1007/s10732-015-9282-5

Cited by 22 publications

(21 citation statements)

References 23 publications

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“…We consider separate sets of instances for the binary and for the proportional and partially binary case because the binary essential case has a significantly lower complexity and we want to maintain comparability to algorithms from the literature. We used instances generated in [6] for the binary case and instances generated as part of our previous work [5] for the proportional and partially binary case. Both instance sets are based on instances from the discrete problem library 1 and can be found online 2 .…”

Section: Computational Resultsmentioning

confidence: 99%

“…The definitions for the binary essential case is taken from [6] and for the proportional case from [5]. In the following let (X, Y ) be a candidate solution to our competitive facility location problem, where X ⊆ I, |X| = p, is the set of locations chosen by the leader and Y ⊆ I, |Y | = r, is the associated set of follower locations.…”

Section: Problem Definitionmentioning

confidence: 99%

“…The algorithmic framework is also used in [6] for binary customer behavior and in [5] for proportional customer behavior, both only considered essential demand. We use an incomplete solution representation only storing the facilities of the leader indicated by the binary vector x = (x 1 , .…”

Section: Evolutionary Algorithmmentioning

confidence: 99%

“…Then we will show a method for how to avoid exact evaluations during the EA and still do not miss potentially good solution candidates due to the approximation of objective values. We introduced this concept in [6] and called it multi-level solution evaluation scheme (ML-ES). It is applicable to models which have a reasonably good LP relaxation bound; here we apply ML-ES only for binary customer behavior.…”

Section: Evolutionary Algorithmmentioning

confidence: 99%

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Models and algorithms for competitive facility location problems with different customer behavior

Biesinger

Raidl

2015

Ann Math Artif Intell

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Competitive facility location problems arise in the context of two noncooperating companies, a leader and a follower, competing for market share from a given set of customers. We assume that the firms place a given number of facilities on locations taken from a discrete set of possible points. For this bi-level optimization problem we consider six different customer behavior scenarios from the literature: binary, proportional and partially binary, each combined with essential and unessential demand. The decision making for the leader and the follower depends on these scenarios. In this work we present mixed integer linear programming models for the follower problem of each scenario and use them in combination with an evolutionary algorithm to optimize the location selection for the leader. A complete solution archive is used to detect already visited candidate solutions and convert them efficiently into similar, not yet considered ones. We present numerical results of our algorithm and compare them to so far state-of-the-art approaches from the literature. Our method shows good performance in all customer behavior scenarios and is able to outperform previous solution procedures on many occasions.

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Section: Computational Resultsmentioning

confidence: 99%

Section: Problem Definitionmentioning

confidence: 99%

Section: Evolutionary Algorithmmentioning

confidence: 99%

Section: Evolutionary Algorithmmentioning

confidence: 99%

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Models and algorithms for competitive facility location problems with different customer behavior

Biesinger

Raidl

2015

Ann Math Artif Intell

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“…They tried to improve the methods' efficiency at no loss to the quality of the resulting solutions. Biesinger et al (2014a) proposed a hybrid genetic algorithm for the same problem. The heuristic approach was based on a genetic algorithm with tabu search as local improvement procedure and a complete solution archive.…”

Section: Models With Inelastic Demandmentioning

confidence: 99%

Competitive location: a state-of-art review

Ashtiani¹

2016

10.5267/j.ijiec

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This paper provides a review on recent works in the field of competitive facility location models based on the following seven components: 1) Variables, 2) Competition type, 3) Solution space, 4) Customer behavior, 5) Demand type, 6) Number of new facilities and 7) Relocation and redesign possibility. First, the components are introduced and then based on these components; different studies are compared with each other via a proposed taxonomy and finally a review on work of each paper is provided.

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