Metaheuristic methods for solving the Bilevel Uncapacitated Facility Location Problem with Clients' Preferences

Marić, Miroslav; Stanimirović, Zorica; Milenković, Nikola

doi:10.1016/j.endm.2012.10.007

Cited by 20 publications

(8 citation statements)

References 6 publications

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“…Moreover, there is an explosion of the related research on metaheuristics. Marić et al (2012) proposed three metaheuristic methods for solving FLPUP, i.e., Particle Swarm Optimization (PSO), Simulated Annealing (SA), and a combination of Reduced and Basic Variable Neighborhood Search Method (RVNS-VNS). To solve a large-scale bilevel FLPUP, Camacho-Vallejo et al (2014b) developed a population-based evolutionary algorithm (EA).…”

Section: Customersmentioning

confidence: 99%

“…This implies that there could be a mismatch between the preferences of the customers and the desirable customer allocation/assignment of the operator. Therefore, when locating the facilities, the operator needs to consider this mismatch, giving rise to a variant of the FLP that is often referred to as the facility location problem with user preferences (FLPUP) or with order (Camacho-Vallejo et al, 2014b;Hansen et al, 2004;Marić et al, 2012;Vasil'ev et al, 2009;Vasilyev and Klimentova, 2010). When the number of facilities to be set up is fixed, the problem is called the P-median problem with user preferences (PUP) (Casas-Ramírez and Camacho-Vallejo, 2017;Camacho-Vallejo et al, 2014a;Díaz et al, 2017).…”

Section: Introductionmentioning

confidence: 99%

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Decomposition approach for Stackelberg P-median problem with user preferences

Tian,

Lin,

2021

Preprint

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The P-median facility location problem with user preferences (PUP) studies an operator that locates P facilities to serve customers/users in a cost-efficient manner, upon anticipating customer preferences and choices. The problem can be visualized as a leader-follower game in which the operator is the leader that opens facilities, whereas the customer is the follower who observes the operator's location decision at first and then seeks services from the most preferred facility. Such a modeling perspective is of practical importance as we have witnessed its applications to various problems, such as the establishment of power plants in energy markets and the location of healthcare service centers for COVID-19 Vaccination. Despite that a considerable number of solution methodologies have been proposed, many of them are heuristic methods whose solution quality cannot be easily verified. Moreover, due to the hardness of the problems, existing exact approaches have limited performance. Motivated by these observations, we aim to develop an efficient exact algorithm for solving large-scale PUP models. We first propose a branch-and-cut decomposition algorithm and then design accelerated techniques to further enhance the performance. Using a broad testbed, we show that our algorithm outperforms various exact approaches by a large margin, and the advantage can go up to several orders of magnitude in terms of computational time in some datasets. Finally, we conduct sensitivity analysis to draw additional implications and to highlight the importance of considering user preferences when they exist.

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Section: Customersmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Decomposition approach for Stackelberg P-median problem with user preferences

Tian,

Lin,

2021

Preprint

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“…Moreover, due to the nature of the allocation problem, alternative exact methods can be easily adapted for solving it. For instance, in [14,15], an exact method based on the ordered matrix of preferences is considered for solving the bilevel version of UFLBP. However, the construction of efficient exact methods cannot be always obtained for solving the lower level problem; it clearly depends on its structure.…”

Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

Analyzing the Performance of a Hybrid Heuristic for Solving a Bilevel Location Problem under Different Approaches to Tackle the Lower Level

Maldonado-Pinto¹,

Casas-Ramírez

Camacho‐Vallejo³

2016

Mathematical Problems in Engineering

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The problem addressed here is a combinatorial bilevel programming problem called the uncapacitated facility location problem with customer’s preferences. A hybrid algorithm is developed for solving a battery of benchmark instances. The algorithm hybridizes an evolutionary algorithm with path relinking; the latter procedure is added into the crossover phase for exploring the trajectory between both parents. The proposed algorithm outperforms the evolutionary algorithm already existing in the literature. Results show that including a more sophisticated procedure for improving the population through the generations accelerates the convergence of the algorithm. In order to support the latter statement, a reduction of around the half of the computational time is obtained by using the hybrid algorithm. Moreover, due to the nature of bilevel problems, if feasible solutions are desired, then the lower level must be solved for each change in the upper level’s current solution. A study for illustrating the impact in the algorithm’s performance when solving the lower level through three different exact or heuristic approaches is made.

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“…It seems that facility location and customers' allocation requirements can be effectively modeled with bilevel programming when taking into account the customers' demand at the facilities that will serve them. Various papers in which the customers are allocated to the facilities according to a predetermined list of preferences can be found in the literature; see [93][94][95][96]. In all those papers, the facility location problem under customers' preferences is studied.…”

Section: Bilevel Allocation For the Supply Chain Modelsmentioning

confidence: 99%

“…In the bilevel program induced, the leader has to locate some facilities, while the follower will allocate the customers optimizing their preestablished preferences towards the facilities. The first three papers (i.e., [93][94][95]) developed valid two-sided bounds for the objective functions invloved in this problem, and the last two works (i.e., [95,96]) implemented heuristic algorithms to process the bilevel model. Moreover, competitive facility location models have been approached with bilevel programming, too.…”

Section: Bilevel Allocation For the Supply Chain Modelsmentioning

confidence: 99%

Bilevel Programming and Applications

Kalashnikov

Dempe

Pérez-Valdés

et al. 2015

Mathematical Problems in Engineering

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A great amount of new applied problems in the area of energy networks has recently arisen that can be efficiently solved only as mixed-integer bilevel programs. Among them are the natural gas cash-out problem, the deregulated electricity market equilibrium problem, biofuel problems, a problem of designing coupled energy carrier networks, and so forth, if we mention only part of such applications. Bilevel models to describe migration processes are also in the list of the most popular new themes of bilevel programming, as well as allocation, information protection, and cybersecurity problems. This survey provides a comprehensive review of some of the above-mentioned new areas including both theoretical and applied results.

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Metaheuristic methods for solving the Bilevel Uncapacitated Facility Location Problem with Clients' Preferences

Cited by 20 publications

References 6 publications

Decomposition approach for Stackelberg P-median problem with user preferences

Decomposition approach for Stackelberg P-median problem with user preferences

Analyzing the Performance of a Hybrid Heuristic for Solving a Bilevel Location Problem under Different Approaches to Tackle the Lower Level

Bilevel Programming and Applications

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