Matheuristics and Exact Methods for the Discrete (r|p)-Centroid Problem

Алексеева, Е. А.; Kochetov, Yury

doi:10.1007/978-3-642-37838-6_7

Cited by 25 publications

(13 citation statements)

References 32 publications

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“…Alekseeva et al [1][2][3] present several heuristic and exact solution approaches. Laporte and Benati [16] developed a tabu search and Roboredo and Pessoa [20] describe a branch-and-cut algorithm.…”

Section: Related Workmentioning

confidence: 99%

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: Related Workmentioning

confidence: 99%

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

Biesinger

Raidl

2015

Ann Math Artif Intell

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“…Based on this fact, the search region may be reduced by using information about local optima that have already been found. Alekseeva and Kochetov (2013) show that the follower's facilities are often in the immediate vicinity of the leader's facilities. The follower attempts to "drag" customers from the leader.…”

Section: Intensification and Diversificationmentioning

confidence: 99%

“…Recent algorithms have been tested using instances with up to 100 customers, 100 potential facilities and p = r = 20 or 30 from the Discrete Location Problems benchmark library 3 . Exact approaches-including the iterative exact method by Alekseeva et al (2010), the branch-and-cut (RP-B&C) method by Roboredo and Pessoa (2013) and the modified iterative exact method (MEM) by Alekseeva and Kochetov (2013)-guarantee global optimality but are very computationally intensive (e.g., more than 10 hours for p = r = 10; see Roboredo and Pessoa (2013)). The iterative exact method by Alekseeva et al (2010) is based on a single-level binary optimization problem with exponentially many constraints and variables.…”

Section: Literature Reviewmentioning

confidence: 99%

“…The RP-B&C method by Roboredo and Pessoa (2013) is similar but with only a polynomial number of variables, and the exponentially many constraints are lifted into stronger inequalities. MEM (Alekseeva and Kochetov 2013) improves the iterative exact method by using a model with only a polynomial number of variables and by using the strengthening inequalities introduced by Roboredo and Pessoa (2013). Heuristics based on operations (e.g., probabilistic swapping) for the p-median problem have shown high accuracy for a relatively small number of iterations.…”

Section: Literature Reviewmentioning

confidence: 99%

“…For both the CFLPD and RPCP, in order to calculate the leader's objective function, we need to solve the follower's problem, which is NP-hard in the strong sense. Some bilevel methods which solve both the leader's and the follower's problems heuristically produce only what are called semi-feasible solutions (Alekseeva and Kochetov 2013). However, the hybridization of heuristics for the upper level with exact approaches for the lower level allows one to find optimal or near-optimal feasible solutions.…”

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confidence: 99%

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The competitive facility location problem under disruption risks

Zhang

Snyder

Ralphs

et al. 2016

Transportation Research Part E: Logistics and Transportation Re

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Two players sequentially locate a fixed number of facilities, competing to capture market share. Facilities face disruption risks, and each customer patronizes the nearest operational facility, regardless of who operates it. The problem therefore combines competitive location and location with disruptions. This combination has been absent from the literature. We model the problem as a Stackelberg game in which the leader locates facilities first, followed by the follower, and formulate the leader's decision problem as a bilevel optimization problem. A variable neighborhood decomposition search heuristic which includes variable fixing and cut generation is developed. Computational results suggest that high quality solutions can be found quickly. Interesting managerial insights are drawn.

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