An efficient solution method for Weber problems with barriers based on genetic algorithms

Bischoff, Martin; Klamroth, Kathrin

doi:10.1016/j.ejor.2005.10.061

Cited by 64 publications

(44 citation statements)

References 27 publications

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“…The location of the new facility is (3.306, − 0.068) with an objective value of 88.326, which is similar to the results given in Bischoff and Klamroth (2007), but contradict the results in Katz and Cooper (1981). The execution time is 0.452s.…”

Section: Barrier Instancessupporting

confidence: 70%

“…The execution time is 0.936s. The values are slightly different than the results found in Aneja and Parlar (1994) and Bischoff and Klamroth (2007), both of which report (8.7667, 4.9797) for the location of the new facility and 119.1387 for the objective value. Figure 16.…”

Section: Barrier Instancescontrasting

confidence: 53%

“…IPOPT 3.11 is used to solve the formulation to optimality, yielding the solution (−1.186, 2.060) with an objective value of 48.257 as shown in Figure 10. This solution is better than the one found in Katz and Cooper (1981), and same with the solutions given in Butt and Cavalier (1996), Klamroth (2001), Bischoff and Klamroth (2007) and Klamroth (2004). The execution time is 0.234s.…”

Section: Barrier Instancesmentioning

confidence: 82%

“…The distance metric is Euclidean. This instance is also studied in various papers, including Butt and Cavalier (1996), Klamroth (2001), Bischoff and Klamroth (2007) and Klamroth (2004).…”

Section: Barrier Instancesmentioning

confidence: 99%

“…McGarvey and Cavalier (2003) develop an iterative solution procedure based on a modified 'Big Square Small Square' branch-and-bound method to solve 1-facility median problem with convex polygonal barriers, where the distance metric is Euclidean. Bischoff and Klamroth (2007) reduce the original problem to a finite series of convex subproblems to solve them by using Weiszfeld algorithm to find a heuristic solution in the case of Euclidean distances. The visibility arguments are also taken into consideration to decrease the number of convex subproblems.…”

Section: Restricted Problems With Barriersmentioning

confidence: 99%

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A modelling framework for solving restricted planar location problems using phi-objects

Oğuz

Bektaş

Bennell

et al. 2016

Journal of the Operational Research Society

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This paper presents a general modelling framework for restricted facility location problems with arbitrarily shaped forbidden regions or barriers, where regions are modelled using phi-objects. Phi-objects are an efficient tool in mathematical modelling of 2D and 3D geometric optimization problems, and are widely used in cutting and packing problems and covering problems. The paper shows that the proposed modelling framework can be applied to both median and centre facility location problems, either with barriers or forbidden regions. The resulting models are either mixed-integer linear or non-linear programming formulations, depending on the shape of the restricted region and the considered distance measure. Using the new framework, all instances from the existing literature for this class of problems are solved to optimality. The paper also introduces and optimally solves a realistic multifacility problem instance derived from an archipelago vulnerable to earthquakes. This problem instance is significantly more complex than any other instance described in the literature.

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Section: Barrier Instancessupporting

confidence: 70%

Section: Barrier Instancescontrasting

confidence: 53%

Section: Barrier Instancesmentioning

confidence: 82%

“…The distance metric is Euclidean. This instance is also studied in various papers, including Butt and Cavalier (1996), Klamroth (2001), Bischoff and Klamroth (2007) and Klamroth (2004).…”

Section: Barrier Instancesmentioning

confidence: 99%

Section: Restricted Problems With Barriersmentioning

confidence: 99%

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