Test Problem Generator for the Multidimensional Assignment Problem

Grundel, Don A.; Pardalos, Pãnos M.

doi:10.1007/s10589-005-4558-6

Cited by 20 publications

(14 citation statements)

References 16 publications

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“…The question of selecting proper test bed is one of the most important questions in heuristic experimental evaluation (Rardin and Uzsoy 2001). While many researchers focused on instances with random independent weights (Andrijich and Caccetta 2001;Balas and Saltzman 1991;Krokhmal et al 2007;Pasiliao et al 2005 and some others) and random instances with predefined solutions (Clemons et al 2004;Grundel and Pardalos 2005;Karapetyan et al 2009), several more sophisticated models are of greater practical interest (Bandelt et al 2004;Burkard et al 1996b;Crama and Spieksma 1992;Frieze and Yadegar 1981;Kuroki and Matsui 2007). There is also a number of papers which consider real-world and pseudo real-world instances (Bekker et al 2005;Murphey et al 1998; but the authors of this paper suppose that these instances do not well represent all the instance classes and building a proper benchmark with the real-world instances is a subject for another research.…”

Section: Test Bedmentioning

confidence: 99%

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Local search heuristics for the multidimensional assignment problem

Gutin

Karapetyan

2010

J Heuristics

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The Multidimensional Assignment Problem (MAP) (abbreviated s-AP in the case of s dimensions) is an extension of the well-known assignment problem. The most studied case of MAP is 3-AP, though the problems with larger values of s also have a large number of applications. We consider several known neighborhoods, generalize them and propose some new ones. The heuristics are evaluated both theoretically and experimentally and dominating algorithms are selected. We also demonstrate that a combination of two neighborhoods may yield a heuristics which is superior to both of its components.

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Section: Test Bedmentioning

confidence: 99%

“…GP instances are generated by an algorithm produced by Grundel and Pardalos (2005). The generator is naturally designed for s-AP for arbitrary large values of s and n. However, it is relatively slow and, thus, it was impossible to generate large GP instances.…”

Section: Theorem 1 For Any N Such That N ≥ 3 Andmentioning

confidence: 99%

Local search heuristics for the multidimensional assignment problem

Gutin

Karapetyan

2010

J Heuristics

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“…Although the names of the cost variables are similar for the starting solutions of each problem, the cost coefficients are randomly generated, and therefore these initial costs are independent from problem to problem. Our method for generating problems is discussed in [3]. …”

Section: Two-exchange Local Searchmentioning

confidence: 99%

Applying Simulated Annealing to the Multidimensional Assignment Problem

Clemons

Grundel

Jeffcoat

2004

Theory and Algorithms for Cooperative Systems

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The multidimensional assignment problem (MAP) is a combinatorial optimization problem that is known to be NP-hard, and therefore, heuristic methods are generally used to find good solutions to it. The problem has many recognized applications such as multi-agent path planning, data association, and multi-searcher problems. Simulated annealing has proven to be effective in solving many combinatorial optimization problems, but we find no references in the literature in which simulated annealing is applied to the MAP. In this chapter, we evaluate a simulated annealing algorithm for solving the MAP and report experimental results using several controlling factors in the algorithm. These factors include the cooling schedule and initial temperature, the neighborhood definition, and the method of finding a starting solution. A design of experiments approach is used to find the most effective controlling factors in the algorithm. Algorithm performance measures include time to solution and quality of solution. For a small problem, the algorithm finds the optimal solution in every case tested. For a large problem, the algorithm finds results that average 1.2 units from the optimal solution. The results show that simulated annealing is an effective method for solving the MAP.

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“…The last class of instances, denoted as GP, is generated using the algorithm proposed in Grundel and Pardalos [14] with random costs coefficients selected uniformly from the interval [1,300]. A detailed explanation on the generation of the cost coefficients can be found in [14].…”

Section: Instancesmentioning

confidence: 99%

Fast separation for the three-index assignment problem

2016

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A critical step in a cutting plane algorithm is separation, i.e., establishing whether a given vector x violates an inequality belonging to a specific class. It is customary to express the time complexity of a separation algorithm in the number of variables n. Here, we argue that a separation algorithm may instead process the vector containing the positive components of x, denoted as supp(x), which offers a more compact representation, especially if x is sparse; we also propose to express the time complexity in terms of |supp(x)|. Although several well-known separation algorithms exploit the sparsity of x, we revisit this idea in order to take sparsity explicitly into account in the time-complexity of separation and also design faster algorithms. We apply this approach to two classes of facet-defining inequalities for the three-index assignment problem, and obtain separation algorithms whose time complexity is linear in |supp(x)| instead of n. We indicate that this can be generalized to the axial k-index assignment problem and we show empirically how the separation algorithms This paper is an improved version of an extended abstract that appeared as "Fast separation algorithms for three index assignment

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Test Problem Generator for the Multidimensional Assignment Problem

Cited by 20 publications

References 16 publications

Local search heuristics for the multidimensional assignment problem

Local search heuristics for the multidimensional assignment problem

Applying Simulated Annealing to the Multidimensional Assignment Problem

Fast separation for the three-index assignment problem

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