On the number of local minima for the multidimensional assignment problem

Grundel, Don A.; Krokhmal, Pavlo A.; Oliveira, Carlos A. S.; Pardalos, Pãnos M.

doi:10.1007/s10878-006-9009-5

Cited by 27 publications

(24 citation statements)

References 22 publications

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“…A solution landscape may be considered rugged if the number of local minima is exponential in the problem's dimensions (Palmer, 1991). Grundel et al (2005aGrundel et al ( , 2007 studied the expected number of local minima in random MAPs. For any p ¼ 2; .…”

Section: Landscape Of Random Mapmentioning

confidence: 99%

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Random assignment problems

Krokhmal

Pardalos

2009

European Journal of Operational Research

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Section: Landscape Of Random Mapmentioning

confidence: 99%

“…In the special case of n ¼ 2, the expected number E½M of local minima in a random MAP can be computed exactly for any continuous distribution of the assignment costs (Grundel et al, 2005a):…”

Section: Landscape Of Random Mapmentioning

confidence: 99%

Random assignment problems

Krokhmal

Pardalos

2009

European Journal of Operational Research

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“…This number of local optima has commonly been taken as a complexity measure of an instance when solving it with a local search algorithm, and many authors have tried to estimate it [1][2][3][4][5][6]. One of the results found when developing these techniques for predicting the number of local optima was that their accuracy is highly affected by the variance of the attraction basin sizes of the local optima.…”

Section: Introductionmentioning

confidence: 99%

Estimating Attraction Basin Sizes

Hernando

Mendiburu

Lozano

2016

Advances in Artificial Intelligence

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Abstract. The performance of local search algorithms is influenced by the properties that the neighborhood imposes on the search space. Among these properties, the number of local optima has been traditionally considered as a complexity measure of the instance, and different methods for its estimation have been developed. The accuracy of these estimators depends on properties such as the relative attraction basin sizes. As calculating the exact attraction basin sizes becomes unaffordable for moderate problem sizes, their estimations are required. The lack of techniques achieving this purpose encourages us to propose two methods that estimate the attraction basin size of a given local optimum. The first method takes uniformly at random solutions from the whole search space, while the second one takes into account the structure defined by the neighborhood. They are tested on different instances of problems in the permutation space, considering the swap and the adjacent swap neighborhoods.

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“…Multidimensional Assignment problems are characterized by a very large number of local minima [9]. Furthermore, the number of feasible solutions grows exponentially with an increase in problem parameters [9,11].…”

Section: Introductionmentioning

confidence: 99%

“…Furthermore, the number of feasible solutions grows exponentially with an increase in problem parameters [9,11]. This inherent complexity of the MAP creates serious difficulties in solving MAP instances of high dimensionality.…”

Section: Introductionmentioning

confidence: 99%

Application of Monkey Search Meta-heuristic to Solving Instances of the Multidimensional Assignment Problem

Kammerdiner

Mucherino

Pardalos

2009

Optimization and Cooperative Control Strategies

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Abstract. This study applies a novel metaheuristic approach called Monkey Search for solving instances of the Multidimensional Assignment Problem (MAP). Monkey Search is a global optimization technique inspired by the behavior of a monkey climbing trees. The combinatorial formulation of the MAP in order to incorporate the matrix representation of feasible solutions is considered. The developed software procedure is tested on randomly generated instances of the MAP, and the results of the numerical experiments are presented in this study.

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On the number of local minima for the multidimensional assignment problem

Cited by 27 publications

References 22 publications

Random assignment problems

Random assignment problems

Estimating Attraction Basin Sizes

Application of Monkey Search Meta-heuristic to Solving Instances of the Multidimensional Assignment Problem

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