Lower bounds for the axial three-index assignment problem

Kim, Bumjin; Hightower, William L.; Hahn, Peter; Zhu, Yi-Rong; Sun, Lu

doi:10.1016/j.ejor.2009.06.019

Cited by 9 publications

(6 citation statements)

References 15 publications

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“…The sub-problem is the approximate muscle without the layers containing the determined triples. The algorithm that we use here for calculating the lower bound is the Projection method followed by a Hungarian algorithm, which is proposed by Kim et al [22]. All the successors of each candidate are sorted in ascending order according to their lower bounds (line (9)).…”

Section: Beam Search For Ap3mentioning

confidence: 99%

Approximate Muscle Guided Beam Search for Three-Index Assignment Problem

Jiang

Zhang

et al. 2014

Lecture Notes in Computer Science

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Abstract. As a well-known NP-hard problem, the Three-Index Assignment Problem (AP3) has attracted lots of research efforts for developing heuristics. However, existing heuristics either obtain less competitive solutions or consume too much running time. In this paper, a new heuristic named Approximate Muscle guided Beam Search (AMBS) is developed to achieve a good trade-off between solution quality and running time. By combining the approximate muscle with beam search, the solution space size can be significantly decreased, thus the time for searching the solution can be sharply reduced. Extensive experimental results on the benchmark indicate that the new algorithm is able to obtain solutions with competitive quality and it can be employed on instances with large-scale. Work of this paper not only proposes a new efficient heuristic, but also provides a promising method to improve the efficiency of beam search.

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Section: Beam Search For Ap3mentioning

confidence: 99%

Approximate Muscle Guided Beam Search for Three-Index Assignment Problem

Jiang

Zhang

et al. 2014

Lecture Notes in Computer Science

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“…Kim et al (2009) describe new bounding methods for the 3AP. For calculating 3AP lower bounds, they use a projection method followed by a Hungarian algorithm based on a new Lagrangean relaxation.…”

Section: Three‐dimensional Assignment Problemsmentioning

confidence: 99%

Exact solution of emerging quadratic assignment problems

Hahn

Zhu²,

Guignard

et al. 2010

Int Trans Operational Res

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We report on a growing class of assignment problems that are increasingly of interest and very challenging in terms of the difficulty they pose to attempts at exact solution. These problems address economic issues in the location and design of factories, hospitals, depots, transportation hubs and military bases. Others involve improvements in communication network design. In this article we survey the latest and best methods available for solving exactly these difficult problems and suggest a taxonomy that provides a framework for combining existing solution methods and sets of computer tools that can be modified and extended to make inroads in solving this growing class of optimization problems.

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“…His Ph.D. research focused on the development of exact and heuristic solution methods for the Q3AP and the GQAP. Kim successfully developed the new lower bounds for the axial 3-dimensional assignment problem [10] required in the branch-and-bound scheme of solving the Q3AP and designed three heuristic solvers for the Q3AP by adapting stochastic local search techniques [7]. His work on the Q3AP contributed to winning the above mentioned NSF Grant.…”

mentioning

confidence: 97%