A path relinking approach with ejection chains for the generalized assignment problem

Yagiura, Mutsunori; Ibaraki, Toshihide; Glover, Fred

doi:10.1016/j.ejor.2004.08.015

Cited by 104 publications

(65 citation statements)

References 23 publications

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“…The results are presented in Table 4. Column Best known reports on the best known upper bounds collected from [1,21,25], column Opt reports on the optimal values (in boldface the values which are better than the best known). Columns Cut&Branch reports on the results yielded by our algorithm, where ♯N odes is the size of the search tree, T ime is the computation time in seconds.…”

Section: Computational Results For the Easy Instancesmentioning

confidence: 99%

“…No optimal solutions are known for the larger instances. Best known upper bounds yielded by heuristics are reported in [1,25].…”

Section: Computational Experiencementioning

confidence: 99%

“…Because of its computational difficulty, GAP is a challenging integer programming problem, which stimulated a wide interest among researchers [1,9,11,14,15,18,19,16,20,21,23,24,25,26].…”

Section: Introductionmentioning

confidence: 99%

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A computational study of exact knapsack separation for the generalized assignment problem

2008

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The Generalized Assignment Problem is a well-known NP-hard combinatorial optimization problem which consists of minimizing the assignment costs of a set of jobs to a set of machines satisfying capacity constraints. Most of the existing algorithms are of a Branch-and-Price type, with lower bounds computed through Dantzig-Wolfe reformulation and column generation.In this paper we propose a cutting plane algorithm working in the space of the variables of the basic formulation, whose core is an exact separation procedure for the knapsack polytopes induced by the capacity constraints. We show that an efficient implementation of the exact separation procedure allows to deal with large-scale instances and to solve to optimality several previously unsolved instances.

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Section: Computational Results For the Easy Instancesmentioning

confidence: 99%

“…No optimal solutions are known for the larger instances. Best known upper bounds yielded by heuristics are reported in [1,25].…”

Section: Computational Experiencementioning

confidence: 99%

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A computational study of exact knapsack separation for the generalized assignment problem

2008

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“…Yagiura et al [17], the eGAP has not been studied much so far, although it is of great practica! relevance.…”

Section: Introductionmentioning

confidence: 99%

Reducing the elastic generalized assignment problem to the standard generalized assignment problem

Büther

2010

Journal of the Operational Research Society

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“…This technique is developed by Glover et.al. [19] and proposed for the generalized assignment problem [38], and for the quadratic assignment problem [41]. The path relinking technique is fundamentally different from the rather unstructured crossover mechanism often used in evolutionary algorithms [19].…”

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confidence: 99%

dynamic resource allocation

SpringerReference

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Computer systems are subject to continuously increasing performance demands. However, energy consumption has become a critical issue, both for high-end large-scale parallel systems [12], as well as for portable devices [34]. In other words, more work needs to be done in less time, preferably with the same or smaller energy budget. Future performance and efficiency goals of computer systems can only be reached with large-scale, heterogeneous architectures [6]. Due to their distributed nature, control software is required to coordinate the parallel execution of applications on such platforms. Abstraction, arbitration and multi-objective optimization are only a subset of the tasks this software has to fulfill [6,31]. The essential problem in all this is the allocation of platform resources to satisfy the needs of an application.This work considers the dynamic resource allocation problem, also known as the run-time mapping problem. This problem consists of task assignment to (processing) elements and communication routing through the interconnect between the elements. In mathematical terms, the combined problem is defined as the multi-resource quadratic assignment and routing problem (MRQARP). An integer linear programming formulation is provided, as well as complexity proofs on the N P-hardness of the problem.This work builds upon state-of-the-art work of Yagiura et al. [39,40,42] on metaheuristics for various generalizations of the generalized assignment problem. Specifically, we focus on the guided local search (GLS) approach for the multi-resource quadratic assignment problem (MRQAP). The quadratic assignment problem defines a cost relation between tasks and between elements. We generalize the multi-resource quadratic assignment problem with the addition of a capacitated interconnect and a communication topology between tasks. Numerical experiments show that the performance of the approach is comparable with commercial solvers. The footprint, the time versus quality trade-off and available metadata make guided local search a suitable candidate for run-time mapping.

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A path relinking approach with ejection chains for the generalized assignment problem

Cited by 104 publications

References 23 publications

A computational study of exact knapsack separation for the generalized assignment problem

A computational study of exact knapsack separation for the generalized assignment problem

Reducing the elastic generalized assignment problem to the standard generalized assignment problem

dynamic resource allocation

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