Lagrangian relaxation guided problem space search heuristics for generalized assignment problems

Jeet, Vishv; Kutanoğlu, Erhan

doi:10.1016/j.ejor.2006.09.060

Cited by 39 publications

(16 citation statements)

References 42 publications

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“…The authors of these works also provide example implementations for combinatorial problems such as the single source capacitated facility location problem. A nicely working example of a Lagrangian metaheuristic applied to the generalized assignment problem can be found in [127].…”

Section: Example 1: Hybrid Metaheuristics Based On Lagrangian Relaxationmentioning

confidence: 99%

Hybrid metaheuristics in combinatorial optimization: A survey

Blum

Puchinger²,

Raidl³

et al. 2011

Applied Soft Computing

651

294

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Research in metaheuristics for combinatorial optimization problems has lately experienced a noteworthy shift towards the hybridization of metaheuristics with other techniques for optimization. At the same time, the focus of research has changed from being rather algorithm-oriented to being more problem-oriented.\ud Nowadays the focus is on solving the problem at hand in the best way possible, rather than\ud promoting a certain metaheuristic. This has led to an enormously fruitful cross-fertilization of different areas of optimization. This cross-fertilization is documented by a multitude of powerful hybrid algorithms that were obtained by combining components from several different optimization techniques. Hereby, hybridization is not restricted to the combination of different metaheuristics but includes, for example, the combination of exact algorithms and metaheuristics. In this work we provide a survey of some of the most important lines of hybridization. The literature review is accompanied by the presentation of illustrative examples.Peer ReviewedPostprint (published version

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Section: Example 1: Hybrid Metaheuristics Based On Lagrangian Relaxationmentioning

confidence: 99%

Hybrid metaheuristics in combinatorial optimization: A survey

Blum

Puchinger²,

Raidl³

et al. 2011

Applied Soft Computing

651

294

View full text Add to dashboard Cite

show abstract

“…Many solutions have been published for the GAP (see, e.g., for surveys). The majority of these algorithmic solutions can be categorized as either search techniques or relaxation techniques.…”

Section: Problem Formulation and Solutionsmentioning

confidence: 99%

“…Search techniques, such as branch‐and‐bound, are algorithms where solutions are profiled through some cost function and elimination and thus reduce the search space. Relaxation algorithms (such as linear programming and Lagrangian) usually find some approximation to a solution and then a feasible solution is found using some simple heuristic (e.g., ).…”

Section: Problem Formulation and Solutionsmentioning

confidence: 99%

Preference‐based zone selection in 802.16 networks

Kitroser

Ben-Shimol

2016

Wireless Communications

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We examine a new problem called the Zone Selection Problem (ZSP) in wireless Orthogonal Frequency‐Division Multiple Access (OFDMA)‐based systems. We consider the case where the mobile station (MS) informs the base station of its preferences regarding possible working modes supported by the system. In Worldwide Interoperability for Microwave Access (WiMAX) systems, which are used as a practical reference system for constraints and specific modes of operations, each working mode must be assigned at a different time interval called a Zone. Such zone may, in the downlink subframe, define a specific transmission scheme, which can be either single‐input single‐output or one of the multiple‐in multiple‐out (MIMO) modes supported by the system. We define ZSP as a problem where the base station assigns MSs to zones in a way that optimizes the system utilization (in terms of resource usage) while trying to satisfy the preferences of the users as much as possible. This makes ZSP a bi‐objective optimization problem. We derive assignment costs from physical channel models that integrate specific MIMO schemes and channel conditions. We provide an exact solution to ZSP by using a combinatorial optimization abstraction. We propose a simplified and practical mode ranking approach that enables the MS to define its preferences regarding operation in the optional MIMO modes in the system. We prove that ZSP is NP‐hard and describe two heuristic solutions: a greedy approach and a local search approach. Simulation results show the performance of the exact algorithms on a realistic WiMAX system assumptions and present the trade‐off between the user preferences and system preferences. Copyright © 2016 John Wiley & Sons, Ltd.

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“…In Section 3, we introduce a greedy randomized Lagrangian repair heuristic paired with a standard subgradient optimization algorithm. Lagrangian relaxation is a classical approach and it has been paired with a variety of heuristic mechanism to obtain high-quality feasible solutions for many problems, e.g., see Galvȃo andReVelle (1996), Haddadi (1997), Tragantalerngsak et al (1997), Lim and Kim (1998), Klose (2000), Jeet and Kutanoglu (2007), Larsson et al (2008), andHolmberg et al (2008). The integration of greedy randomized repair mechanisms and Lagrangian relaxations is not as widely documented, although recently Pessôa et al (2008) propose the use of a greedy randomized adaptive search procedure (GRASP) and path-relinking to achieve feasibility from solutions to a Lagrangian relaxation of the k-set covering problem.…”

Section: Introductionmentioning

confidence: 99%