A Lagrangian-based heuristic for large-scale set covering problems

Ceria, Sebastián; Nobili, Paolo; Sassano, Antonio

doi:10.1007/bf01581106

Cited by 123 publications

(65 citation statements)

References 10 publications

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“…The set-covering model has been intensely studied for at least 25 years. Ceria et al (1997) give a nice historical survey. The widespread practical success of set-covering models for combinatorial optimization problems follows largely from the empirically typical tightness of the bound given by the associated linear-programming relaxations.…”

Section: Introductionmentioning

confidence: 99%

A Joint Location-Inventory Model

Shen

Coullard²,

Daskin³

2003

Transportation Science

574

403

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W e consider a joint location-inventory problem involving a single supplier and multiple retailers. Associated with each retailer is some variable demand. Due to this variability, some amount of safety stock must be maintained to achieve suitable service levels. However, risk-pooling benefits may be achieved by allowing some retailers to serve as distribution centers (and therefore inventory storage locations) for other retailers. The problem is to determine which retailers should serve as distribution centers and how to allocate the other retailers to the distribution centers. We formulate this problem as a nonlinear integer-programming model. We then restructure this model into a set-covering integer-programming model. The pricing problem that must be solved as part of the column generation algorithm for the set-covering model involves a nonlinear term in the retailerdistribution-center allocation terms. We show that this pricing problem can (theoretically) be solved efficiently, in general, and we show how to solve it practically in two important cases. We present computational results on several instances of sizes ranging from 33 to 150 retailers. In all cases, the lower bound from the linear-programming relaxation to the set-covering model gives the optimal solution.

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Section: Introductionmentioning

confidence: 99%

A Joint Location-Inventory Model

Shen

Coullard²,

Daskin³

2003

Transportation Science

574

403

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“…Among the first approaches that use LR is the heuristic of Beasley [17]. Currently, state-of-the-art algorithms for the set covering problem are, at least in part, based on exploiting information from LR [29,32]. Ways of integrating information gained in LR into a tabu search algorithm is given in [56] and computational results are presented for an example application to the capacitated warehouse location problem.…”

Section: Discussionmentioning

confidence: 99%

Usage of Exact Algorithms to Enhance Stochastic Local Search Algorithms

Dumitrescu

Stützle

2009

Matheuristics

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Exact mathematical programming techniques such as branch-andbound or dynamic programming and stochastic local search techniques have traditionally been seen as being two general but distinct approaches for the effective solution of combinatorial optimization problems, each having particular advantages and disadvantages. In several research efforts true hybrid algorithms, which exploit ideas from both fields, have been proposed. In this chapter we review some of the main ideas of several such combinations and illustrate them with examples from the literature. Our focus here is on algorithms that have the main framework given by the local search and use exact algorithms to solve subproblems.

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“…A heuristic-based approach [5] will be used to identify keywords and concepts expressed by the user and to generate an initial query. Subsequently related terms (synonyms) of the keywords and concepts are also identified for query expansion.…”

Section: Initial Query Generationmentioning

confidence: 99%