Variable Formulation Search for the Cutwidth Minimization Problem

Pardo, Eduardo G.; Mladenović, Nenad; Pantrigo, Juan José

doi:10.1016/j.asoc.2013.01.016

Cited by 60 publications

(14 citation statements)

References 32 publications

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“…See [18,19] for a recent thorough review. VNS has been successfully applied to a wide variety of optimization problems such as Max-Cut [7], Antibandwidth [24], or Cutwidth [30]. However, as far as we know, the adaptation of VNS to multi-objective optimization problems has been mainly ignored by the research community.…”

Section: Variable Neighborhood Search (Vns) Is a Metaheuristic Proposmentioning

confidence: 98%

“…We have selected this problem since each objective function separately is extremely hard to solve for most of the search procedures since they present a flat landscape (see for instance [8,31], or [30]). It means that there may be many different points with the same objective function value, which makes that most of the moves performed by a search procedure result in a null value.…”

Section: Multi-objective Antibandwidth-cutwidth Problemmentioning

confidence: 99%

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Multi-objective variable neighborhood search: an application to combinatorial optimization problems

et al. 2014

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Solutions to real-life optimization problems usually have to be evaluated considering multiple conflicting objectives. These kind of problems, known as multi-objective optimization problems, have been mainly solved in the past by using evolutionary algorithms. In this paper, we explore the adaptation of the Variable Neighborhood Search (VNS) metaheuristic to solve multi-objective combinatorial optimization problems. In particular, we describe how to design the shake procedure, the improvement method and the acceptance criterion within different VNS schemas (Reduced VNS, Variable Neighborhood Descent and General VNS), when two or more objectives are considered. We validate these proposals over two multi-objective combinatorial optimization problems.

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Section: Variable Neighborhood Search (Vns) Is a Metaheuristic Proposmentioning

confidence: 98%

Section: Multi-objective Antibandwidth-cutwidth Problemmentioning

confidence: 99%

Multi-objective variable neighborhood search: an application to combinatorial optimization problems

et al. 2014

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“…A related approach is variable space search, which has been applied to graph colouring (Hertz et al [23,24]). Other related approaches are variable formulation search which has been applied to the cutwidth minimisation problem [19,45] and variable objective search which has been applied to the maximum independent set problem [13].…”

Section: Formulation Space Searchmentioning

confidence: 99%

Packing unequal rectangles and squares in a fixed size circular container using formulation space search

López

Beasley

2018

Computers & Operations Research

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In this paper we formulate the problem of packing unequal rectangles/squares into a fixed size circular container as a mixed-integer nonlinear program. Here we pack rectangles so as to maximise some objective (e.g. maximise the number of rectangles packed or maximise the total area of the rectangles packed). We show how we can eliminate a nonlinear maximisation term that arises in one of the constraints in our formulation. We indicate the amendments that can be made to the formulation for the special case where we are maximising the number of squares packed. A formulation space search heuristic is presented and computational results given for publicly available test problems involving up to 30 rectangles/squares. Our heuristic deals with the case where the rectangles are of fixed orientation (so cannot be rotated) and with the case where the rectangles can be rotated through ninety degrees.

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“…Finally, the third one explores in parallel the set of predefined neighborhoods. The authors illustrate the performance of these strategies by considering a previous state‐of‐the‐art algorithm designated for the cutwidth minimization problem (Pardo et al., ).…”

Section: Parallel Variable Neighborhood Searchmentioning

confidence: 99%

A parallel variable neighborhood search approach for the obnoxious p‐median problem

Herrán

Colmenar

Martı́

et al. 2018

Int Trans Operational Res

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The obnoxious p‐median problem consists of selecting p locations, considered facilities, in a way that the sum of the distances from each nonfacility location, called customers, to its nearest facility is maximized. This is an scriptNP‐hard problem that can be formulated as an integer linear program. In this paper, we propose the application of a variable neighborhood search (VNS) method to effectively tackle this problem. First, we develop new and fast local search procedures to be integrated into the basic VNS methodology. Then, some parameters of the algorithm are tuned in order to improve its performance. The best VNS variant is parallelized and compared with the best previous methods, namely branch and cut, tabu search, and GRASP over a wide set of instances. Experimental results show that the proposed VNS outperforms previous methods in the state of the art. This fact is finally confirmed by conducting nonparametric statistical tests.

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Variable Formulation Search for the Cutwidth Minimization Problem

Cited by 60 publications

References 32 publications

Multi-objective variable neighborhood search: an application to combinatorial optimization problems

Multi-objective variable neighborhood search: an application to combinatorial optimization problems

Packing unequal rectangles and squares in a fixed size circular container using formulation space search

A parallel variable neighborhood search approach for the obnoxious p‐median problem

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