An annotated bibliography of GRASP – Part I: Algorithms

Festa, Paola; Resende, Maurício G. C.

doi:10.1111/j.1475-3995.2009.00663.x

Cited by 153 publications

(46 citation statements)

References 37 publications

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“…Applications to other problems (see e.g. Festa and Resende 2009a;Resende and Ribeiro 2010) have shown that Reactive GRASP outperforms the basic algorithm. These results motivated the study of the behavior of GRASP for different strategies for the variation of the value of the RCL parameter α.…”

Section: A Template For Graspmentioning

confidence: 97%

GRASP: Greedy Randomized Adaptive Search Procedures

Resende

Ribeiro

2013

Search Methodologies

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others. The method described in this chapter represents another example of such a technique. Metaheuristics are based on distinct paradigms and offer different mechanisms to escape from locally optimal solutions. They are among the most effective solution strategies for solving combinatorial optimization problems in practice and have been applied to a wide array of academic and real-world problems. The customization (or instantiation) of a metaheuristic to a given problem yields a heuristic for that problem.In this chapter, we consider the combinatorial optimization problem of minimizing f (S) over all solutions S ∈ X, which is defined by a finite set E = {e 1 ,..., e n } (called the ground set), by a set of feasible solutions X ⊆ 2 E and by an objective function f : 2 E → R. The ground set E, the objective function f , and the constraints defining the set of feasible solutions X are specific for each problem. We seek an optimal solution S * ∈ X such that f (S * ) ≤ f (S), ∀S ∈ X.GRASP, which stands for greedy randomized adaptive search procedures Resende 1989, 1995), is a multistart, or iterative, metaheuristic in which

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Section: A Template For Graspmentioning

confidence: 97%

GRASP: Greedy Randomized Adaptive Search Procedures

Resende

Ribeiro

2013

Search Methodologies

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“…Some examples are the studies of Berger and Barkaoui [4], Prins [36], Mester and Braysy [33] or Nagata [35]. Another important approach to the VRP is given by the Greedy Randomized Adaptive Search Procedure or GRASP [13,15,38]. A GRASP algorithm is a multi-start or iterative process in which each GRASP iteration consists of two phases: a construction phase-in which a feasible solution is produced-and a local search phase-in which a local optimum in the neighborhood of the constructed solution is sought.…”

Section: Previous Work On the Capacitated Vehicle Routing Problemmentioning

confidence: 99%

“…14 Add the modified routes to LastModi f ied. 15 If the list is empty, set k ← k + 1; otherwise set k ← 1.…”

Section: Pseudo-code For the Variable Neighborhood Descent Proceduresmentioning

confidence: 99%

Combining probabilistic algorithms, Constraint Programming and Lagrangian Relaxation to solve the Vehicle Routing Problem

Guimarans

Herrero

Riera

et al. 2011

Ann Math Artif Intell

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This paper presents an original hybrid approach to solve the Capacitated Vehicle Routing Problem (CVRP). The approach combines a Probabilistic Algorithm with Constraint Programming (CP) and Lagrangian Relaxation (LR). After introducing the CVRP and reviewing the existing literature on the topic, the paper proposes an approach based on a probabilistic Variable Neighbourhood Search (VNS) algorithm. Given a CVRP instance, this algorithm uses a randomized version of the classical Clarke and Wright Savings constructive heuristic to generate a starting solution. This starting solution is then improved through a local search process which combines: (a) LR to optimise each individual route, and (b) CP to quickly verify the feasibility of new proposed solutions. The efficiency of our approach is analysed after testing some well-known CVRP benchmarks. Benefits of our hybrid approach over already existing approaches are also discussed. In particular, the potential flexibility of our methodology is highlighted.

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“…This task has generated considerable interest over the past few decades, particularly related to the analysis of high-dimensional gene expression data in information retrieval, knowledge discovery, and data mining [1]. Since the problem has been shown to be NP-complete, we have recently designed and implemented a GRASP metaheuristic [2,3,4]. The greedy criterion used in the construction phase uses the Euclidean distance to build spanning trees of the graph representing the input data matrix.…”

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confidence: 99%

A new GRASP metaheuristic for biclustering of gene expression data

Ferone

Facchiano

Festa

2016

Preprint

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The term biclustering stands for simultaneous clustering of both genes and conditions. This task has generated considerable interest over the past few decades, particularly related to the analysis of high-dimensional gene expression data in information retrieval, knowledge discovery, and data mining [1]. Since the problem has been shown to be NP-complete, we have recently designed and implemented a GRASP metaheuristic [2,3,4]. The greedy criterion used in the construction phase uses the Euclidean distance to build spanning trees of the graph representing the input data matrix. Once obtained a complete solution, the local search procedure tries to both enlarge the current solution and to improve its H-score exchanging rows and columns. The proposed approach has been tested on 5 synthetic datasets [5]: 1) constant biclusters; 2) constant, upregulated biclusters; 3) shiftscale biclusters; 4) shift biclusters, and 5) scale biclusters.Compared with state-of-the-art competitors, its behaviour is excellent on shift datasets and is very good on all other datasets except for scaled ones. In order to improve its behaviour on scaled data as well and to reduce running times, we have designed and preliminarily tested a variant of the existing GRASP, whose local search phase returns an approximate local optimal solution. The resulting algorithm promises to be a more efficient, general, and robust method for the biclustering of all kinds of possible biological data.

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An annotated bibliography of GRASP – Part I: Algorithms

Cited by 153 publications

References 37 publications

GRASP: Greedy Randomized Adaptive Search Procedures

GRASP: Greedy Randomized Adaptive Search Procedures

Combining probabilistic algorithms, Constraint Programming and Lagrangian Relaxation to solve the Vehicle Routing Problem

A new GRASP metaheuristic for biclustering of gene expression data

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