Vicente Campos’s research while affiliated with University of Valencia and other places

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Publications (34)


Scatter Search and Path Relinking
  • Chapter

January 2013

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17 Reads

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14 Citations

Yuhui Shi

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Juan-José Pantrigo

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Scatter search (SS) and path relinking (PR) are evolutionary methods that have been successfully applied to a wide range of hard optimization problems. The fundamental concepts and principles of the methods were first proposed in the 1970s and 1980s, and were based on formulations, dating back to the 1960s, for combining decision rules and problem constraints. The methods use strategies for search diversification and intensification that have proved effective in a variety of optimization problems and that have sometimes been embedded in other evolutionary methods to yield improved performance. This paper examines the scatter search and path relinking methodologies from both conceptual and practical points of view, and identifies certain connections between their strategies and those adopted more recently by particle swarm optimization. The authors describe key elements of the SS & PR approaches and apply them to a hard combinatorial optimization problem: the minimum linear arrangement problem, which has been used in applications of structural engineering, VLSI and software testing.


Figure 1: Objective function computation for a graph G and an arrangement f.
Figure 2: Schematic Representation of a Basic SS Design  
Figure 6. Move illustration 1 In the case where a vertex has an even number of adjacent neighbors, so that the labels of two of these neighbors could be considered candidates for a median, then selecting any value between and including the two candidates will minimize the sum of the absolute values of the differences. This property is not restricted to label values that are positive integers, but holds for any finite collection of real valued labels  
Figure 7. Evolution of the best SS solution  
Scatter Search and Path Relinking : A Tutorial on the Linear Arrangement Problem
  • Article
  • Full-text available

April 2011

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289 Reads

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10 Citations

Scatter search SS and path relinking PR are evolutionary methods that have been successfully applied to a wide range of hard optimization problems. The fundamental concepts and principles of the methods were first proposed in the 1970s and 1980s, and were based on formulations, dating back to the 1960s, for combining decision rules and problem constraints. The methods use strategies for search diversification and intensification that have proved effective in a variety of optimization problems and that have sometimes been embedded in other evolutionary methods to yield improved performance. This paper examines the scatter search and path relinking methodologies from both conceptual and practical points of view, and identifies certain connections between their strategies and those adopted more recently by particle swarm optimization. The authors describe key elements of the SS & PR approaches and apply them to a hard combinatorial optimization problem: the minimum linear arrangement problem, which has been used in applications of structural engineering, VLSI and software testing.

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Table 8 . Comparison on 80 large instances
Adaptive memory programming for matrix bandwidth minimization

March 2011

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83 Reads

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22 Citations

Annals of Operations Research

In this paper we explore the influence of adaptive memory in the performance of heuristic methods when solving a hard combinatorial optimization problem. Specifically, we tackle the adaptation of tabu search and scatter search to the bandwidth minimization problem. It consists of finding a permutation of the rows and columns of a given matrix which keeps the non-zero elements in a band that is as close as possible to the main diagonal. This is a classic problem, introduced in the late sixties, that also has a well-known formulation in terms of graphs. Different exact and heuristic approaches have been proposed for the bandwidth problem. Our contribution consists of two new algorithms, one based on the tabu search methodology and the other based on the scatter search framework. We also present a hybrid method combining both for improved outcomes. Extensive computational testing shows the influence of the different elements in heuristic search, such as neighborhood definition, local search, combination methods and the use of memory. We compare our proposals with the most recent and advanced methods for this problem, concluding that our new methods can compete with them in speed and running time. KeywordsHeuristic search–Memory programming–Tabu search–Scatter search


An algorithm for the Rural Postman problem on a directed graph

March 2009

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1,861 Reads

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90 Citations

The Directed Rural Postman Problem (DRPP) is a general case of the Chinese Postman Problem where a subset of the set of arcs of a given directed graph is ‘required’ to be traversed at minimum cost. If this subset does not form a weakly connected graph but forms a number of disconnected components the problem is NP-Complete, and is also a generalization of the asymmetric Travelling Salesman Problem. In this paper we present a branch and bound algorithm for the exact solution of the DRPP based on bounds computed from Lagrangean Relaxation (with shortest spanning arborescence sub-problems) and on the fathoming of some of the tree nodes by the solution of minimum cost flow problems. Computational results are given for graphs of up to 80 vertices, 179 arcs and 71 ‘required’ arcs.


Figure 1: Scheme of a Scatter Search procedure
A Scatter Search Algorithm for the Split Delivery Vehicle Routing Problem

September 2008

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210 Reads

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23 Citations

Studies in Computational Intelligence

In this chapter we present a metaheuristic procedure constructed for the special case of the Vehicle Routing Problem in which the demands of clients can be split, i.e., any client can be serviced by more than one vehicle. The proposed algorithm, based on the scatter search methodology, produces a feasible solution using the minimum number of vehicles. The quality of the obtained results is comparable to the best results known up to date on a set of instances previously published in the literature.


Figure 4. Move illustration  
Table 5 reports the statistics Best, Dev. Best and Time of the GRASP+PR algorithm with different values of the pr parameter. 
Heuristics for the Minimum Linear Arrangement Problem

July 2008

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851 Reads

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1 Citation

The linear arrangement minimization problem consists of finding a labeling or arrangement of the vertices of a graph that minimizes the sum of the absolute values of the differences between the labels of adjacent vertices. This is a well-known NP-hard problem that presents a challenge to solution methods based on heuristic optimization. Many linear arrangement reduction algorithms have recently been developed and applied to structural engineering, VLSI and software testing. We undertake the development of different heuristic procedures with the goal of uncovering the most effective designs to tackle this difficult but important problem. Specifically, we consider the adaptation of constructive, local search, GRASP and Path Relinking methods for the linear arrangement minimization. We perform computational experiments with previously reported instances to first study the effects of changes in critical search parameters and then to compare the efficiency of our proposal with previous solution procedures.


A branch and bound algorithm for the matrix bandwidth minimization

February 2008

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201 Reads

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51 Citations

European Journal of Operational Research

In this article, we first review previous exact approaches as well as theoretical contributions for the problem of reducing the bandwidth of a matrix. This problem consists of finding a permutation of the rows and columns of a given matrix which keeps the non-zero elements in a band that is as close as possible to the main diagonal. This NP-complete problem can also be formulated as a labeling of vertices on a graph, where edges are the non-zero elements of the corresponding symmetrical matrix. We propose a new branch and bound algorithm and new expressions for known lower bounds for this problem. Empirical results with a collection of previously reported instances indicate that the proposed algorithm compares favourably to previous methods.


A New Metaheuristic for the Vehicle Routing Problem with Split Demands

January 2007

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221 Reads

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37 Citations

Lecture Notes in Computer Science

In this paper we present a metaheuristic procedure constructed for the special case of the Vehicle Routing Problem in which the demands of the clients can be split, i.e., any client can be serviced by more than one vehicle. The proposed algorithm, based on the scatter search methodology, produces a feasible solution using the minimum number of vehicles. The results obtained compare with the best results known up to date on a set of instances previously published in the literature.


Variable neighborhood search for the linear ordering problem

December 2006

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162 Reads

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73 Citations

Computers & Operations Research

Given a matrix of weights, the linear ordering problem (LOP) consists of finding a permutation of the columns and rows in order to maximize the sum of the weights in the upper triangle. This NP-complete problem can also be formulated in terms of graphs, as finding an acyclic tournament with a maximal sum of arc weights in a complete weighted graph. In this paper, we first review the previous methods for the LOP and then propose a heuristic algorithm based on the variable neighborhood search (VNS) methodology. The method combines different neighborhoods for an efficient exploration of the search space. We explore different search strategies and propose a hybrid method in which the VNS is coupled with a short-term tabu search for improved outcomes. Our extensive experimentation with both real and random instances shows that the proposed procedure competes with the best-known algorithms in terms of solution quality, and has reasonable computing-time requirements. Variable neighborhood search (VNS) is a metaheuristic method that has recently been shown to yield promising outcomes for solving combinatorial optimization problems. Based on a systematic change of neighborhood in a local search procedure, VNS uses both deterministic and random strategies in search for the global optimum. In this paper, we present a VNS implementation designed to find high quality solutions for the NP-hard LOP, which has a significant number of applications in practice. The LOP, for example, is equivalent to the so-called triangulation problem for input-output tables in economics. Our implementation incorporates innovative mechanisms to include



Citations (31)


... While analogous in compositional terms with mutation operators, their role is however much different: mutation operators are intended to inject diversity in the population, therefore promoting exploration; local-search operators are on the other hand intensifying components, oriented toward exploitation, and fine tuning of solutions. This behavior can be achieved using any standalone method, such as hill climbing, simulated annealing, tabu search, VNS, etc. (Glover et al. 2021;Montes de Oca et al. 2012). However, it is important to note that even though using an off-the-shelf local-search method within the main cycle of an EA can often provide a performance boost, a more sensible approach is required to ensure the cost-effectiveness of such a design decision, taking into account different issues: ...

Reference:

Harnessing memetic algorithms: a practical guide
Tabu search tutorial. A Graph Drawing Application
  • Citing Article
  • June 2021

Top

... The SS method explores the solution space by improving and combining a small set of solutions. The combination method applies path relinking [33], which generates new solutions by connecting high-quality solutions. It implements a local search that, starting from one of these solutions, swaps its elements one by one with the elements in another high-quality solution. ...

Scatter Search and Path Relinking
  • Citing Chapter
  • January 2013

... Duarte and his colleagues in [89], [33], [90], [91], [92], [93] and Martí and her colleagues in [94], [90], [95], [96], [97], [93], [92] have offered their contribution to solving various operations and research problems using the metaheuristic method. In addition, Martí in [98], [99], [100], [101], [102] has also applied the metaheuristics method in solving several problems in graph theory. In another place, Hajiaghaei-Keshteli, an Iranian researcher, is a prominent researcher. ...

Heuristics for the Min-Max Arc Crossing Problem in Graphs
  • Citing Article
  • May 2018

Expert Systems with Applications

... The capacitated clustering problem (CCP) consists of forming a specified number of clusters or groups from a set of elements in such a way that the sum of the weights of the elements in each cluster is within some capacity limits, and the sum of the benefits between the pairs of elements in the same cluster is maximized (e.g., [111,302,388,513,782,783,845,875,929]). This problem is also known as the node capacitated graph partitioning problem [917]. ...

Randomized Heuristics for the Capacitated Clustering Problem
  • Citing Article
  • July 2017

Information Sciences

... Dispersion maximization problems consist in finding a collection of elements from a given set, such that the dissimilarity among them is maximized. Specifically, this dissimilarity (or diversity among the selected elements) is defined differently depending on the practical application example under study, giving rise to several models (Prokopyev et al., 2009;Martí et al., 2022;Martí et al., 2013;Martínez-Gavara et al., 2017). The two most popular diversity models in the literature are the maximum diversity problem (MDP) and the max-min diversity problem (MMDP). ...

Heuristic solution approaches for the maximum minsum dispersion problem

Journal of Global Optimization

... The study proposed efficient heuristic methods that outperform previous approaches, utilize memory structures to enhance search algorithms, and are compared with previous heuristics using benchmark instances and incorporating frequency information in the constructive method. Corberán et al. (2016) addressed the capacitated single-assignment HLP with modular link capacities. They developed a metaheuristic algorithm based on strategic oscillation, originally used in tabu search. ...

Strategic oscillation for the capacitated hub location problem with modular links

Journal of Heuristics

... Clustering performance can be boosted by leveraging the constraints that confine the search space. Several types of constraints are utilized in constrained clustering: Manuscript cluster-level constraints, such as cardinality constraints [1], [2], [3], [4], [5], [6], [7], [8] and capacity constraints [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], instance-level constraints [27], such as must-link and cannot-link constraints [28], and rank constraint [29]. Capacitated clustering is an important type of constrained clustering. ...

Tabu search and GRASP for the capacitated clustering problem

Computational Optimization and Applications

... The inclusion of randomness in this procedure increases diversity, so it is interesting to generate more than a single solution to assure that a wide portion of the search space is explored. As it is customary in GRASP (Campos et al. 2014;Ferone et al. 2019), we perform 100 independent constructions. ...

GRASP with path relinking for the orienteering problem
  • Citing Article
  • December 2014

Journal of the Operational Research Society

... In this MOLP model, the first objective corresponds to the harvest costs' minimization (Z 1 ); the second objective corresponds to the harvest days' minimization (Z 2 ); and the third objective corresponds to the harvest fruit in the optimal conditions' maximization (Z 3 ). The two applied MOLP methods are two solution strategies of the MO-GRASP algorithm (algorithms a and b), that is, two solution strategies of the multi-objective greedy randomized adaptive search procedure (Martí et al., 2015). After executing every MO-GRASP algorithm 1000 times for solving the MOLP model, two sets of solutions were obtained, S a and S b ; one set of 1000 solutions for every algorithm. ...

Multiobjective GRASP with path relinking
  • Citing Article
  • January 2015

European Journal of Operational Research

... Implementation of this method is systematic rather than probabilistic. For problems that have permutation type of representation, an adaptive structured combination based on the absolute position of the elements is presented as effective in Campos et al. (2000). ...

An Experimental Evaluation of a Scatter Search for the Linear Ordering Problem

Journal of Global Optimization