Search results for "Metaheuristic"
showing 10 items of 153 documents
GRASP and path relinking for the equitable dispersion problem
2013
The equitable dispersion problem consists in selecting a subset of elements from a given set in such a way that a measure of dispersion is maximized. In particular, we target the Max-Mean dispersion model in which the average distance between the selected elements is maximized. We first review previous methods and mathematical formulations for this and related dispersion problems and then propose a GRASP with a Path Relinking in which the local search is based on the Variable Neighborhood methodology. Our method is specially suited for instances in which the distances represent affinity and are not restricted to take non-negative values. The computational experience with 120 instances shows…
Variable neighborhood search for the linear ordering problem
2006
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 cou…
Tabu search for the Max–Mean Dispersion Problem
2015
In this paper, we address a variant of a classical optimization model in the context of maximizing the diversity of a set of elements. In particular, we propose heuristics to maximize the mean dispersion of the selected elements in a given set. This NP-hard problem was recently introduced as the maximum mean dispersion problem (MaxMeanDP), and it models several real problems, from pollution control to ranking of web pages. In this paper, we first review the previous methods for the MaxMeanDP, and then explore different tabu search approaches, and their influence on the quality of the solutions obtained. As a result, we propose a dynamic tabu search algorithm, based on three different neighb…
Reducing the bandwidth of a sparse matrix with tabu search
2001
The bandwidth of a matrix { } ij a A = is defined as the maximum absolute difference between i and j for which 0 ≠ ij a . The problem of reducing the bandwidth of a matrix consists of finding a permutation of the rows and columns that keeps the nonzero elements in a band that is as close as possible to the main diagonal of the matrix. This NP-complete problem can also be formulated as a labeling of vertices on a graph, where edges are the nonzero elements of the corresponding symmetrical matrix. Many bandwidth reduction algorithms have been developed since the 1960s and applied to structural engineering, fluid dynamics and network analysis. For the most part, these procedures do not incorpo…
GRASP and path relinking for the matrix bandwidth minimization
2004
In this article we develop a greedy randomized adaptive search procedure (GRASP) 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 nonzero elements in a band that is as close as possible to the main diagonal. The proposed method may be coupled with a Path Relinking strategy to search for improved outcomes. Empirical results indicate that the proposed GRASP implementation compares favourably to classical heuristics. GRASP with Path Relinking is also found to be competitive with a recently published tabu search algorithm that is considered one of the best currently available for band…
Tabu search and GRASP for the maximum diversity problem
2007
In this paper, we develop new heuristic procedures for the maximum diversity problem (MDP). This NP-hard problem has a significant number of practical applications such as environmental balance, telecommunication services or genetic engineering. The proposed algorithm is based on the tabu search methodology and incorporates memory structures for both construction and improvement. Although proposed in seminal tabu search papers, memory-based constructions have often been implemented in naive ways that disregard important elements of the fundamental tabu search proposals. We will compare our tabu search construction with a memory-less design and with previous algorithms recently developed for…
Separating capacity constraints in the CVRP using tabu search
1998
Abstract Branch and Cut methods have shown to be very successful in the resolution of some hard combinatorial optimization problems. The success has been remarkable for the Symmetric Traveling Salesman Problem (TSP). The crucial part in the method is the cutting plane algorithm: the algorithm that looks for valid inequalities that cut off the current nonfeasible linear program (LP) solution. In turn this part relies on a good knowledge of the corresponding polyhedron and our ability to design algorithms that can identify violated valid inequalities. This paper deals with the separation of the capacity constraints for the Capacitated Vehicle Routing Problem (CVRP). Three algorithms are prese…
Metaheuristics for the linear ordering problem with cumulative costs
2012
The linear ordering problem with cumulative costs (LOPCC) is a variant of the well-known linear ordering problem, in which a cumulative propagation makes the objective function highly non-linear. The LOPCC has been recently introduced in the context of mobile-phone telecommunications. In this paper we propose two metaheuristic methods for this NP-hard problem. The first one is based on the GRASP methodology, while the second one implements an Iterated Greedy-Strategic Oscillation procedure. We also propose a post-processing based on Path Relinking to obtain improved outcomes. We compare our methods with the state-of-the-art procedures on a set of 218 previously reported instances. The compa…
A hybrid metaheuristic for the cyclic antibandwidth problem
2013
We propose a hybrid artificial bee colony algorithm for the cyclic antibandwidth problem.We present a computational comparison of different parameter settings.We derive a fine-tuning hybrid artificial bee colony algorithm.The proposal is very competitive with the state-of-the-art algorithm for the cyclic antibandwidth problem. In this paper, we propose a hybrid metaheuristic algorithm to solve the cyclic antibandwidth problem. This hard optimization problem consists of embedding an n-vertex graph into the cycle Cn, such that the minimum distance (measured in the cycle) of adjacent vertices is maximized. It constitutes a natural extension of the well-known antibandwidth problem, and can be v…
Multi-start methods for combinatorial optimization
2013
Abstract Multi-start methods strategically sample the solution space of an optimization problem. The most successful of these methods have two phases that are alternated for a certain number of global iterations. The first phase generates a solution and the second seeks to improve the outcome. Each global iteration produces a solution that is typically a local optimum, and the best overall solution is the output of the algorithm. The interaction between the two phases creates a balance between search diversification (structural variation) and search intensification (improvement), to yield an effective means for generating high-quality solutions. This survey briefly sketches historical devel…