Search results for "Tabu"
showing 10 items of 180 documents
Vehicle Routing Problem with Time Windows, Part I: Route Construction and Local Search Algorithms
2005
This paper presents a survey of the research on the vehicle routing problem with time windows (VRPTW). The VRPTW can be described as the problem of designing least cost routes from one depot to a set of geographically scattered points. The routes must be designed in such a way that each point is visited only once by exactly one vehicle within a given time interval, all routes start and end at the depot, and the total demands of all points on one particular route must not exceed the capacity of the vehicle. Both traditional heuristic route construction methods and recent local search algorithms are examined. The basic features of each method are described, and experimental results for Solom…
Heuristics for the Mixed Rural Postman Problem
2000
Abstract The Rural Postman Problem on a mixed graph (MRPP) consists of finding a minimum cost tour which traverses, at least once, the arcs and edges of a given subset of the arcs and edges of the graph. This problem is known to be NP-hard. This paper presents two heuristic approaches to solve it. An approximate algorithm based on the resolution of some flow and matching problems and a tabu search implementation is presented. The tabu search algorithm seeks high-quality tours by means of a switching mechanism in an intensification phase and two levels of diversification. Computational results are presented to assess the merits of the method. Scope and purpose Routing Problems arise in sever…
A tabu search algorithm for large-scale guillotine (un)constrained two-dimensional cutting problems
2002
Abstract In this paper we develop several heuristic algorithms for the two-dimensional cutting problem (TDC) in which a single stock sheet has to be cut into a set of small pieces, while maximising the value of the pieces cut. They can be considered to be general purpose algorithms because they solve the four versions of the TDC: weighted and unweighted, constrained and unconstrained. We begin by proposing two constructive procedures based on simple bounds obtained by solving one-dimensional knapsack problems. We then use these constructive algorithms as building blocks for more complex procedures. We have developed a greedy randomised adaptive search procedure (GRASP) which is very fast an…
Scheduling in a continuous galvanizing line
2009
In this paper we address a sequencing problem in a Continuous Galvanizing Line of a Spanish Steel Company. Production scheduling in this context is an extremely complex task which needs to take into account many constraints. We present a conceptually simple model and a Tabu Search (TS) algorithm that efficiently solves it. The TS moves are defined in order to repair non-satisfied constraints, leading to smaller and more efficient neighbourhoods. The TS co-ordinates several intensification and diversification procedures guided by an evaluation function based on a shifting penalty strategy. This function reinforces the anticycling mechanism and makes the algorithm avoid already visited soluti…
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…
A tabu thresholding algorithm for arc crossing minimization in bipartite graphs
1996
Acyclic directed graphs are commonly used to model complex systems. The most important criterion to obtain a readable map of an acyclic graph is that of minimizing the number of arc crossings. In this paper, we present a heuristic for solving the problem of minimizing the number of arc crossings in a bipartite graph. It consists of a novel and easier implementation of fundamental tabu search ideas without explicit use of memory structures (a tabu thresholding approach). Computational results are reported on a set of 250 randomly generated test problems. Our algorithm has been compared with the two best heuristics published in the literature and with the optimal solutions for the test proble…
Adaptive memory programming for constrained global optimization
2010
The problem of finding a global optimum of a constrained multimodal function has been the subject of intensive study in recent years. Several effective global optimization algorithms for constrained problems have been developed; among them, the multi-start procedures discussed in Ugray et al. [1] are the most effective. We present some new multi-start methods based on the framework of adaptive memory programming (AMP), which involve memory structures that are superimposed on a local optimizer. Computational comparisons involving widely used gradient-based local solvers, such as Conopt and OQNLP, are performed on a testbed of 41 problems that have been used to calibrate the performance of su…
An Aggressive Search Procedure for the Bipartite Drawing Problem
1996
Graphs are used to represent reality in several areas of knowledge. This has generated considerable interest in graph drawing algorithms. Arc crossing minimization is a fundamental aesthetic criterion to obtain a readable map of a graph. The problem of minimizing the number of arc crossings in a bipartite graph (BDP) is NP-complete. In this paper we present an aggressive search scheme for the BDP based on the Intensification, Diversification and Strategic Oscillation elements of Tabu Search. Several algorithms can be obtained with this scheme by implementing different evaluators in the move definitions. In this paper we propose two variants. Computational results are reported on a set of 30…
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…