-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 bandwidth minimization.

In this paper we deal with the Windy Rural Postman Problem. This problem generalizes several important Arc Routing Problems and has interesting real-life applications. Here, we present several heuristics whose study has lead to the design of a Scatter Search algorithm for the Windy Rural Postman Problem. Extensive computational experiments over different sets of instances, with sizes up to 988 nodes and 3952 edges, are also presented.

-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.

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 neighbourhood 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.