Scatter Search for Network Design Problem

Abstract

A fixed charge capacitated multicommodity network design problem on undirected networks is addressed. At the present time, there exists no algorithm that can solve large instances, common in several applications, in a reasonable period of time. This paper presents an efficient procedure using a scatter search framework. Computational experiments on a large set of randomly generated problems show that this procedure is capable of finding good solutions to large-scale problems within a reasonable amount of time.

A cycle-based evolutionary algorithm for the fixed-charge capacitated multi-commodity network design problem

“…When updating the pool of solutions, the dissimilarity of solutions is considered as an additional component in calculating the solution value. Alvarez et al (2005) describe an SS algorithm for the MCNDP. They use GRASP, originally proposed by Feo and Resende (1995), to produce a diversified initial set of solutions.…”

“…A feasibility restoration mechanism is also available for solutions that are infeasible. In contrast to the recombination process of Alvarez et al (2005), our SS does not consider commodity paths to build a solution; instead, independent arcs are combined to create offspring. We believe that the latter enhances the SS algorithm's capabilities, as more combinations can occur when arcs instead of paths are combined together, leading to a rich pool of offspring.…”

“…These instances differ from one another with respect to the nature of the arc capacities, which are either loose (L) or tight (T), and with respect to the relative importance of fixed costs (F) and the variable flow costs (V) per unit of flow. There also exist benchmark instances described by Alvarez et al (2005) defined on an undirected graph using edges as opposed to a directed graph using arcs. These define a different problem than the one we address in this paper, as is discussed by Crainic et al (2000), and is the reason why this set is not considered here.…”

“…The algorithm described by Alvarez et al (2005) could not be included in the comparisons as the authors do not report any results with the instances tested here; instead they use their own benchmark instances. The reason for not being able to test our algorithm on the Alvarez et al (2005) benchmark set is that these instances are based on an undirected graph and work with edges, whereas the problem we solve is on a directed graph and our algorithm has been developed to operate on arcs. Table 4 The first seven rows describe, to the best that we were able to extract, the computational resources used to run the algorithms.…”

Mixed network design using hybrid scatter search

“…They showed that the designed population-based algorithms provide better results compared to other methods. Later, Alvarez et al (2005) proposed a scatter search approach for solving a general network design problem for undirected networks. They showed that this algorithm is capable for finding good solutions in large-scale problems within a reasonable time.…”