Abstract

This paper deals with optimal load balancing in telecommunication networks. For a capacitated telecommunications network with single path routing and an estimated traffic demand matrix, we wish to determine the routing paths aiming at min-max optimization of link loads. To solve this problem, we propose a column (path) generation based heuristic. In the first step, we use column generation to solve a linear programming relaxation of the basic problem (obtaining a lower bound and a set of paths). In the second step, we apply a multi-start local search heuristic with path-relinking to the search space defined by the paths found in the first step. In order to assess the merits of this approach, we also implemented a search heuristic which is equivalent to the second step of the proposed one but with no constraints on the set of paths that can be used. Through a set of computational results, we show that the proposed heuristic is efficient in obtaining near optimal routing solutions within short running times. Moreover, the comparison of the two heuristics show that constraining the search space to the columns given by column generation gives better results since this solution space contains good quality solutions and, due to its size, enables to find them in short running times.

Abstract

Given a capacitated telecommunications network with single path routing and an estimated traffic demand matrix, we aim to determine the routing path of each traffic commodity such that the whole set of paths provide an optimal network load balancing. In a recent paper, we have proposed a column generation based heuristic where, in the first step, we use column generation to solve a linear programming relaxation of the original problem (obtaining, in this way, a lower bound and a set of paths for each commodity) and, in the second step, we apply a multi-start local search with path relinking heuristic on the solution space defined by the paths of the first step. Here, we propose a hybridization approach of the metaheuristic with column generation that can be seen as an enhanced version of the previous approach: we run column generation not only at the beginning (to define the initial search space) but also during the search. These additional column generation steps consist in solving a perturbed problem defined by the incumbent solution. In the previous paper, we have shown that the first approach is efficient in obtaining near optimal routing solutions within short running times. With the enhanced version, we show through computational results that the additional paths, introduced by the additional column generation steps, either improve the efficiency of the algorithm or show similar efficiency in the cases where the original algorithm is already very efficient. This work has been conducted under the project PTDC/EIA-EIA/100645/2008 "SearchCol: Meta-heuristic Search by Column generation" (funded by FCT) and under the European FP7 Network of Excellence "Euro-NF". Dorabella Santos was funded by Portuguese FCT under post-doc grant SFRH/BPD/41581/2007. Michal Pioro was funded by Polish Ministry of Science and Higher Education under research grant N517 397334.