Link load balancing optimization of telecommunication networks: A column generation based heuristic approach

Abstract

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.

Randomized rounding algorithms for large scale unsplittable flow problems

“…As introduced above, it is NP-hard to find an optimal solution or even to give a constant-factor approximation to the unsplittable flow problem. Thus, the literature investigated various randomized search procedures such as genetic algorithms (Cox, 1991;Masri et al, 2019), tabu search (Anderson et al, 1993;Laguna and Glover, 1993;Xu et al, 1997), local search and GRASP (Santos et al, 2013b(Santos et al, ,a, 2010Alvelos and Valério de Carvalho, 2007;Masri et al, 2015Masri et al, , 2019 or ant colony optimization (Li et al, 2010;Masri et al, 2011). One of the major difficulties encountered when solving the unsplittable flow problem with a meta-heuristic is to efficiently create useful paths for the commodities.…”

Randomized rounding algorithms for large scale unsplittable flow problems

“…As introduced above, it is NP-hard to find an optimal solution or even to give a constant-factor approximation to the unsplittable flow problem. Thus, the literature investigated various randomized search procedures such as genetic algorithms (Cox 1991;Masri et al 2019), tabu search (Anderson et al 1993;Laguna and Glover 1993;Xu et al 1997), local search and GRASP (Santos et al 2010(Santos et al , 2013aAlvelos and Valério de Carvalho 2007;Masri et al 2015Masri et al , 2019 or ant colony optimization (Li et al 2010;Masri et al 2011). One of the major difficulties encountered when solving the unsplittable flow problem with a meta-heuristic is to efficiently create useful paths for the commodities.…”

“…A different idea used in Santos et al (2013b), Santos et al (2013a), Santos et al (2010) and Alvelos and Valério de Carvalho (2007) is to consider paths extracted from the linear relaxation of the problem. The linear relaxation is solved with a column generation algorithm applied to the path formulation.…”

A Path Generation Approach to Embedding of Virtual Networks

“…Combining these two steps together even further enhances this efficiency, yet the resulting mathematical program is even harder to solve. Finally, path generation based formulations for multi-commodity flow based problems are proposed in a number of approaches such as [24]. In these formulations the source and end nodes for each flow are known a priori, which reduces the complexity of the problem, compared to the oneshot VNE that we solve in this paper.…”