Exact and approximate approaches for the Pareto front generation of the single path multicommodity flow problem

A major problem in communication networks is how to efficiently define the routing paths and to allocate bandwidths in order to satisfy a given collection of transmission requests. In this paper, we study this routing problem by modeling it as a bi-objective single path multicommodity flow problem (SMCFP). Two conflicting objective functions are simultaneously optimized: the delay and reliability of the generated paths. To tackle the complexity of this problem (NP-hard), most of the existing studies proposed approximate methods and metaheuristics as solution approaches. In this paper, we propose to adapt the augmented $$\epsilon $$ ϵ -constraint method in order to solve small sized instances of the bi-SMCFP. For large scale problems, we develop three metaheuristics: a multiobjective multi-operator genetic algorithm, an adaptive multiobjective variable neighborhood search and new hybrid method combining the $$\epsilon $$ ϵ -constraint with the evolutionary metaheuristic. The idea of the hybridization schema is to first use the metaheuristic to generate a good approximation of the Pareto front, then to enhance the quality of the solutions using the $$\epsilon $$ ϵ -constraint method to push them toward the exact Pareto front. An intelligent decomposition scheme is used to reduce the size of the search space before applying the exact method. Computational results demonstrate the efficiency of the proposed hybrid algorithm using instances derived from real network topology and other randomly generated instances.