The congested multicommodity network design problem

•A new fixed-charge multicommodity network design problem with congestion at nodes.•A reformulation of the problem as a mixed integer second order cone program.•An efficient evolutionary algorithm that combines iterated local search and scatter search.•Computational experiments on new benchmark instances and real case data.

This paper studies a version of the fixed-charge multicommodity network design problem where in addition to the traditional costs of flow and design, congestion at nodes is explicitly considered. The problem is initially modeled as a nonlinear integer programming formulation and two solution approaches are proposed: (i) a reformulation of the problem as a mixed integer second order cone program to optimally solve the problem for small to medium scale problem instances, and (ii) an evolutionary algorithm using elements of iterated local search and scatter search to provide upper bounds. Extensive computational results on new benchmark problem instances and on real case data are presented.