A multi-objective optimization model for a reliable generalized flow network design

•Reliability estimation approach for the generalized flow network design.•Optimizing the network design with conflicting objectives of cost, flow and reliability.•Measuring different efficiency metrics for competitive metaheuristic approaches.•Aiding decision maker to choose best compromise solution by a fuzzy-based mechanism.•For the model, NSGA-III is superior to MOPSO and NSGA-II in convergence rate and running time. Design of a reliable network in presence of flow loss has become the primary objective of today’s network designers. However, there are other important conflicting objectives that hinder the process of efficient network design. This study proposes a multi-objective optimization model for reliable communication flow networks, including maximizing the network reliability, minimizing total cost, and maximizing network flow, simultaneously. The total cost comprises the cost of construction of network arcs and the cost of flow, while arcs may fail to operate in full-capacity and may only function to a fraction of their capacity. The reliability-based network-design is modeled as a mixed-integer linear programming and solved by three metaheuristic multi-objective methods namely multi-objective particle swarm optimization (MOPSO) and two versions of non-dominated sorting genetic algorithm (i.e., NSGA-II and NSGA-III). In order to select the best compromise solution from the Pareto front members, a fuzzy-based mechanism is utilized. Finally, in order to measure the performance of the three algorithms, several numerical examples in small and large-scale are solved. The computational results indicate that NSGA-III is superior to MOPSO and NSGA-II in terms of convergence rate and running time especially for large-scale problems.