NSGA-II for solving multiobjective integer minimum cost flow problem with probabilistic tree-based representation

Abstract

Network flow optimisation has many real-world applications. The minimum cost flow problem (MCFP) is the most common network flow problem, which can also be formulated as a multiobjective optimisation problem, with multiple criteria such as time, cost, and distance being considered simultaneously. Although there exist several multiobjective mathematical programming techniques, they often assume linearity or convexity of the cost functions, which are unrealistic in many real-world situations. In this paper, we propose to use the non-dominated sorting genetic algorithm, NSGA-II, to solve this sort of Multiobjective MCFPs (MOMCFPs), because of its robustness in dealing with optimisation problems of linear as well as nonlinear properties. We adopt a probabilistic tree-based representation scheme, and apply NSGA-II to solve the multiobjective integer minimum cost flow problem (MOIMCFP). Our experimental results demonstrate that the proposed method has superior performance compared to those of the mathematical programming methods in terms of the quality as well as the diversity of solutions approximating the Pareto front. In particular, the proposed method is robust in handling linear as well as nonlinear cost functions.