User-Preference Based Evolutionary Algorithms for Solving Multi-Objective Nonlinear Minimum Cost Flow Problems

Network flow optimisation has various applications such as communication, transportation, computer networks and logistics. The minimum cost flow problem (MCFP) is the most common network flow problem, which can be formulated as a multi-objective optimisation, with multiple criteria such as time, cost, distance and risk. In many real-world scenarios, decision-makers (DMs) aim for solutions in a preferred region(s). Using a reference point(s) allows the algorithm to efficiently search in the vicinity of the preferred regions instead of the entire search space. This paper introduces evolutionary multi-objective algorithms (EMOs) by employing a novel probability tree-based representation scheme (denoted as PTbNSGA-II and PTbMOEA/D) to address multi-objective integer minimum cost flow problems (MOIMCFPs) incorporating nonlinear cost functions. We also propose user-preference based EMO algorithms to solve MOIMCFPs using preference information (denoted as r-PTbNSGA-II and R-PTbMOEA/D). Since the algorithms utilise preference-based information, they have significantly lower computational costs compared to those of conventional EMOs. The performance of the proposed methods is evaluated on a set of 30 MOIMCFP instances. The experimental results demonstrate the superiority of PTbNSGA-II over PTbMOEA/D in finding high-quality solutions as well as the superiority of r-PTbNSGA-II over R-PTbMOEA/D in efficiently finding the high-quality solutions close to the preferred region.<p></p>