Multi-objective Windy Postman Problem in a Fuzzy Transportation Network

Researchers have become increasingly captivated by the windy postman problem (WPP), a major combinatorial optimisation problem with several practical applications. It is crucial to take the experts’ belief levels into account when modelling such a real-world application since these applications frequently involve uncertain aspects. A fuzzy set is one of the tools that might be regarded as appropriate for modelling such human perspectives. Applying fuzzy set theory to a multi-objective windy postman problem is the focus of this study. Maximising the overall profit and minimising the transportable time of the route visited by a postman are the objectives of the problem. In an effort to solve the fuzzy multi-objective windy postman problem (FMWPP), we have developed a chance-constrained programming model (CCPM). Subsequently, the epsilon-constraint method, a classical multi-objective solution methodology, is used to solve the deterministic transformation of the relevant CCPM. Moreover, the model is solved using two multi-objective genetic algorithms (MOGAs): fast Pareto genetic algorithm (FastPGA) and nondominated sorting genetic algorithm II (NSGAII). To demonstrate the proposed model, a numerical example is presented. We conclude by comparing the performance of the MOGAs on four randomly generated FMWPP instances.