Capacitated Windy Rural Postman Problem with Several Vehicles: A Hybrid Multi-Objective Simulated Annealing Algorithm

This paper presents the capacitated Windy Rural Postman Problem with several vehicles. For this problem, two objectives are considered. One of them is the minimization of the total cost of all vehicle routes expressed by the sum of the total traversing cost and another one is reduction of the maximum cost of vehicle route in order to find a set of equitable tours for the vehicles. Mathematical formulation is provided. The multi-objective simulated annealing (MOSA) algorithm has been modified for solving this bi-objective NP-hard problem. To increase algorithm performance, Taguchi technique is applied to design experiments for tuning parameters of the algorithm. Numerical experiments are proposed to show efficiency of the model. Finally, the results of the MOSA have been compared with MOCS (multi-objective Cuckoo Search algorithm) to validate the performance of the proposed algorithm. The experimental results indicate that the proposed algorithm provides good solutions and performs significantly better than the MOCS.