Multi-objective harmony search algorithm for capacitated location-routing problem of reverse logistics using fuzzy membership approach

Location-routing problem is a problem that integrates both facility location problem and vehicle routing problem. The problem is aimed to solve the allocation of customers to the established depots and optimize the distance between the open depot and the assigned customers. This study considers multi-objective where the first objective is minimizing the cost of operating depot and cost of travel distance, meanwhile in the second objective is maximizing the profit from customer’s returns. As the problem is known as NP-hard problem and have the conflict objectives, metaheuristic method which is Multi-objective Harmony Search Algorithm (MOHSA) was proposed. The multi-local search neighborhood technique is applied in this algorithm. A numerical analysis is conducted in simulated dataset to find a set of Pareto front by non-dominated sorting genetic algorithm II (NSGA-II) in MOHSA using both fuzzy membership approach and the trade-off ranking method. The best method is determined by the evaluation of performance metric. The results show that the fuzzy membership approach can gives the better compromise solution as compared to the trade-off ranking method.

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