A New Multi-Objective Green Location Routing Problem with Heterogonous Fleet of Vehicles and Fuel Constraint

This paper introduces a new variant of Multi-Objective Green Location Routing Problem (MOGLRP) in which the start and end location of each route can be distinct. In this paper, the authors present a new mathematical formulation for the MOGLRP with consideration of environmentally issues. MOGLRP states for the problem of finding routes for vehicles to serve a set of customers while minimizes the total traveled distance, minimizes the total cost including vehicle fixed cost and variable travel cost and the co2 emissions. In order to solve the proposed model, two solution methods are used. Firstly, an exact method which is able to solve small sized problems is applied. Since the exact methods are not able to solve NP-hard problems in a reasonable time, the second method which is called multi-objective evolutionary algorithms (MOEA) are taken into account to deal with large instances. Furthermore, four well-known multi-objective evolutionary algorithms, including non-dominated sorting genetic algorithm (NSGA-II) and multi-objective particle swarm optimization (MOPSO), Strength Pareto Evolutionary Algorithm II (SPEA- II) and Pareto Envelope-based Selection Algorithm II (PESA-II) are used to compare obtained results. A comparison results show the proficiency of the proposed algorithm with respect to the four performance metrics, including quantity metric, diversification metric, spacing metrics and mean ideal distance. Finally, concluding remarks and future research directions are provided.