Efficient Meta-Heuristic Approach for the Multi-Objective Green p-Hub Centre Routing Problem

The design of responsive and green networks necessarily entails the optimisation of multiple conflicting objectives with strategic, tactical, or operational decisions. This paper addresses a bi-objective green p-hub centre routing problem with hub location-allocation decisions and vehicle routing decisions. In their respective routes, vehicles may only travel using one selected speed between each node pair. The objectives are the minimisation of the worst service time and the environmental costs incurred during the transportation of all necessary demand flows, respectively. Since the studied problem is NP-hard, a meta-heuristic approach based on the non-dominated sorting genetic algorithm-II meta-heuristic is proposed. Additionally, min-max location and sequential allocation-routing method is developed to generate initial solutions. Furthermore, problemspecific crossover and mutation operators are implemented to efficiently explore the search space. Whereas, a novel rankbased speed selection procedure is devised to determine the appropriate travel speeds for generated off-springs based on their relative ranks in current population. Computational experiments are performed on the Australian Post (AP) dataset, and results indicate that our proposed heuristic approach provides good solutions in competitive CPU times. Finally, a discussion on the obtained Pareto frontier approximations is offered, and analysis is conducted on the effects of key decision parameters such as the number of located hub nodes, and the number of vehicles available at open hubs.