A bi-objective transportation-location arc routing problem

Abstract

Location and routing problems belong to well-known optimization ones, whose combinations have merged as a location-routing problem (LRP). Arc routing has recently become a popular interest of researchers. Accordingly, the location-arc routing problem (LARP) is defined. This paper deals with a location-arc routing problem when there are transportation decisions from suppliers to established depots (TLARP). It is addressed by developing a bi-objective mathematical model to optimize the total costs and makespan. An augmented ε-constraint algorithm is employed to find the true Pareto solutions. Then two meta-heuristics are considered: non-dominated sorting genetic algorithm II (NSGA-II) and multi-objective late acceptance hill-climbing (MOLAHC) algorithm. There are four heuristics regarding NSGA-II, its combination with MOLAHC, and having/not having a local search (LS). Results demonstrate that NSGA-II+LS is the best and hybrid+LS is the second best heuristics while the solving time of hybrid+LS is significantly less than the time of NSGA-II+LS.