A Comparison of NSGA II and MOSA for Solving Multi-depots Time-dependent Vehicle Routing Problem with Heterogeneous Fleet

Subject Areas : طراحی آزمایشات

Behrouz  Afshar-nadjafi ¹ (Assistant Professor, Department of Industrial Engineering, Faculty of Industrial and Mechanical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran)
Arian  Razmi-farooji ² (MSc, Department of Industrial Engineering, Faculty of Industrial and Mechanical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran)

Received: 2014-07-20 Accepted : 2014-09-20 Published : 2014-12-01

Keywords: Bi-objective optimization, Time-dependent Vehicle Routing Problem, Meta-heuristics, NSGA II, MOSA,

Abstract :

Time-dependent Vehicle Routing Problem is one of the most applicable but least-studied variants of routing and scheduling problems. In this paper, a novel mathematical formulation of time-dependent vehicle routing problems with heterogeneous fleet, hard time widows and multiple depots, is proposed. To deal with the traffic congestions, we also considered that the vehicles are not forced to come back to the depots, from which they were departed. In order to solve our bi-objective formulation, we presented two well-known Meta-heuristic algorithms, namely NSGA II and MOSA and compared their performance based on a set of randomly generated test problems. The results confirm that our MILP model is valid and both NSGA II and MOSA work properly. While NSGA II finds closer solutions to the true Pareto front, MOSA finds evenly- distributed solutions which allows the algorithm to search the space more diversely.