Using multiobjective metaheuristics to solve VRP with uncertain demands

In real life optimization problems, it is very important to have high quality solutions (optimal). But when uncertainty becomes part of the optimization problem, solutions should be optimal and robust to the uncertain environmental changes. This paper focuses on finding robust optimal solution for the vehicle routing problem with stochastic demands VRPSD. In this case when the uncertainty of the customers demands enters this problem, the classical methods of VRP can not be used to obtain optimal solutions. We need new methods with new strategies to have robust optimal solution. For that we propose two bi-objective models, depending on the multi-objective evolutionary algorithms MOEAs: IBEA, MOGA and NSGAII. We compare the robustness degree of the two models and also we compare the performance of the three MOEAs over these two models.

[1]  Nicolas Jozefowiez,et al.  The vehicle routing problem: Latest advances and new challenges , 2007 .

[2]  Gilbert Laporte,et al.  An Exact Algorithm for the Vehicle Routing Problem with Stochastic Demands and Customers , 1995, Transp. Sci..

[3]  Russell Bent,et al.  Scenario-Based Planning for Partially Dynamic Vehicle Routing with Stochastic Customers , 2004, Oper. Res..

[4]  T. Ray.  Constrained robust optimal design using a multiobjective evolutionary algorithm , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[5]  El-Ghazali Talbi,et al.  ParadisEO-MOEO: A Framework for Evolutionary Multi-objective Optimization , 2007, EMO.

[6]  Dimitris Bertsimas,et al.  Computational Approaches to Stochastic Vehicle Routing Problems , 1995, Transp. Sci..

[7]  Sang Joon Kim,et al.  A Mathematical Theory of Communication , 2006 .

[8]  George B. Dantzig,et al.  The Truck Dispatching Problem , 1959 .

[9]  El-Ghazali Talbi,et al.  Metaheuristics - From Design to Implementation , 2009 .

[10]  Eckart Zitzler,et al.  Indicator-Based Selection in Multiobjective Search , 2004, PPSN.

[11]  Bernhard Sendhoff,et al.  Trade-Off between Performance and Robustness: An Evolutionary Multiobjective Approach , 2003, EMO.

[12]  H. Ishibuchi,et al.  MOGA: multi-objective genetic algorithms , 1995, Proceedings of 1995 IEEE International Conference on Evolutionary Computation.

[13]  Nicolas Jozefowiez,et al.  Multi-objective vehicle routing problems , 2008, Eur. J. Oper. Res..

[14]  Shengxiang Yang,et al.  Evolutionary Computation in Dynamic and Uncertain Environments , 2007, Studies in Computational Intelligence.

[15]  F. Tillman.  The Multiple Terminal Delivery Problem with Probabilistic Demands , 1969 .

[16]  Kalyanmoy Deb,et al.  Introducing Robustness in Multi-Objective Optimization , 2006, Evolutionary Computation.

[17]  Kay Chen Tan,et al.  A Multiobjective Evolutionary Algorithm for Solving Vehicle Routing Problem with Stochastic Demand , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[18]  Mauro Birattari,et al.  Hybrid Metaheuristics for the Vehicle Routing Problem with Stochastic Demands , 2005, J. Math. Model. Algorithms.

[19]  K.L. Mak,et al.  A genetic algorithm for vehicle routing problems with stochastic demand and soft time windows , 2004, Proceedings of the 2004 IEEE Systems and Information Engineering Design Symposium, 2004..

[20]  Gilbert Laporte,et al.  STOCHASTIC VEHICLE ROUTING. , 1996 .

[21]  E. R. Petersen.  STOCHASTIC VEHICLE ROUTING PROBLEM WITH RESTOCKING. , 2000 .

[22]  Aaron Sloman,et al.  Parallel Problem Solving from Nature – PPSN XVI , 2000 .

[23]  Lothar Thiele,et al.  A Tutorial on the Performance Assessment of Stochastic Multiobjective Optimizers , 2006 .

[24]  Jürgen Branke,et al.  Evolutionary optimization in uncertain environments-a survey , 2005, IEEE Transactions on Evolutionary Computation.

[25]  Xin Yao,et al.  Parallel Problem Solving from Nature PPSN VI , 2000, Lecture Notes in Computer Science.

[26]  Zuhaimy Ismail,et al.  Adaptive permutation-based genetic algorithm for solving VRP with stochastic demands , 2008 .

[27]  Jürgen Branke,et al.  Efficient search for robust solutions by means of evolutionary algorithms and fitness approximation , 2006, IEEE Transactions on Evolutionary Computation.

[28]  Allan Larsen,et al.  The Dynamic Vehicle Routing Problem , 2000 .