Solving stochastic multiobjective vehicle routing problem using probabilistic metaheuristic

In this paper we propose a new metaheuristic algorithm for solving stochastic multiobjective combinatorial optimization(SMOCO) problems. Indeed, we find that the various initiatives that have been launched recently on this subject, they propose the classical metaheuristics to solve a stochastic multi-objective problems,but when the stochasticity effects is not taken into account, the choice of an arbitrary value leading to a particular configuration and a high loss of information. To conserve the stochastic nature of SMOCO problems,the pareto ranking should be defined on the random objectives functions directly rather than converted deterministic objectives. From these considerations, the scope of this research should consist of: (i)Proposed novel methodology of stochastic optimality for ranking objective functions characterized by non-continuous and no closed form expression. This novel approach is based on combinatorial probability and can be incorporated in a multiobjective evolutionary algorithm. (ii)Provide probabilistic approaches to elitism and diversification in multiobjective evolutionary algorithms. Finally, The behavior of the resulting Probabilistic Multi-objective Evolutionary Algorithms (PrMOEAs) is empirically investigated on the multi-objective stochastic VRP problem.

[1]  Jörg Fliege,et al.  Stochastic Multiobjective Optimization: Sample Average Approximation and Applications , 2011, J. Optim. Theory Appl..

[2]  Angel A. Juan,et al.  A review of simheuristics: Extending metaheuristics to deal with stochastic combinatorial optimization problems , 2015 .

[3]  Moshe Shaked,et al.  Multivariate Stochastic Orders , 2007 .

[4]  Eckart Zitzler,et al.  Handling Uncertainty in Indicator-Based Multiobjective Optimization , 2006 .

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

[6]  Walter J. Gutjahr,et al.  Two Metaheuristics for Multiobjective Stochastic Combinatorial Optimization , 2005, SAGA.

[7]  Yao Zhang,et al.  A method for stochastic multiple criteria decision making based on dominance degrees , 2011, Inf. Sci..

[8]  Michel Gendreau,et al.  Stochastic Vehicle Routing Problems , 2014, Vehicle Routing.

[9]  Norio Baba,et al.  Three Approaches for Solving the Stochastic Multiobjective Programming Problem , 1992 .

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

[11]  Rafael Caballero,et al.  Stochastic approach versus multiobjective approach for obtaining efficient solutions in stochastic multiobjective programming problems , 2002, Eur. J. Oper. Res..

[12]  Henri Bonnel,et al.  Optimization over the Pareto outcome set associated with a convex bi-objective optimization problem: theoretical results, deterministic algorithm and application to the stochastic case , 2015, J. Glob. Optim..

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

[14]  Kay Chen Tan,et al.  Handling Uncertainties in Evolutionary Multi-Objective Optimization , 2008, WCCI.

[15]  Kalyanmoy Deb,et al.  A Fast Elitist Non-dominated Sorting Genetic Algorithm for Multi-objective Optimisation: NSGA-II , 2000, PPSN.

[16]  Mitsuo Gen,et al.  Effective multiobjective EDA for bi-criteria stochastic job-shop scheduling problem , 2017, J. Intell. Manuf..

[17]  Henri Bonnel,et al.  Stochastic Optimization over a Pareto Set Associated with a Stochastic Multi-Objective Optimization Problem , 2014, J. Optim. Theory Appl..

[18]  Rajan Filomeno Coelho,et al.  Probabilistic Dominance in Multiobjective Reliability-Based Optimization: Theory and Implementation , 2015, IEEE Transactions on Evolutionary Computation.

[19]  Walter J. Gutjahr,et al.  Stochastic multi-objective optimization: a survey on non-scalarizing methods , 2016, Ann. Oper. Res..

[20]  John R. Birge,et al.  Introduction to Stochastic programming (2nd edition), Springer verlag, New York , 2011 .

[21]  Gilbert Laporte,et al.  Stochastic Vehicle Routing Problems , 2009, Encyclopedia of Optimization.

[22]  Evan J. Hughes,et al.  Evolutionary Multi-objective Ranking with Uncertainty and Noise , 2001, EMO.

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

[24]  Eshetie Berhan,et al.  Stochastic Vehicle Routing Problem: A Literature Survey , 2014, J. Inf. Knowl. Manag..

[25]  RåHW Fkryd Multiobjective Bayesian Optimization Algorithm for Combinatorial Problems : Theory and practice , 2002 .

[26]  John R. Birge,et al.  Introduction to Stochastic Programming , 1997 .