An Investigation of a Bi-level Non-dominated Sorting Algorithm for Production-Distribution Planning System

Bi-Level Optimization Problems (BLOPs) belong to a class of challenging problems where one optimization problem acts as a constraint to another optimization level. These problems commonly appear in many real-life applications including: transportation, game-playing, chemical engineering, etc. Indeed, multi-objective BLOP is a natural extension of the single objective BLOP that bring more computational challenges related to the multi-objective hierarchical decision making. In this context, a well-known algorithm called NSGA-II was presented in the literature among the most cited Multi-Objective Evolutionary Algorithm (MOEA) in this research area. The most prominent features of NSGA-II are its simplicity, elitist approach and a non-parametric method for diversity. For this reason, in this work, we propose a bi-level version of NSGA-II, called Bi-NSGA-II, in an attempt to exploit NSGA-II features in tackling problems involving bi-level multiple conflicting criteria. The main motivation of this paper is to investigate the performance of the proposed variant on a bi-level production distribution problem in supply chain management formulated as a Multi-objective Bi-level MDVRP (M-Bi-MDVRP). The paper reveals three Bi-NSGA-II variants for solving the M-Bi-MDVRP basing on different variation operators (M-VMX, VMX, SBX and RBX). The experimental results showed the remarkable ability of our adopted algorithm for solving such NP-hard problem.

[1]  Christine L. Mumford,et al.  Investigating genetic algorithms for solving the multiple vehicle pickup and delivery problem with time window , 2009 .

[2]  Samy Bengio,et al.  The Vehicle Routing Problem with Time Windows Part II: Genetic Search , 1996, INFORMS J. Comput..

[3]  Kalyanmoy Deb,et al.  Solving Bilevel Multi-Objective Optimization Problems Using Evolutionary Algorithms , 2009, EMO.

[4]  G. Laporte,et al.  A tabu search heuristic for periodic and multi-depot vehicle routing problems , 1997, Networks.

[5]  K. Deb,et al.  An Evolutionary Approach for Bilevel Multi-objective Problems , 2009 .

[6]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

[7]  M G Bell.  Transportation networks: recent methodological advances: selected proceedings of the 4th EURO Transportation Meeting , 1998 .

[8]  Abir Chaabani,et al.  A new co-evolutionary decomposition-based algorithm for bi-level combinatorial optimization , 2015, Applied Intelligence.

[9]  G. Anandalingam,et al.  Genetic algorithm based approach to bi-level linear programming , 1994 .

[10]  Kalyanmoy Deb,et al.  Bilevel Multi-Objective Optimization and Decision Making , 2013 .

[11]  Abir Chaabani,et al.  Transfer of learning with the co-evolutionary decomposition-based algorithm-II: a realization on the bi-level production-distribution planning system , 2018, Applied Intelligence.

[12]  Robert G. Jeroslow,et al.  The polynomial hierarchy and a simple model for competitive analysis , 1985, Math. Program..

[13]  Francisco Herrera,et al.  A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms , 2011, Swarm Evol. Comput..

[14]  Abir Chaabani,et al.  A memetic evolutionary algorithm for bi-level combinatorial optimization: A realization between Bi-MDVRP and Bi-CVRP , 2016, 2016 IEEE Congress on Evolutionary Computation (CEC).