Using MOPSO to Solve Multiobjective Bilevel Linear Problems

In this paper we propose a multiobjective particle swarm optimization (MOPSO) algorithm to solve bilevel linear programming problems with multiple objective functions at the upper level. A strategy based on an achievement scalarizing function is proposed for the global best selection and its performance is compared with other selection techniques. The outcomes of the algorithm on some bi-objective instances are compared with those obtained by an exact procedure that we developed before. The results indicate that the algorithm seems to be effective in solving this type of problems. In particular, the proposed selection technique provides a good convergence towards the Pareto front.

[1]  Gabriele Eichfelder,et al.  Multiobjective bilevel optimization , 2010, Math. Program..

[2]  Carlos A. Coello Coello,et al.  Multi-Objective Particle Swarm Optimizers: An Experimental Comparison , 2009, EMO.

[3]  M. M. El Shafei,et al.  An Approach for Solving Multi-objective Bi- Level Linear Programming Based on Genetic Algorithm , 2010 .

[4]  Xiaodong Li,et al.  Better Spread and Convergence: Particle Swarm Multiobjective Optimization Using the Maximin Fitness Function , 2004, GECCO.

[5]  Kalyanmoy Deb,et al.  An Efficient and Accurate Solution Methodology for Bilevel Multi-Objective Programming Problems Using a Hybrid Evolutionary-Local-Search Algorithm , 2010, Evolutionary Computation.

[6]  Lothar Thiele,et al.  Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach , 1999, IEEE Trans. Evol. Comput..

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

[8]  Jonathan E. Fieldsend,et al.  A MOPSO Algorithm Based Exclusively on Pareto Dominance Concepts , 2005, EMO.

[9]  Sanaz Mostaghim,et al.  Bilevel Optimization of Multi-Component Chemical Systems Using Particle Swarm Optimization , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[10]  Prospero C. Naval,et al.  An effective use of crowding distance in multiobjective particle swarm optimization , 2005, GECCO '05.

[11]  Carlos A. Coello Coello,et al.  Improving PSO-Based Multi-objective Optimization Using Crowding, Mutation and epsilon-Dominance , 2005, EMO.

[12]  C. Coello,et al.  Improving PSO-based Multi-Objective Optimization using Crowding , Mutation and �-Dominance , 2005 .

[13]  Xinping Shi,et al.  Model and interactive algorithm of bi-level multi-objective decision-making with multiple interconnected decision makers , 2001 .

[14]  Stephan Dempe,et al.  Computing the Pareto frontier of a bi-objective bi-level linear problem using a multiobjective mixed-integer programming algorithm , 2012 .

[15]  Mahyar A. Amouzegar,et al.  Test problem construction for linear bilevel programming problems , 1996, J. Glob. Optim..