A new proposal for multi-objective optimization using differential evolution and rough sets theory

This paper presents a new multi-objective evolutionary algorithm (MOEA) based on differential evolution and rough sets theory. The proposed approach adopts an external archive in order to retain the nondominated solutions found during the evolutionary process. Additionally, the approach also incorporates the concept of paε-dominance to get a good distribution of the solutions retained. The main idea of the approach is to use differential evolution (DE) as our main search engine, trying to translate its good convergence properties exhibited in single-objective optimization to the multi-objective case. Rough sets theory is adopted in a second stage of the search in order to improve the spread of the nondominated solutions that have been found so far. Our hybrid approach is validated using standard test functions and metrics commonly adopted in the specialized literature. Our results are compared with respect to the NSGA-II, which is a MOEA representative of the state-of-the-art in the area.

[1]  K..  Multiobjective Optimization Using a Pareto Differential Evolution Approach , 2022 .

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

[3]  Marco Laumanns,et al.  Performance assessment of multiobjective optimizers: an analysis and review , 2003, IEEE Trans. Evol. Comput..

[4]  Joshua D. Knowles,et al.  Multiobjective Optimization on a Budget of 250 Evaluations , 2005, EMO.

[5]  Marco Laumanns,et al.  Combining Convergence and Diversity in Evolutionary Multiobjective Optimization , 2002, Evolutionary Computation.

[6]  R. Storn,et al.  Differential Evolution: A Practical Approach to Global Optimization (Natural Computing Series) , 2005 .

[7]  Lothar Thiele,et al.  Comparison of Multiobjective Evolutionary Algorithms: Empirical Results , 2000, Evolutionary Computation.

[8]  Marco Laumanns,et al.  Scalable Test Problems for Evolutionary Multiobjective Optimization , 2005, Evolutionary Multiobjective Optimization.

[9]  Gary B. Lamont,et al.  Evolutionary Algorithms for Solving Multi-Objective Problems , 2002, Genetic Algorithms and Evolutionary Computation.

[10]  Dimitris K. Tasoulis,et al.  Vector evaluated differential evolution for multiobjective optimization , 2004, Proceedings of the 2004 Congress on Evolutionary Computation (IEEE Cat. No.04TH8753).

[11]  Jouni Lampinen,et al.  An Extension of Generalized Differential Evolution for Multi-objective Optimization with Constraints , 2004, PPSN.

[12]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

[13]  Carlos A. Coello Coello,et al.  Pareto-adaptive -dominance , 2007, Evolutionary Computation.

[14]  Xiaodong Li,et al.  Solving Rotated Multi-objective Optimization Problems Using Differential Evolution , 2004, Australian Conference on Artificial Intelligence.

[15]  Arthur C. Sanderson,et al.  Pareto-based multi-objective differential evolution , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

[16]  B. Babu,et al.  Differential evolution for multi-objective optimization , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

[17]  Bogdan Filipic,et al.  DEMO: Differential Evolution for Multiobjective Optimization , 2005, EMO.

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

[19]  H. Abbass.  The self-adaptive Pareto differential evolution algorithm , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[20]  Mauro Birattari,et al.  Swarm Intelligence , 2012, Lecture Notes in Computer Science.