DIFFERENTIAL EVOLUTION WITH DYNAMIC ADAPTATION OF PARAMETERS BASED ON A FUZZY LOGIC AUGMENTATION APPROACH

Öz

This paper proposes an improvement to the Differential Evolution algorithm using a fuzzy logic augmentation. The main contribution is to dynamically adapt the parameters of mutation (F) and crossover (CR) using a fuzzy system, with the aim that the fuzzy system calculates the optimal parameters of the differential evolution algorithm during execution for obtaining better solutions, in this way arriving to the proposed new fuzzy differential evolution algorithm. In this paper experiments are performed with a set of mathematical functions using the original algorithm and the proposed method. Based on a statistical comparison of the original and proposed method, we can state that the fuzzy differential evolution algorithm outperforms the original differential evolution method.

Anahtar Kelimeler

• Differential Evolution,Fuzzy Logic,Dynamic Parameters

Kaynakça

1. Aguas-Marmolejo S. J., Castillo O.: Optimization of Membership Functions for Type-1 and Type 2 Fuzzy Controllers of an Autonomous Mobile Robot Using PSO. Recent Advances on Hybrid Intelligent Systems 2013: 97-104
2. Astudillo L., Melin P., Castillo O.: Optimization of a Fuzzy Tracking Controller for an Autonomous Mobile Robot under Perturbed Torques by Means of a Chemical Optimization Paradigm. Recent Advances on Hybrid Intelligent Systems 2013: 3-20
3. Eftekhari M., Katebi S.D., Karimi M., A.H. Jahanmir: Eliciting transparent fuzzy model using differential evolution, School of Engineering, Shiraz University, Shiraz, Iran, Applied Soft Computing 8 (2008) 466–476.
4. Fierro R., Castillo O., Design of Fuzzy Control Systems with Different PSO Variants. Recent Advances on Hybrid Intelligent Systems 2013: 81-88
5. Hachicha N., Jarboui B., Siarry P.: A fuzzy logic control using a differential evolution algorithm aimed at modelling the financial market dynamics, Institut Supérieur de Commerce et de Comptabilité de Bizerte, Zarzouna 7021, Bizerte, Tunisia, Information Sciences 181 (2011) 79–91
6. Lizárraga E., Castillo O., Soria J.: A Method to Solve the Traveling Salesman Problem Using Ant Colony Optimization Variants with Ant Set Partitioning. Recent Advances on Hybrid Intelligent Systems 2013: 237-2461
7. Melendez A., Castillo O.: Evolutionary Optimization of the Fuzzy Integrator in a Navigation System for a Mobile Robot. Recent Advances on Hybrid Intelligent Systems 2013: 21-31
8. Melin P., Olivas F., Castillo O., Valdez F., Soria J., García J.: Optimal design of fuzzy classification systems using PSO with dynamic parameter adaptation through fuzzy logic. Expert Syst. Appl. 40(8): 3196-3206 (2013)

9. Mezura-Montes E. and Palomeque-Ortiz A., Self-adaptive and Deterministic Parameter Control in Differential Evolution for Constrained Optimization.Efren Mezura-Montes, Laboratorio Nacional de Informatica Avanzada (LANIA A.C.), Rebsamen 80, Centro, Xalapa, Veracruz, 91000, MEXICO 2009.
10. Neyoy H., Castillo O., José Soria: Dynamic Fuzzy Logic Parameter Tuning for ACO and Its Application in TSP Problems. Recent Advances on Hybrid Intelligent Systems 2013: 259-271.
11. Oh S.-K., Kim W.-D., Pedrycz W., Design of optimized cascade fuzzy controller based on differential evolution: Simulation studies and practical insights, Department of Electrical Engineering, The University of Suwon, Engineering Applications of Artificial Intelligence 25 (2012) 520–532.
12. Olivas F., Castillo O.: Particle Swarm Optimization with Dynamic Parameter Adaptation Using Fuzzy Logic for Benchmark Mathematical Functions. Recent Advances on Hybrid Intelligent Systems 2013: 247-258
13. Peraza C., Valdez F. and Castillo O., A Harmony Search Algorithm Comparison with Genetic Algorithms, , Fuzzy Logic Augmentation of Nature-Inspired Optimization Metaheuristics, Studies in Computational Intelligence 574,Springer International Publishing Switzerland 2015.
14. Peraza Cinthia, Valdez Fevrier, Castillo Oscar, An Improved Harmony Search Algorithm Using Fuzzy Logic for the Optimization of Mathematical Functions, Design of Intelligent Systems Based on Fuzzy Logic, Neural Networks and Nature-Inspired Optimization,605-615,Springer International Publishing (2015).
15. Perez Jonathan J., Valdez F., Castillo O. : A new bat algorithm with fuzzy logic for dynamical parameter adaptation and its applicability to fuzzy control design, Fuzzy logic augmentation of nature-inspired optimization meta heuristics, pp. 65-80, Springer (2015).
16. Price, Storn R., Lampinen J. A., Differential Evolution, Kenneth V., Springer 2005.
17. Price K., Storn R. and Lampinen J. A. Differential Evolution: A Practical Approach to Global Optimization (Natural Computing Series), 2005: Springer
18. Rahnamayan S., Tizhoosh, H. R., Salama M. M. A. Opposition-Based Differential Evolution, Evolutionary Computation, IEEE Transaction on (Volume: 12, Issue: 1), 2008, pp. 64-79..
19. Raofen W., Zhang J., Zhang Y., Wang X.: Assessment of human operator functional state using a novel differential evolution optimization based adaptive fuzzy model, Lab for Brain-Computer Interfaces and Control, East China University of Science and Technology, Shanghai 200237, PR China, Biomedical Signal Processing and Control 7 (2012) 490– 498.
20. Shi Y.-J., Teng H.-F., and Li Z.-Q., "Cooperative Co-evolutionary differential evolution for function optimization", Proc. 1st Int. Conf. Advances in Natural Comput, pp.1080 -1088, 2005
21. Sk. I., Swagatam D., Saurav G., Subhrajit R., Ponnuthurai N. S., An Adaptive Differential Evolution Algorithm With Novel Mutation and Crossover Strategies for Global Numerical Optimization, IEEE Transactions on systems, man, and Cybernetics—Part b: Cybernetics, vol. 42, no. 2, April 2012
22. Sombra A., Valdez F., Melin P., Castillo O.: A new gravitational search algorithm using fuzzy logic to parameter adaptation. IEEE Congress on Evolutionary Computation 2013: 1068-1074
23. Storn R. "On the usage of differential evolution for function optimization", Proc. Biennial Conf. North Amer. Fuzzy Inf. Process. Soc., pp.519 -523 1996
24. Storn R. and Price K. Journal of Global Optimization 11, pp.341 -359 1997
25. Swagatam D., Ajith A., Uday K. C., Amit K., Differential Evolution Using a Neighborhood-based Mutation Operator, Department of Electronics and Telecommunication Engineering, Jadavpur University, Kolkata 700032, India
26. Sun J., Zhang Q. and Tsang E., "DE/EDA: A new evolutionary algorithm for global optimization", Inf. Sci., vol. 169, pp.249 -262 2004.
27. Valdez F., Melin P., Castillo O., Evolutionary method combining particle swarm optimization and genetic algorithms using fuzzy logic for decision making, in: Proceedings of the IEEE International Conference on Fuzzy Systems, 2009, pp. 2114–2119.
28. Valdez F., Melin P., Castillo O.: Parallel Particle Swarm Optimization with Parameters Adaptation Using Fuzzy Logic. MICAI (2) 2012: 374-385
29. Valdez F., Melin P., Castillo O.: Bio-inspired Optimization Methods on Graphic Processing Unit for Minimization of Complex Mathematical Functions. Recent Advances on Hybrid Intelligent Systems 2013: 313-322.
30. Valdez F., P. Melin, O. Castillo: An improved evolutionary method with fuzzy logic for combining Particle Swarm Optimization and Genetic Algorithms. Applied Soft Computing 11 (2011) 2625–2632
31. Vucetic D., Fuzzy differential evolution algorithm, The University of Western Ontario, London, Ontario, Canada, 2012.
32. Wilcoxon, F. (1945) "Individual Comparisons by Ranking Methods. Biometrics 1, 80-83.
33. Zelinka I. Real-time deterministic chaos control by means of selected evolutionary techniques, Engineering Applications of Artificial Intelligence 22 (2009) 283–297.