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Kedar Nath Das

Hybrid Binary Coded GA for Constrained Optimization. Kedar Nath Das. NIT SILCHAR, ASSAM, INDIA. MOST GENERAL OPTIMIZATION PROBLEM Minimize (Maximize) f (X), where s.t. X  S  , where S is defined by. To Find the Global Optimal Solution. Approaches.

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Kedar Nath Das

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  1. Hybrid Binary Coded GA for Constrained Optimization KedarNath Das NIT SILCHAR, ASSAM, INDIA

  2. MOST GENERAL OPTIMIZATION PROBLEM Minimize (Maximize) f (X), where s.t. XS  , where S is defined by

  3. To Find the Global Optimal Solution Approaches DETERMINISTIC APPROACH PROBABILISTIC APPROACH Many • Genetic Algorithm • Memetic Algorithm • Random Search Methods • Tabu Search • Ant Colony Optimization • Particle Swarm Optimization, etc…..

  4. Working Principle of GA • Encoding • Selection • Crossover • Mutation • Elitism (Opt.) Repetition

  5. USED GA OPERATORS Mating pool 23 24 23 24 30 37 20 26 20 26 38 37 a) Roulette Wheel Selection b) Tournament Selection

  6. c) One Point Cross-Over d) Uniform Cross-Over

  7. e) Bit-Wise Mutation f) Elitism 12 17 18 2 45 2 12 8 20 41 2 2 8 12 20 Process of Elitism After Mutation Bigin of a GA cycle End of the GA cycle

  8. Quadratic Approximation (Hybridization) • Select the individuals R1, with the best fitness value. Choose two random individuals R2 and R3. • Find the point of minima (child) of the quadratic surface passing through R1, R2 and R3 defined as: Child = 0.5*

  9. Selection Strategy for Constrained Optimization

  10. (A) Selection Strategy for Mating Pool • Roulette Wheel Selection • Penalty Parameter: • Fitness: where

  11. (B) Selection Strategy for Best Individuals in a population: Tournament Selection

  12. 4

  13. Methodology of HBGA-C Step 1: Begin with a random population (P) of size 10*N Step 2: Evaluation fitness of P(t) Step3: Stop if it satisfies the stopping criteria Step 4: Select the individuals taking the tournament selection strategy Step 5: Apply Single Point Crossover Step 6:Apply Bitwise Mutation Step 7: Hybridize with Quadratic Approximation Step 8: Apply Complete Elitism through tournament selection

  14. BGA: Pc – Pm performance

  15. HBGA: Pc – Pm performance

  16. Finetune for BGA-C

  17. Finetune for HBGA-C

  18. Recommended Values for Pc and Pm:

  19. RESULTS

  20. Success Rate

  21. No. of Function Calls

  22. Mean Function Values

  23. S. D.

  24. Time

  25. Analysis of Results HBGA-C Vs. BGA-C HBGA-C is……… …….than BGA-C

  26. Conclusion • HBGA-C >>> BGA-C (in more percentage of success) • HBGA-C >>> BGA-C (in less no. of function evaluation) • HBGA-C >>> BGA-C (in less S. D.) • HBGA-C >>> BGA-C (in better obj. fun. value) • HBGA-C <<< BGA-C (in time)

  27. References: [1] A. Osyczka, S. Krenich and S. Kundu. Proportional and Tournament Selections for Constrained Optimization Problems using GAs. Evolutionary Optimization, an Int. Jr. on the internet, 1(1): pp. 89-92, 1999. [2] A. Osyczka. Evolutionary Algorithms for Single and Multi-criteria Design Optimization, Physica-Verlag Heidelberg, New York, 2002. [3] C. A. Coella and M. E. Mezura. Constraint-Handling in Genetic Algorithms through the use of dominance-based tournament selection. Advance Engineering Informatics, 16: pp. 193-203, 2002. [4] D. Orvosh and L. Davis. Using a Genetic Algorithm to Optimize problems with Feasibility Constraints. Proceeding of the Sixth Int. Conf. on Gas, Echelman, L. J. Ed., pp. 548-552, 1995. [5] H. Myung and J. H. Kim. Hybrid Evolutionary Programming for Heavily Constrained Problems. Bio-Systems, 38, pp. 29-43, 1996. [6] J. H. Kim and H. Myung. A Two Phase Evolutionary Programming for general Constrained Optimization Problem. Proceedings of the Fifth Annual Conf. on Evolutionary Programming, San Diego, 1996. [7] K. Deb and S. Agarwal. A Niched-Penalty Approach for Constraint Handling GAs, Proceeding of the ICANNGA, Portoroz, Slovenia, 1999. [8] K. Deb. A Robust Optimal Design Technique Component Design in Evolutionary Algorithms in Engineering Applications. Springer Verlag, pp. 497-514, 1997.

  28. [9] K. Deb. Optimization for Engineering Design: Algorithms and Examples, Prentice-Hall of India, NewDelhi, 1995. [10] K. Deep and K. N. Das. Choice of selection and crossover on some Benchmark problems. Int. Jr. of Computer, Mathematical Sciences and Applications, Vol.1, No. 1, 99-117, 2007. [11] K. Deep and K. N. Das. Quadratic approximation based Hybrid Genetic Algorithm for Function Optimization. AMC, Elsevier, Vol. 203: 86-98, 2008. [12] K. N. Das. Design and Applications of Hybrid Genetic Algorithms for Function Optimization. PhD thesis, Indian Institute of Technology, Roorkee, India, Dec. 2007 . [13] S. Akhtar, K. Tai and T. Ray. A Socio-Behavioural Simulation Model for Engineering Design Optimization, 34(4): pp.341-354, 2002. [14] S. Kundu and A. Osyczka. Genetic Multi-criteria Optimization of structural systems. Proceedings of the 19th ICTAM, Kyoto, Japan, IUTAM, 272, 1996. [15] Z. Michalewicz. Genetic Algorithms, Numerical Optimization and Constraints. Proceedings of Sixth Int. Conf. on Genetic Algorithms, Echelman L. J. Ed., pp. 151-158, 1995.

  29. Thank You

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