Öz
Kaynakça
- [1] K. Deb and R. Datta, "A fast and accurate solution of constrained optimization problems using a hybrid bi-objective and penalty function approach," presented at the IEEE Congress on Evolutionary Computation (CEC), Barcelona 2010.
- [2] K. Deb, Optimization for Engineering Design. new Delhi: PHI, India, 1995.
- [3] D. E. Goldberg, Genetic Algorithms. Reading, Massachusetts: Addison Wesley, 1989.
- [4] C. A. C. Coello, D. A. Veldhuizen, and G. B. Lamont, Evolutionary Algorithms for Solving Multiobjective Problems. Boston: Kluwer Academic Publishers, 2003.
- [5] K. Deb, Multiobjective Optimization using Evolutionary Algorithms: John Wiley & Sons, 2001.
- [6] C. M. Fonseca, "An overview of evolutionary algorithms in multiobjective optimization," Evolutionary Computation, vol. 3, pp. 1- 16, 1995.
- [7] C. A. C. Coello, "An updated survey of Ga-based multi-objective optimization techniques," ACM Computing Surveys, vol. 32, pp. 109- 143, 2000.
- [8] K. Deb, "An efficient constraint handling method for genetic algorithms.," Computer Methods in Applied Mechanics and Engineering, vol. 186, p. 28, 2000.
- [9] C. A. C. Coello, "Use of a self-adaptive penalty approach for engineering optimization problems," Ciomputers in Industry, vol. 41, pp. 113-127, 2000.
- [10] O. Ciftcioglu, M. S. Bittermann, and I. S. Sariyildiz, "Precision Evolutionary Optimization - Part I: Nonlinear Ranking Approach," presented at the GECCO 2012, Philadelphia, 2012.
- [11] S. Gass and T. Saaty, "The computational algorithm for the parametric objective function," Naval Research Logistics Quarterly, vol. 2, p. 7, 1955.
- [12] L. Zadeh, "Non-scalar-valued performance criteria," IEEE Trans. Automatic Control, vol. 8, p. 2, 1963.
- [13] K. Miettinen, Nonlinear Multiobjective Optimization. Boston: Kluwer Academic, 1999.
- [14] Y. Y. Haimes, L. S. Lasdon, and D. A. Wismer, "On a bicriterion formulation of the problems of integrated system identification and system optimization," IEEE Trans. Systems, Man, and Cybernetics, vol. 1, p. 2, 1971.
- [15] K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, "A fast and elitist multi-objective genetic algorithm: NSGA-II," IEEE Transactions on Evolutionary Computation, vol. 6, pp. 182-197, 2000.
- [16] K. Deb and R. B. Agrawal, "Simulated binary crossover for continuous search space," Complex Systems, vol. 9, pp. 115-148, 1995.
- [17] K. Deb and M. Goyal, "A combined genetic adaptive search (GeneAS) for engineering design," Computer Science and Informatics, vol. 26, pp. 30-45, 1996.
- [18] W. Hock and K. Schittkowski, "Test Examples for Nonlinear Programming Codes. ," in Lecture Notes in Economics and Mathematical Systems, ed Berlin: Springer-Verlag, 1981.
- [19] C. Floundas and P. Pardalos., A Collection of Test Problems for Constrained Global Optimization, vol. 455. Berlin, Germany: SpringerVerlag, 1987.
Öz
Implementation and applications of a new approach to multiobjective optimization by evolutionary algorithms are presented. After non-dominated sorting for Pareto formation, a novel non-linear ranking is proposed during the fitness evaluation and tournament selection, as well as elitism. The non-linear ranking is based on a probabilistic model, which models the density of the genetic population throughout the generations by means of an exponential distribution. From this model, a
robust probabilistic distance measure is established. The distance comprises a penalty parameter in an embedded form, which plays an important role for the convergence of the optimization process as it varies in an adaptive form during the generations in progress. Because of the embedded form, the penalty parameter is inherently tuned for every constraint, making the convergence, robust, fast, accurate, and stable. By the nonlinear ranking procedure, also the stiffness among the constraints is handled effectively. Convergence process is backed-up with an additional probabilistic threshold applied to the population, classifying them as productive and unproductive infeasible solutions. The details of the underlying theoretical work are presented in the first part of this sequel. The present work at hand describes the algorithmic implementation in detail, and the outstanding performance of the optimization process is exemplified by computer experiments. The problems used in the experiments are selected from the existing literature for the purpose of eventual benchmark comparisons.
Anahtar Kelimeler
Evolutionary algorithm multiobjective optimization constraint optimization probabilistic modeling
Kaynakça
- [1] K. Deb and R. Datta, "A fast and accurate solution of constrained optimization problems using a hybrid bi-objective and penalty function approach," presented at the IEEE Congress on Evolutionary Computation (CEC), Barcelona 2010.
- [2] K. Deb, Optimization for Engineering Design. new Delhi: PHI, India, 1995.
- [3] D. E. Goldberg, Genetic Algorithms. Reading, Massachusetts: Addison Wesley, 1989.
- [4] C. A. C. Coello, D. A. Veldhuizen, and G. B. Lamont, Evolutionary Algorithms for Solving Multiobjective Problems. Boston: Kluwer Academic Publishers, 2003.
- [5] K. Deb, Multiobjective Optimization using Evolutionary Algorithms: John Wiley & Sons, 2001.
- [6] C. M. Fonseca, "An overview of evolutionary algorithms in multiobjective optimization," Evolutionary Computation, vol. 3, pp. 1- 16, 1995.
- [7] C. A. C. Coello, "An updated survey of Ga-based multi-objective optimization techniques," ACM Computing Surveys, vol. 32, pp. 109- 143, 2000.
- [8] K. Deb, "An efficient constraint handling method for genetic algorithms.," Computer Methods in Applied Mechanics and Engineering, vol. 186, p. 28, 2000.
- [9] C. A. C. Coello, "Use of a self-adaptive penalty approach for engineering optimization problems," Ciomputers in Industry, vol. 41, pp. 113-127, 2000.
- [10] O. Ciftcioglu, M. S. Bittermann, and I. S. Sariyildiz, "Precision Evolutionary Optimization - Part I: Nonlinear Ranking Approach," presented at the GECCO 2012, Philadelphia, 2012.
- [11] S. Gass and T. Saaty, "The computational algorithm for the parametric objective function," Naval Research Logistics Quarterly, vol. 2, p. 7, 1955.
- [12] L. Zadeh, "Non-scalar-valued performance criteria," IEEE Trans. Automatic Control, vol. 8, p. 2, 1963.
- [13] K. Miettinen, Nonlinear Multiobjective Optimization. Boston: Kluwer Academic, 1999.
- [14] Y. Y. Haimes, L. S. Lasdon, and D. A. Wismer, "On a bicriterion formulation of the problems of integrated system identification and system optimization," IEEE Trans. Systems, Man, and Cybernetics, vol. 1, p. 2, 1971.
- [15] K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, "A fast and elitist multi-objective genetic algorithm: NSGA-II," IEEE Transactions on Evolutionary Computation, vol. 6, pp. 182-197, 2000.
- [16] K. Deb and R. B. Agrawal, "Simulated binary crossover for continuous search space," Complex Systems, vol. 9, pp. 115-148, 1995.
- [17] K. Deb and M. Goyal, "A combined genetic adaptive search (GeneAS) for engineering design," Computer Science and Informatics, vol. 26, pp. 30-45, 1996.
- [18] W. Hock and K. Schittkowski, "Test Examples for Nonlinear Programming Codes. ," in Lecture Notes in Economics and Mathematical Systems, ed Berlin: Springer-Verlag, 1981.
- [19] C. Floundas and P. Pardalos., A Collection of Test Problems for Constrained Global Optimization, vol. 455. Berlin, Germany: SpringerVerlag, 1987.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Elektrik Mühendisliği |
| Bölüm | Articles |
| Yazarlar | |
| Yayımlanma Tarihi | 30 Aralık 2016 |
| Yayımlandığı Sayı | Yıl 2016 Cilt: 1 Sayı: 1 |
