Paper:

# Real-Coded Genetic Algorithm for Solving Generalized Polynomial Programming Problems

## Jui-Yu Wu and Yun-Kung Chung

Department of Industrial Engineering and Management, Yuan Ze University, 135 Yuan-Tung Road, Chung-Li 320, Taiwan

Generalized polynomial programming (GPP) is a nonlinear programming (NLP) method based on a nonconvex objective function, which is subject to nonconvex inequality constraints. Hence, a GPP problem has multiple local optima in its constrained solution space. General NLP techniques use local optimization, and therefore do not easily solve GPP problems. Some deterministic global optimization approaches have been developed to overcome this drawback of NLP methods. Although these approaches yield a global solution to a GPP problem, they can be mathematically tedious. Therefore, this study presents a real-coded genetic algorithm (RGA), which is a stochastic global optimization method, to find a global solution to a GPP problem. The proposed RGA is used to solve a set of GPP problems. The best solution obtained by the RGA is compared with the known global solution to each test problem. Numerical results show that the proposed RGA converges to a global solution to a GPP problem.

*J. Adv. Comput. Intell. Intell. Inform.*, Vol.11, No.4, pp. 358-364, 2007.

- [1] C. A. Coello Coello, “Theoretical and Numerical Constraint-Handling Techniques Used with Evolutionary Algorithms: A Survey of the State of the Art,” Computer Methods in Applied Mechanics and Engineering, 191, 11-12, pp. 1245-1287, 2002.
- [2] K. Deb, “An Efficient Constraint Handling Method for Genetic Algorithms,” Computer Methods in Applied Mechanics and Engineering, 186, 2-4, pp. 311-338, 2000.
- [3] L. J. Eshelman and J. D. Schaffer, “Real-Coded Genetic Algorithms and Interval-Schemata,” Foundations of Genetic Algorithms 2, San Mateo, CA, USA, pp. 187-202, 1993.
- [4] C. A. Floudas, P. M. Pardalos et al., “Handbook of Test Problems in Local and Global Optimization,” Kluwer, Boston, USA, pp. 85-105, 1999.
- [5] C. A. Floudas, “Deterministic Global Optimization,” Kluwer, Boston, USA, pp. 257-287, 1999.
- [6] C. R. Houck, J. A. Joines et al., “A Genetic Algorithm for Function Optimization: A Matlab Implementation,” North Carolina State University, Raleigh, NC, Technical Report NSCU-IE, September, 1995.
- [7] T. R. Jefferson and C. H. Scott, “Generalized Geometric Programming Applied to Problems of Optimal Control: I. Theory,” J. of Optimization Theory and Applications, Vol.26, No.1, pp. 117-129, 1978.
- [8] K. Y. Lee and P. S. Mohamed, “A Real-Coded Genetic Algorithm Involving a Hybrid Crossover Method for Power Plant Control System Design,” Proc. of the 2002 Congress on Evolutionary Computation, Honolulu, HI, USA, pp. 1069-1074, 2002.
- [9] C. D. Maranas and C. A. Floudas, “Global Optimization in Generalized Geometric Programming,” Computers and Chemical Engineering, Vol.21, No.4, pp. 351-369, 1997.
- [10] Z. Michalewicz, “Genetic Algorithms + Data Structures = Evolution Programs,” Springer, NY, USA, 1999.
- [11] U. Passy, “Generalized Weighted Mean Programming,” SIAM J. on Applied Mathematics, Vol.20, No.4, pp. 763-778, 1971.
- [12] U. Passy and D. J. Wilde, “Generalized Polynomial Optimization,” SIAM J. on Applied Mathematics, Vol.15, No.5, pp. 1344-1356, 1967.
- [13] M. J. Rijckaert and X. M. Martens, “Comparison of Generalized Geometric Programming Algorithms,” J. of Optimization Theory and Applications, Vol.26, No.2, pp. 205-242, 1978.
- [14] P. Shen and K. Zhang, “Global Optimization of Signomial Geometric Progranning Using Linear Relaxation,” Applied Mathematics and Computation, Vol.150, No.1, pp. 99-114, 2004.
- [15] P. Siarry, A. Pétrowski et al., “A Multipopulation Genetic Algorithm Aimed at Multimodal Optimization,” Advances in Engineering Software, Vol.33, No.4, pp. 207-213, 2002.

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