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A robust algorithm for solving nonlinear programming problems. (English) Zbl 0999.65053
Summary: We introduce a new algorithm for solving nonlinear programming (NLP) problems. It is an extension of the algorithm of T. Guo and L. Kang [Wuhan Univ. J. Nat. Sci. 4, No. 4, 409-414 (1999; Zbl 0960.90083)] which possesses enhanced capabilities for solving NLP problems. These capabilities include: a) extending the variable subspace, b) adding a search process over subspaces and normalized constraints, c) using an adaptive penalty function, and d) adding the ability to deal with integer NLP problems, 0-1 NLP problems, and mixed-integer NLP problems which have equality constraints. These four enhancements increase the capabilities of the algorithm to solve nonlinear programming problems in a more robust and universal way. This paper presetns results of numerical experiments which show that the new algorithm is not only more robust and universal than its competitors, but also its performance level is higher than any others in the literature.

MSC:
65K05 Numerical mathematical programming methods
90C30 Nonlinear programming
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[1] DOI: 10.1007/BF02832273 · Zbl 0960.90083 · doi:10.1007/BF02832273
[2] Deb K., Evolutionary algorithm in engineering application pp 497– (1997) · doi:10.1007/978-3-662-03423-1_27
[3] Coello, C. A. Self-adaptive penalties for GA-based optimization. Proceedings of the Congress on Evolutionary Computation. Washington, D. C., USA. pp.537–580. IEEE Press.
[4] DOI: 10.1016/S0304-3975(99)00091-2 · Zbl 0938.68081 · doi:10.1016/S0304-3975(99)00091-2
[5] DOI: 10.1115/1.2912596 · doi:10.1115/1.2912596
[6] DOI: 10.1080/03052159108941075 · doi:10.1080/03052159108941075
[7] DOI: 10.1115/1.2919393 · doi:10.1115/1.2919393
[8] Cao, Y. J. and Wu, Q. H. ”Mechanical design optimization by mixed-variable evolutionary programming”. Proceedings of the 1997 International Conference on Evolutionary Computation. Indianapolis, Indiana. pp.443–446.
[9] Lin, Y.C. ”A hybrid method of evolutionary algorithms for mixed-integer nonlinear optimization problem”. Proceedings of Congress on Evolutionary Computation. pp.2159–2166. (3
[10] Hock W., ”Test examples for nonlinear programming codes” (1981) · Zbl 0452.90038 · doi:10.1007/978-3-642-48320-2
[11] Qin N., Quick learning SAS optimization software (1998)
[12] Michalewicz, Z., Logan, T. and Swaminathan, S. ”Evolutionary operations for continuous convex parameter space”. Proceedings of 3rd Annual Conf On Evolutionary Programming. pp.84–97. River Edge, NJ: World Scientific.
[13] Keane, A. J. ”Experience with optimizers in structural design”. Proceedings of the Conference on Adaptive Computing in Engineering Design and Control. pp.14–27.
[14] El-Beltagy M. A., Proceedings of Genetic and Evolutionary Computation pp 196– (1999)
[15] Qian S., ”Operation research” (1990)
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