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Solving constrained optimization problems using a novel genetic algorithm. (English) Zbl 1159.65063
Summary: A novel genetic algorithm is described in this paper for the problem of constrained optimization. The algorithm incorporates modified genetic operators that preserve the feasibility of the trial solutions encoded in the chromosomes, the stochastic application of a local search procedure and a stopping rule which is based on asymptotic considerations. The algorithm is tested on a series of well-known test problems and a comparison is made against the algorithms C-SOMGA and DONLP2.
65K05Mathematical programming (numerical methods)
90C15Stochastic programming
[1]Sauer, O. A.; Shepard, D. M.; Mackie, T. R.: Application of constrained optimization to radiotherapy planning, Medical physics 26, 2359-2366 (1999)
[2]Birgin, E. G.; Chambouleyron, I.; Martínez, J. M.: Estimation of the optical constants and the thickness of thin films using unconstrained optimization, Journal of computational physics 151, 862-880 (1999) · Zbl 1017.74501 · doi:10.1006/jcph.1999.6224
[3]Yang, C.; Meza, J. C.; Wang, L. W.: A constrained optimization algorithm for total energy minimization in electronic structure calculations, Journal of computational physics 217, 709-721 (2006) · Zbl 1102.81340 · doi:10.1016/j.jcp.2006.01.030
[4]Lee, K. D.; Eyi, S.: Transonic airfoil design by constrained optimization, Journal of aircraft 30, 805-806 (1993)
[5]F.P. Seelos, R.E. Arvidson, Bounded variable least squares – application of a constrained optimization algorithm to the analysis of TES Emissivity Spectra, in: 34th Annual Lunar and Planetary Science Conference, March 17 – 21, 2003, League City, Texas (abstract no. 1817).
[6]Field, M. J.: Constrained optimization of ab initio and semiempirical Hartree – Fock wave functions using direct minimization or simulated annealing, Journal of physical chemistry 95, 5104-5108 (1991)
[7]Williams, G. A.; Dugan, J. M.; Altman, R. B.: Constrained global optimization for estimating molecular structure from atomic distances, Journal of computational biology 8, 523-547 (2001)
[8]Baker, J.; Bergeron, D.: Constrained optimization in Cartesian coordinates, Journal of computational chemistry 14, 1339-1346 (1993)
[9]Bertram, J. E. A.; Ruina, A.: Multiple walking speed – frequency relations are predicted by constrained optimization, Journal of theoretical biology 209, 445-453 (2001)
[10]Bertram, J. E. A.: Constrained optimization in human walking: cost minimization and gait plasticity, Journal of experimental biology 208, 979-991 (2005)
[11]I. Iakovidis, R.M. Gulrajani, Regularization of the inverse epicardial solution using linearly constrained optimization, in: Engineering in Medicine and Biology Society, Proceedings of the Annual International Conference of the IEEE Publication Date: 31 October – 3 November, 1991. vol. 13, pp. 698 – 699.
[12]Bertsekas, D. P.: Constrained optimization and Lagrange multiplier methods, (1982) · Zbl 0572.90067
[13]Bertsekas, D. P.; Ozdaglar, A. E.: Pseudonormality and a Lagrange multiplier theory for constrained optimization, Journal of optimization theory and applications 114, 287-343 (2004) · Zbl 1026.90092 · doi:10.1023/A:1016083601322
[14]Gill, P. E.; Murray, W.: The computation of Lagrange-multiplier estimates for constrained minimization, Mathematical programming 17, 32-60 (1979) · Zbl 0423.90073 · doi:10.1007/BF01588224
[15]Powell, M. J. D.; Yuan, Y.: A trust region algorithm for equality constrained optimization, Mathematical programming 49, 189-211 (2005) · Zbl 0816.90121 · doi:10.1007/BF01588787
[16]Byrd, R. H.; Schnabel, R. B.; Shultz, G. A.: A trust region algorithm for nonlinearly constrained optimization, SIAM journal on numerical analysis 24, 1152-1170 (1987) · Zbl 0631.65068 · doi:10.1137/0724076
[17]D.M. Gay, A trust-region approach to linearly constrained optimization, Lecture Notes in Mathematics, vol. 1066, 1984, pp. 72 – 105 (Áñãåíôéí (ñïéôåéêüó)). · Zbl 0531.65036
[18]Markót, M. Cs.; Fernández, J.; Casado, L. G.; Csendes, T.: New interval methods for constrained global optimization, Mathematical programming 106, 287-318 (2005) · Zbl 1134.90497 · doi:10.1007/s10107-005-0607-2
[19]Ichida, K.: Constrained optimization using interval analysis, Computers and industrial engineering 31, 933-937 (1996)
[20]Lillo, W. E.; Hui, S.; Zak, S. H.: Neural networks for constrained optimization problems, International journal of circuit theory and applications 21, 385-399 (1993) · Zbl 0800.68678 · doi:10.1002/cta.4490210408
[21]Lillo, W. E.; Loh, M. H.; Hui, S.; Zak, S. H.: On solving constrained optimization problems with neural networks: a penalty method approach, IEEE transactions on neural networks 4, 931-940 (1993)
[22]Zhang, S.; Zhu, X.; Zou, L. H.: Second-order neural nets for constrained optimization, IEEE transactions on neural networks 3, 1021-1024 (1992)
[23]Lucidi, S.; Sciandrone, M.; Tseng, P.: Objective-derivative-free methods for constrained optimization, Mathematical programming 92, 37-59 (1999) · Zbl 1024.90062 · doi:10.1007/s101070100266
[24]G. Liuzzi, S. Lucidi, A derivative-free algorithm for nonlinear programming, TR 17/05, Department of Computer and Systems Science, Antonio Ruberti, University of Rome, La Sapienza, 2005.
[25]Subrahmanyam, M. B.: An extension of the simplex method to constrained nonlinear optimization, Journal of optimization theory and applications 62, 311-319 (1989) · Zbl 0651.90062 · doi:10.1007/BF00941060
[26]Deep, K.; Dipti: A self-organizing migrating genetic algorithm for constrained optimization, Applied mathematics and computation 198, 237-250 (2008) · Zbl 1137.65040 · doi:10.1016/j.amc.2007.08.032
[27]Homaifar, A.: Constrained optimization via genetic algorithms, Simulation 62, 242-253 (1994)
[28]Venkatraman, S.; Yen, G. G.: A generic framework for constrained optimization using genetic algorithms, IEEE transactions on evolutionary computation 9, 424-435 (2005)
[29]Michalewicz, Z.; Schoenauer, M.: Evolutionary algorithms for constrained parameter optimization problems, Evolutionary computation 4, 1-32 (1996)
[30]Summanwar, V. S.; Jayaraman, V. K.; Kulkarni, B. D.; Kusumakar, H. S.; Gupta, K.; Rajesh, J.: Solution of constrained optimization problems by multi-objective genetic algorithm, Computers and chemical engineering 26, 1481-1492 (2002)
[31]He, Q.; Wang, L.: A hybrid particle swarm optimization with a feasibility – based rule for constrained optimization, Applied mathematics and computation 186, 1407-1422 (2007) · Zbl 1117.65088 · doi:10.1016/j.amc.2006.07.134
[32]X.H.Hu, R.C. Eberhart, Solving constrained nonlinear optimization problems with particle swarm optimization, in: N. Callaos (Ed.), Proceedings of the Sixth World Multiconference on Systematics, Cybergenetics and Informatics, Orlando, FL, 2002, pp. 203 – 206.
[33]Sarimveis, H.; Nikolakopoulos, A.: A line up evolutionary algorithm for solving nonlinear constrained optimization problems, Computers and operations research 32, 1499-1514 (2005) · Zbl 1122.90433 · doi:10.1016/j.cor.2003.11.015
[34]Becerra, R. L.; Coello, C. A. C.: Cultured differential evolution for constrained optimization, Computer methods in applied mechanics and engineering 195, 4303-4322 (2006) · Zbl 1123.74039 · doi:10.1016/j.cma.2005.09.006
[35]M.J.D. Powell, A Direct search optimization method that models the objective and constraint functions by linear interpolation, DAMTP/NA5, Cambridge, England.
[36]Tsoulos, I. G.: Modifications of real code genetic algorithm for global optimization, Applied mathematics and computation 203, 598-607 (2008) · Zbl 1157.65391 · doi:10.1016/j.amc.2008.05.005
[37]Levy, A. V.; Montalvo, A.: The tunneling algorithm for global optimization of functions, SIAM journal of scientific and statistical computing 6, 15-29 (1985) · Zbl 0601.65050 · doi:10.1137/0906002
[38]Salkin, H. M.: Integer programming, (1975) · Zbl 0319.90038
[39]Himmelblau, D. M.: Applied nonlinear programming, (1972) · Zbl 0241.90051
[40]Hess, R.: A heuristic search for estimating a global solution of non convex programming problems, Operations research 21, 1267-1280 (1973) · Zbl 0281.90067 · doi:10.1287/opre.21.6.1267
[41]Schittkowski, K.: More examples for mathematical programming codes, Lecture notes in economics and mathematical systems, 282 (1987) · Zbl 0658.90060
[42]Chootinan, P.; Chen, A.: Constraint handling in genetic algorithms using a gradient – based repair method, Computer and operations research 33, 2263-2281 (2006) · Zbl 1086.90058 · doi:10.1016/j.cor.2005.02.002
[43]Lin, Y. C.; Hwang, K. S.; Wang, F. S.: Hybrid differential evolution with multiplier updating method for nonlinear constrained optimization problems, , 872-877 (2002)
[44]J.J. Liang, T.P. Runarsson, E. Mezura-Montes, M. Clerc, P.N. Suganthan, C.A.C. Coello, K. Deb, Problem definitions and evaluation criteria for the CEC2006 special session on constrained real-parameter optimization. lt;http://www.ntu.edu.sg/home/EPNSugan/indexfiles/CEC-06/CEC06.htmgt;.
[45]Coello, C. A. C.: Use of a self-adaptive penalty approach for engineering optimization problems, Computers and industrial engineering 41, 113-127 (2000)
[46]Spelluci, P.: An SQP method for general nonlinear programs using only equality constrained subproblems, Mathematical programming 82, 413-448 (1998) · Zbl 0930.90082 · doi:10.1007/BF01580078
[47]Spelluci, P.: A new technique for inconsistent problems in the SQP method, Mathematical methods of operational research 47, 355-400 (1998)