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Hybridizing harmony search algorithm with sequential quadratic programming for engineering optimization problems. (English) Zbl 1194.74243
Summary: This study presents a hybrid harmony search algorithm (HHSA) to solve engineering optimization problems with continuous design variables. Although the harmony search algorithm (HSA) has proven its ability of finding near global regions within a reasonable time, it is comparatively inefficient in performing local search. In this study sequential quadratic programming (SQP) is employed to speed up local search and improve precision of the HSA solutions. Moreover, an empirical study is performed in order to determine the impact of various parameters of the HSA on convergence behavior. Various benchmark engineering optimization problems are used to illustrate the effectiveness and robustness of the proposed algorithm. Numerical results reveal that the proposed hybrid algorithm, in most cases is more effective than the HSA and other meta-heuristic or deterministic methods.

MSC:
74P10 Optimization of other properties in solid mechanics
90C20 Quadratic programming
Software:
Genocop
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[1] Houck, C.R.; Joines, J.A.; Kay, M.G., Comparison of genetic algorithms, random start, and two-opt switching for solving large location – allocation problems, Comput. operat. res., 23, 6, 587-596, (1996) · Zbl 0847.90091
[2] Houck, C.R.; Joines, J.A.; Wilson, J.R., Empirical investigation of the benefits of partial lamarckianism, Evol. comput., 5, 1, 31-60, (1997)
[3] Michalewicz, Z., Genetic algorithms+data structures=evolutionary programming, (1994), Springer-Verlag New York
[4] Joines, J.A.; Kay, M.G., Utilizing hybrid genetic algorithms, ()
[5] P. Moscato, On evolution, search, optimization, genetic algorithms and martial arts: towards memetic algorithms, California Institute of Technology, Pasadena, Technical Report 826, 1989.
[6] Moscato, P.; Cotta, C., A gentle introduction to memetic algorithms, () · Zbl 1107.90459
[7] H. Bersini, B. Renders, Hybridizing genetic algorithms with hill-climbing methods for global optimization: two possible ways, in: Proceedings of the IEEE International Symposium Evolutionary Computation, Orlando, FL, 1994.
[8] Merz, C.J., A principal components approach to combining regression estimates, Mach. learn., 36, 1, 9-32, (1999)
[9] He, J.; Xu, J.; Yao, X., Solving equations by hybrid evolutionary computation techniques, IEEE trans. evol. comput., 4, 3, 295-304, (2000)
[10] ()
[11] Mahdavi, M.; Fesanghary, M.; Damangir, E., An improved harmony search algorithm for solving optimization problems, Appl. math. comput., 188, 1567-1579, (2007) · Zbl 1119.65053
[12] Geem, Z.W.; Kim, J.H.; Loganathan, G.V., A new heuristic optimization algorithm: harmony search, Simulation, 76, 2, 60-68, (2001)
[13] Geem, Z.W.; Tseng, C.; Park, Y., Harmony search for generalized orienteering problem: best touring in China, Springer lecture notes comput. sci., 3412, 741-750, (2005)
[14] Kim, J.H.; Geem, Z.W.; Kim, E.S., Parameter estimation of the nonlinear muskingum model using harmony search, J. am. water resour. assoc., 37, 5, 1131-1138, (2001)
[15] Geem, Z.W.; Kim, J.H.; Loganathan, G.V., Harmony search optimization: application to pipe network design, Int. J. model. simulat., 22, 2, 125-133, (2002)
[16] Geem, Z.W., Optimal cost design of water distribution networks using harmony search, Engrg. optim., 38, 3, 259-280, (2006)
[17] Lee, K.S.; Geem, Z.W., A new structural optimization method based on the harmony search algorithm, Comput. struct., 82, 9-10, 781-798, (2004)
[18] Lee, K.S.; Geem, Z.W., A new meta-heuristic algorithm for continues engineering optimization: harmony search theory and practice, Comput. methods appl. mech. engrg., 194, 3902-3933, (2004) · Zbl 1096.74042
[19] M.G.H. Omran, M. Mahdavi, Global-best harmony search, Appl. Math. Comput. (2007), doi:10.1016/j.amc.2007.09.004. · Zbl 1146.90091
[20] Z.W. Geem, Novel derivative of harmony search algorithm for discrete design variables, Appl. Math. Comput., doi:10.1016/j.amc.2007.09.049. · Zbl 1146.90501
[21] P.T. Boggs, J.W. Tolle, Sequential quadratic programming, Acta Numer. 4 (1995) 1-52. · Zbl 0828.65060
[22] Spellucci, P., An SQP method for general nonlinear programs using only equality constrained subproblems, Math. program., 82, 413-448, (1998) · Zbl 0930.90082
[23] Himmelblau, D.M., Applied nonlinear programming, (1972), McGraw-Hill New York · Zbl 0521.93057
[24] Gen, M.; Cheng, R., Genetic algorithms & engineering design, (1997), Wiley New York
[25] Coello, C.A.C., Use of a self-adaptive penalty approach for engineering optimization problems, Comput. ind., 41, 2, 113-127, (2000)
[26] Homaifar, A.; Lai, S.H.-V.; Qi, X., Constrained optimization via genetic algorithms, Simulation, 62, 4, 242-254, (1994)
[27] Y. Shi, R.C. Eberhart, A modified particle swarm optimizer, in: Proceedings of the International Congress on Evolutionary Computation 1998, IEEE Service Center, Piscataway, NJ, 1998.
[28] Deb, K., An efficient constraint handling method for genetic algorithms, Comput. methods appl. mech. engrg., 186, 311-338, (2000) · Zbl 1028.90533
[29] Michalewicz, Z., Genetic algorithms, numerical optimization, and constraints, ()
[30] Reklaitis, G.V.; Ravindran, A.; Ragsdell, K.M., Engineering optimization methods and applications, (1983), Wiley New York
[31] Siddall, J.N., Analytical decision-making in engineering design, (1972), Prentice-Hall New Jersey
[32] Ragsdell, K.M.; Phillips, D.T., Optimal design of a class of welded structures using geometric programming, ASME J. engrg. ind. ser. B, 98, 3, 1021-1025, (1976)
[33] Deb, K., Optimal design of a welded beam via genetic algorithms, Aiaa j., 29, 11, 2013-2015, (1991)
[34] Coello, C.A.C., Constraint-handling using an evolutionary multiobjective optimization technique, Civil engrg. environ. syst., 17, 319-346, (2000)
[35] L.A. Schmit, J.H. Miura, Approximation Concepts for Efficient Structural Synthesis, NASA CR-2552, NASA, Washington, 1976.
[36] Venkayya, V.B., Design of optimum structures, Comput. struct., 1, 1-2, 265-309, (1971)
[37] P. Rizzi, Optimization of multi-constrained structures based on optimality criteria, in: Conference on AIAA/ASME/SAE 17th Structures, Structural Dynamics, and Materials, King of Drussia, Pennsylvania, 1976.
[38] Khan, M.R.; Willmert, K.D.; Thornton, W.A., An optimality criterion method for large-scale structures, Aiaa j., 17, 7, 753-761, (1979)
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