Abstract
In this paper, the basic characteristics of particle swarm optimization (PSO) for the global search are discussed at first, and then the PSO for the mixed discrete nonlinear problems (MDNLP) is suggested. The penalty function approach to handle the discrete design variables is employed, in which the discrete design variables are handled as the continuous ones by penalizing at the intervals. As a result, a useful method to determine the penalty parameter of penalty term for the discrete design variables is proposed. Through typical mathematical and structural optimization problems, the validity of the proposed approach for the MDNLP is examined.
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References
Arora JS et al (1994) Methods for optimization of nonlinear problems with discrete variables: a review. Struct Optim 8:69–85
Fourie PC, Groenwold AA (2002) The particle swarm optimization algorithm in size and shape optimization. Struct Multidisc Optim 23(4):259–267
Fu JF et al (1991) A mixed integer-discrete continuous programming and its application to engineering design optimization. Eng Optim 17:263–280
He S et al (2004) An improved particle swarm optimizer for mechanical design optimization problems. Eng Optim 35–5:585–605
Hsu YH et al (1995) A two stage sequential approximation method for non-linear discrete variable optimization. ASME Design Engineering Technical Conference, Boston, pp 197–202
Kannan BK, Kramer SN (1994) An augmented lagrange multiplier based method for mixed integer discrete continuous optimization and its applications to mechanical design. Trans ASME J Mech Des 116:405–411
Kennedy J, Eberhart RC (1997) A discrete binary version of the particle swarm optimization algorithm. Proceedings of the 1997 Conference on Systems. Man, and Cybernetics, pp 4104–4109
Kennedy J, Eberhart RC (2001) Swarm intelligence. Morgan Kaufmann, San Mateo
Kitayama S, Yamazaki K (2005) Generalized random tunneling algorithm for continuous design variables. Trans ASME J Mech Des 127:408–414
Parsopoulos KE, Vrahatis MN (2002) Recent approaches to global optimization problems through particle swarm optimization. Nat Comput 1:235–306
Qian Z et al (1993) A genetic algorithm for solving mixed discrete optimization problems, DE-Vol.65-1. Adv Des Autom 1:499–503
Rao SS (1996) Engineering optimization: theory and practice. Wiley InterScience, New York
Sandgren E (1990) Nonlinear and discrete programming in mechanical design optimization. Trans ASME J Mech Des 112:223–229
Shin DK et al (1990) A penalty approach for nonlinear optimization with discrete design variables. Eng Optim 16:29–42
Venter G, Sobieski JS (2003) Particle swarm optimization. AIAA J 41(8):1583–1589
Venter G, Sobieski JS (2004) Multidisciplinary optimization of a transport aircraft wing using particle swarm optimization. Struct Multidisc Optim 26(1–2):121–131
Yoshida H et al (2000) A particle swarm optimization for reactive power and voltage control considering voltage security assessment. IEEE Trans Power Syst 15(4):1232–1239
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Kitayama, S., Arakawa, M. & Yamazaki, K. Penalty function approach for the mixed discrete nonlinear problems by particle swarm optimization. Struct Multidisc Optim 32, 191–202 (2006). https://doi.org/10.1007/s00158-006-0021-2
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DOI: https://doi.org/10.1007/s00158-006-0021-2