A hybrid PSO approach for solving non-convex optimization problems

• Autorzy: Ganesan T. , Vasant P. , Elamvazuthy I.
• Języki publikacji: EN

Abstrakty

EN

The aim of this paper is to propose an improved particle swarm optimization (PSO) procedure for non-convex optimization problems. This approach embeds classical methods which are the Kuhn-Tucker (KT) conditions and the Hessian matrix into the fitness function. This generates a semi-classical PSO algorithm (SPSO). The classical component improves the PSO method in terms of its capacity to search for optimal solutions in non-convex scenarios. In this work, the development and the testing of the refined the SPSO algorithm was carried out. The SPSO algorithm was tested against two engineering design problems which were; ‘optimization of the design of a pressure vessel’ (P1) and the ‘optimization of the design of a tension/compression spring’ (P2). The computational performance of the SPSO algorithm was then compared against the modified particle swarm optimization (PSO) algorithm of previous work on the same engineering problems. Comparative studies and analysis were then carried out based on the optimized results. It was observed that the SPSO provides a better minimum with a higher quality constraint satisfaction as compared to the PSO approach in the previous work.

Słowa kluczowe

EN

Kuhn-Tucker conditions (KT); non-convex optimization; particle swarm optimization (PSO); semi-classical particle swarm optimization (SPSO)

• Wydawca: Polish Academy of Sciences, Committee of Automatic Control and Robotics
• Czasopismo: Archives of Control Sciences
• Rocznik: 2012
• Tom: Vol. 22, no. 1
• Strony: 87--105
• Opis fizyczny: Bibliogr. 22 poz., rys., tab., wzory

Twórcy

autor

Ganesan T.

autor

Vasant P.

autor

Elamvazuthy I.

• Department of Mechanical Engineering, University Technology Petronas, Malaysia

Bibliografia

• [1] J. V. Outrata, M. Kocvara and J. Zowe: Nonsmooth approach to optimization problems with equilibrium constraints. Nonconvex optimization and its applications. Kluwer Academic Publishers, Dordrecht, The Netherlands, 1998.
• [2] D. P. Bertsekas: Nonlinear programming. Athena Scientific, Belmont, Massachusetts, second ed. (1999).
• [3] Y. Chen and M. Florian: The nonlinear bilevel programming problem: Formulations, regularity and optimality conditions. Optimization, 32 (1995), 193-209.
• [4] J. H. Holland: Adaptation in natural and artificial systems: An Introductory analysis with applications to biology. Control and Artificial Intelligence. MIT Press, USA, 1992.
• [5] J. R. Koza: Genetic programming: On the programming of computers by means of natural selection. MIT Press, USA, 1992.
• [6] J. Kennedy (1995) R. Eberhart: Particle swarm optimization. IEEE Proceedings of the Int. Conf. on Neural Networks, Perth, Australia, (1995).
• [7] N. Phuangpornpitak, W. Prommee, S. Tia and W. Phuangpornpitak: A study of particle swarm technique for renewable energy power systems. PEA-AIT Int. Conf. on Energy and Sustainable Development: Issues and Strategies, Thailand, (2010), 1-7.
• [8] V. N. Dieu and W. Ongsakul: Economic dispatch with emission and transmission constraints by augmented Lagrange Hopfield network. Trans. in Power System Optimization (GJTO) www.pcoglobal.com/gjto.htm
• [9] V. N. Dieu and W. Ongsakul: Enhanced merit order and augmented Lagrange Hopfield network for ramp rate constrained unit commitment. Proc. of IEEE Power System Society General Meeting, Canada, (2006)
• [10] Y. Huang and C. Yu: Improved Lagrange nonlinear programming neural networks for inequality constraints. Proc. of Int. Joint Conf. on Neural Networks, Orlando, Florida, USA, (2007).
• [11] H. W. Kuhn and A. W. Tucker: Nonlinear programming. Proc. of 2nd Berkeley Symp., Berkeley, University of California Press. (1951), 481-492.
• [12] K. Binmore and J. Davies: Calculus concepts and methods. Cambridge University Press, 2007.
• [13] E. Sandgren: Nonlinear integer and discrete programming in mechanical design optimization. J. of Mechanical Deigns - T. ASME, 112(2), (1990), 223-229.
• [14] A. Belegundu: A study of mathematical programming methods for structural optimization. PhD thesis, Department of Civil Environmental Engineering, University of Iowa, Iowa, 1982.
• [15] C. A. Coello: Solving engineering optimization problems with simple constrained particle swarm optimizer. Informatica, 32 (2008), 319-326.
• [16] Y. Shi and R. Eberhart: A modified particle swarm optimizer. Proc. of the IEEE Int. Conf. on Evolutionary Computation, (1998), 69-73.
• [17] F. van Den Bergh: An analysis of particle swarm optimizers. PhD thesis, University of Pretoria, 2001.
• [18] E. Zitzler, M. Laumanns and S. Bleuler: A tutorial on evolutionary multiobjective optimization. In X. Gandibleux and others, editors, Metaheuristics for Multiobjective Optimisation, Lecture Notes in Economics and Mathematical Systems, Springer, 2004.
• [19] H. E. Rose: Linear algebra. A pure mathematical approach. Springer, 2002, 57-60.
• [20] F. Glover: Tabu search, Part I. ORSA J. on Computing, 1(3), (1989), 190-206.
• [21] J. A. Bland and G.P. Dawson: Tabu search and design optimization. Computer - aided design, 23(3) (1991), 195-201.
• [22] A. Thesen: Design and evaluation of tabu search algorithms for Mmultiprocessor scheuling. J. of Hueristics, 4 (1998), 141-160.