Solution of singular optimal control problems using the improved differential evolution algorithm

• Autorzy: Lobato F. S. , Steffen, Jr V. , Silva Neto A. J.
• Języki publikacji: EN

Abstrakty

EN

The Differential Evolution algorithm, like other evolutionary techniques, presents as main disadvantage the high number of objective function evaluations as compared with classical methods. To overcome this disadvantage, this work proposes a new strategy for the dynamic updating of the population size to reduce the number of objective function evaluations. This strategy is based on the definition of convergence rate to evaluate the homogeneity of the population in the evolutionary process. The methodology is applied to the solution of singular optimal control problems in chemical and mechanical engineering. The results demonstrated that the methodology proposed represents a promising alternative as compared with other competing strategies.

Słowa kluczowe

EN

differential evolution algorithm; optimal control; dynamic updating; population; convergence rate; mechanical engineering; chemical engineering

• Wydawca: University of Social Sciences
• Czasopismo: Journal of Artificial Intelligence and Soft Computing Research
• Rocznik: 2011
• Tom: Vol. 1, No. 3
• Strony: 195--206
• Opis fizyczny: Bibliogr. 40 poz., rys.

Twórcy

autor

Lobato F. S.

• School of Chemical Engineering, Federal University of Uberlàndia

autor

Steffen, Jr V.

• School of Mechanical Engineering, Federal University of Uberlàndia, Av. Joaõ Naves de Ávila 2121, Campus Santa Mônica, P.O. Box 593, 38408-144, Uberlândia-MG, Brazil

autor

Silva Neto A. J.

• Department of Mechanical Engineering and Energy, Polytechnic Institute - IPRJ, State University of Rio de Janeiro, Rua Alberto Rangel, s/n◦, Vila Nova 28630-050, Nova Friburgo-RJ, Brazil

Bibliografia

• [1] A. E. Bryson and Y. C. Ho. Applied Optimal Control. Hemisphere Publishing, Washington, 1975.
• [2] W. F. Feehery. Dynamic Optimization with Path Constraints. PhD thesis, MIT, 1998.
• [3] F. S. Lobato, Hybrid Approach for Dynamic Optimization Problems, M.Sc. Thesis, FEQUI/UFU, Uberlándia, Brazil, 2004 (in portuguese).
• [4] O. von Stryk and R. Bulirsch, Direct and Indirect Methods for Trajectory Optimization. Annals SOLUTION of Operations Research, Vol. 37, pages 357–373,1992.
• [5] O. von Stryk, User’s Guide for DIRCOL - A Direct Collocation Method for the Numerical Solution of Optimal Control Problems. Technische Universitat Darmastadt, Fachgebiet Simulation and Systemoptimierung (SIM), 1999.
• [6] L. T. Biegler, A. M. Cervantes and A. Wachter, Advances in Simultaneous Strategies for Dynamic Process Optimization. Chemical Engineering Science, Vol. 57, pages 575–593, 2002.
• [7] R. Storn and K. V. Price, Differential Evolution: A Simple and Efficient Adaptive Scheme for Global Optimization Over Continuous Spaces. International Computer Science Institute, Vol. 12, pages 1–16, 1995.
• [8] M. D. Kapadi and R. D. Gudi, Optimal Control of Fed-batch Fermentation involving Multiple Feeds using Differential Evolution, Process Biochemistry, Vol. 39, pages 1709–1721.
• [9] F. S. Lobato, L. C. Oliveira-Lopes, V. V. Murata and V. Steffen Jr., Solution of Multi-objective Optimal Control Problems with Index Fluctuation using Differential Evolution. 6th Brazilian Conference on Dynamics, Control and Applications – DINCON, 2007.
• [10] F. Wang and J. Chiou, Optimal Control and Optimal Time Location Problems of Differential-Algebraic Systems by Differential Evolution, Ind. Eng. Chem. Res., Vol. 36, pages 5348–5357, 1997.
• [11] A. Chowdhury, A. Ghosh, S. Das and A. Abraham, A Hybrid Evolutionary Direct Search Technique for Solving Optimal Control Problems, 10th International Conference on Hybrid Intelligent Systems (HIS 2010), Atlanta, USA, 2010.
• [12] S. Vellev, An Adaptive Genetic Algorithm with Dynamic Population Size for Optimizing Join Queries, In International Conference: Intelligent Information and Engineering Systems, INFOS 2008, Varna, Bulgaria, June-July, 2008.
• [13] E. Balsa-Canto, A. A. Alonso and V. S. Vassiliadis, Efficient Optimal Control of Bioprocess using Second-order Information, Ind. Eng. Chem. Res., Vol. 39, pages 4287–4295, 2000.
• [14] L. T. Biegler and V. M. Zavala, Large-scale Nonlinear Programming using IPOPT: An Integrating Framework for Enterprise-Wide Dynamic Optimization, Computers and Chemical Engineering, Vol. 33, pages 575–582, 2009.
• [15] R. M. Storn, K. V. Price and J. A. Lampinen, Differential Evolution - A Practical Approach to Global Optimization. Springer - Natural Computing Series, 2005.
• [16] S. Das and P. N. Suganthan, Differential Evolution: A Survey of the State-of-the-Art, IEEE Trans. on Evolutionary Computation, DOI:10.1109/TEVC.2010.2059031, 2011.
• [17] R. Storn, Differential Evolution Design of an IIRfilter with Requirements for Magnitude and Group Delay, International Computer Science Institute, TR-95-026, 1995.
• [18] B. V. Babu and R. P. Singh. Synthesis and Optimization of Heat Integrated Distillation Systems using Differential Evolution, in Proceedings of All-India seminar on Chemical Engineering Progress on Resource Development.
• [19] F. S. Lobato and V. Steffen Jr., Engineering System Design with Multi-objective Differential Evolution, 19 International Congress of Mechanical Engineering - COBEM 2007.
• [20] F. S. Lobato, E. B. Arruda, M. A. S. Barrozo and V. Steffen Jr., Estimation of Drying Parameters in Rotary Dryers using Differential Evolution. Journal of Physics. Conference Series, Vol. 135, pages 1–8, 2008.
• [21] F. S. Lobato, V. Steffen Jr. and A. J. Silva Neto. Solution of Inverse Radiative Transfer Problems in Two-layer Participating Media with Differential Evolution, EngOpt 2008 - International Conference on Engineering Optimization, Rio de Janeiro - Brasil, 2008.
• [22] V. C. Mariani, A. G. B. Lima and L. S. Coelho, Apparent Thermal Diffusivity Estimation of the Banana During Drying using Inverse Method, Journal of Food Engineering, Vol. 85, pp. 569–579, 2008.
• [23] F. S. Lobato, C. E. Figueira, R. R. Soares and V. Steffen Jr., A Comparative Study of Gibbs Free Energy Minimization in a Real System Using Heuristic Methods. Computer-Aided Chemical Engineering, Vol .27, pages 1059–1064, 2009.
• [24] F. S. Lobato, V. Steffen Jr. and A. J. Silva Neto, Estimation of Space-dependent Single Scattering Albedo in Radiative Transfer Problems, Inverse Problems, Design and Optimization Symposium, João Pessoa, Brazil, August 25–27, 2010.
• [25] F. S. Lobato, V. Steffen Jr. and A. J. Silva Neto, AComparative Study of the Application of Differential Evolution and Simulated Annealing in Inverse Radiative Transfer Problems. Journal of the Brazilian Society of Mechanical Sciences and Engineering, Vol. XXXII, pages 518–526, 2010.
• [26] F. S. Lobato, V. Steffen Jr. and A. J. Silva Neto, Self-Adaptive Differential Evolution Based on the Concept of Population Diversity Applied to Simultaneous Estimation of Anisotropic Scattering Phase Function, Albedo and Optical Thickness. Computer Modeling in Engineering & Sciences, Vol. 1, pages 1–17, 2010.
• [27] A. Biswas, S. Das, A. Abraham and S. Dasgupta, Design of Fractional order PID Controllers with an Improved Differential Evolution, Engineering Applications of Artificial Intelligence, Elsevier Science, Vol. 22, No. 2, pages 343–350, 2009.
• [28] S. Y. Sun, Yc. Quiang, Y. Liang, Y. Liu and Q. Pan, Dynamic Population Size Based on Particle Swarm Optimization, ISICA 2007, Spring-Verlag Berlin, pages 382–392, 2007.
• [29] D. J. Gunn and W. J. Thomas, Mass Transport and Chemical Reaction in Multifunctional Catalyst Systems, Chemical Engineering Science, vol. 20, pages 89–100, 1965.
• [30] J. S. Logsdon, Efficient Determination of Optimal Control Profiles for Differential Algebraic Systems, Ph.D. thesis, Carnegie Mellon University, Pittsburgh, PA, 1990.
• [31] V. Vassiliadis, Computational Solution of Dynamic Optimization Problems with General Differential-Algebraic Constraints, Ph.D. thesis, University of London, London, UK, 1993.
• [32] F. S. Lobato and V. Steffen Jr., Solution of Optimal Control Problems using Multi-Particle Collisionalgoritm, 9th Conference on Dynamics, Control and Their Applications, June 07–11, 2010.
• [33] M. L. Bell and R. W. H. Sargent, Optimal Control of Inequality Constrained DAE Systems, Computersand Chemical Engineering, Vol. 24, pages2385–2404, 2000.
• [34] O. Bilous and N. R. Amundson, Optimum Temperature Gradients in Tubular Reactors II: Numerical Study, Chemical Engineering Science, Vol. 5,pages 115–126, 1956.
• [35] G. Marroquin andW. L. Luyben, Practical Control Studies of Batch Reactors using Realistic Mathematical Models, Chemical Engineering Science, Vol. 28, pages 993–1003, 1973.
• [36] R. Luus and O. N. Okongwu, Towards Practical Optimal Control of Batch Reactors, Chemical Engineering Journal, Vol. 75, pages 1–9, 1999.
• [37] H. S. Tsien and R. C. Evans, Optimum Thrust Programming for a Sounding Rocket, American Rocket Society Journal, Vol. 21, pages 99–107, 1951.
• [38] B. Garfinkel, A Solution of the Goddard Problem, SIAM Journal, Vol. 1, pages 349–368, 1963.
• [39] A. K. Qin, V. L. Huang, and P. N. Suganthan, Differential Evolution Algorithm with Strategy Adaptation for Global Numerical Optimization, IEEE Trans. on Evolutionary Computations, DOI: 10.1109/TEVC.2008.927706, pages 398–417, 2009.
• [40] R. Mallipeddi, P. N. Suganthan, Q. K. Pan and M. F. Tasgetiren, Differential Evolution Algorithm with Ensemble of Parameters and Mutation Strategies, Applied Soft Computing, DOI:10.1016/j.asoc.2010.04.024, 2011 (Accepted).