Abstract
Equality constraints are difficult to handle by any optimization algorithm, including evolutionary methods. Much of the existing studies have concentrated on handling inequality constraints. Such methods may or may not work well in handling equality constraints. The presence of equality constraints in an optimization problem decreases the feasible region significantly. In this paper, we borrow our existing hybrid evolutionary-cum-classical approach developed for inequality constraints and modify it to be suitable for handling equality constraints. This modified hybrid approach uses an evolutionary multi-objective optimization (EMO) algorithm to find a trade-off frontier in terms of minimizing the objective function and the constraint violation. A suitable penalty parameter is obtained from the frontier and then used to form a penalized objective function. The procedure is repeated after a few generations for the hybrid procedure to adaptively find the constrained minimum. Unlike other equality constraint handling methods, our proposed procedure does not require the equality constraints to be transformed into an inequality constraint. We validate the efficiency of our method on six problems with only equality constraints and two problems with mixed equality and inequality constraints.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Deb, K.: Optimization for Engineering Design: Algorithms and Examples. Prentice-Hall, New Delhi (1995)
Reklaitis, G.V., Ravindran, A., Ragsdell, K.M.: Engineering Optimization Methods and Applications. Wiley, New York (1983)
Richardson, J.T., Palmer, M.R., Liepins, G.E., Hilliard, M.R.: Some guidelines for genetic algorithms with penalty functions. In: Proceedings of the 3rd International Conference on Genetic Algorithms, pp. 191–197. Morgan Kaufmann Publishers Inc., San Francisco (1989)
Gen, M., Cheng, R.: A survey of penalty techniques in genetic algorithms. In: Proceedings of IEEE International Conference on Evolutionary Computation. IEEE Press, Los Alamitos (1996)
Deb, K.: An efficient constraint handling method for genetic algorithms. Computer Methods in Applied Mechanics and Engineering 186(2-4), 311–338 (2000)
Coello, C., Carlos, A.: Use of a self-adaptive penalty approach for engineering optimization problems. Computers in Industry 41(2), 113–127 (2000)
Surry, P.D., Radcliffe, N.J., Boyd, I.D.: A multi-objective approach to constrained optimisation of gas supply networks: The COMOGA method. In: Fogarty, T.C. (ed.) AISB-WS 1995. LNCS, vol. 993, pp. 166–180. Springer, Heidelberg (1995)
Camponogara, E., Talukdar, S.N.: A genetic algorithm for constrained and multiobjective optimization. In: 3rd Nordic Workshop on Genetic Algorithms and Their Applications (3NWGA), pp. 49–62 (1997)
Angantyr, A., Andersson, J., Aidanpaa, J.-O.: Constrained optimization based on a multiobjective evolutionary algorithm. In: Proceedings of Congress on Evolutionary Computation, pp. 1560–1567 (2003)
Coello, C.A.C.: Treating objectives as constraints for single objective optimization. Engineering Optimization 32(3), 275–308 (2000)
Deb, K., Lele, S., Datta, R.: A hybrid evolutionary multi-objective and SQP based procedure for constrained optimization. In: Kang, L., Liu, Y., Zeng, S. (eds.) ISICA 2007. LNCS, vol. 4683, pp. 36–45. Springer, Heidelberg (2007)
Echeverri, M.G., Lezama, J.M.L., Romero, R.: An efficient constraint handling methodology for multi-objective evolutionary algorithms. Revista Facultad de Ingenieria-Universidad de Antioquia 49, 141–150 (2009)
Burke, E.K., Smith, A.J.: Hybrid evolutionary techniques for the maintenance schedulingproblem. IEEE Transactions on Power Systems 15(1), 122–128 (2000)
Fatourechi, M., Bashashati, A., Ward, R.K., Birch, G.E.: A hybrid genetic algorithm approach for improving the performance of the LF-ASD brain computer interface. In: Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2005, vol. 5 (2005)
Victoire, T., Jeyakumar, A.E.: A modified hybrid EP-SQP approach for dynamic dispatch with valve-point effect. International Journal of Electrical Power & Energy Systems 27(8), 594–601 (2005)
Hinterding, R.: Constrained parameter optimisation: equality constraints. In: Proceedings of the 2001 Congress on Evolutionary Computation, vol. 1, pp. 687–692. IEEE, Los Alamitos (2002)
Peconick, G., Wanner, E.F., Takahashi, R.H.C.: Projection-based local search operator for multiple equality constraints within genetic algorithms. In: IEEE Congress on Evolutionary Computation, CEC 2007, pp. 3043–3049. IEEE, Los Alamitos (2008)
Lin, C.Y., Wu, W.H.: Adaptive penalty strategies in genetic search for problems with inequality and equality constraints. In: IUTAM Symposium on Evolutionary Methods in Mechanics, pp. 241–250. Springer, Heidelberg (2004)
Shang, W., Zhao, S., Shen, Y.: A flexible tolerance genetic algorithm for optimal problems with nonlinear equality constraints. Advanced Engineering Informatics 23(3), 253–264 (2009)
Deb, K., Datta, R.: A fast and accurate solution of constrained optimization problems using a hybrid bi-objective and penalty function approach. In: Proceedings of the Congress on Evolutionary Computation (CEC 2010), pp. 1–8 (2010)
Deb, K.: Multi-objective optimization using evolutionary algorithms. Wiley, Chichester (2001)
Liang, J.J., Runarsson, T.P., Mezura-Montes, E., Clerc, M., Suganthan, P.N., Coello Coello, C.A., Deb, K.: Problem definitions and evaluation criteria for the CEC 2006: Special session on constrained real-parameter optimization. Technical report, Nanyang Technological University, Singapore (2006)
Zavala, A.E.M., Aguirre, A.H., Diharce, E.R.V.: Continuous Constrained Optimization with Dynamic Tolerance Using the COPSO Algorithm, pp. 1–24. Springer, Heidelberg (2009)
Takahama, T., Sakai, S.: Solving Difficult Constrained Optimization Problems by the ε Constrained Differential Evolution with Gradient-Based Mutation, pp. 51–72. Springer, Heidelberg (2009)
Brest, J.: Constrained Real-Parameter Optimization with ε Self-Adaptive Differential Evolution, pp. 73–94. Springer, Heidelberg (2009)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Datta, R., Deb, K. (2011). A Bi-objective Based Hybrid Evolutionary-Classical Algorithm for Handling Equality Constraints. In: Takahashi, R.H.C., Deb, K., Wanner, E.F., Greco, S. (eds) Evolutionary Multi-Criterion Optimization. EMO 2011. Lecture Notes in Computer Science, vol 6576. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19893-9_22
Download citation
DOI: https://doi.org/10.1007/978-3-642-19893-9_22
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-19892-2
Online ISBN: 978-3-642-19893-9
eBook Packages: Computer ScienceComputer Science (R0)