Abstract
Most real world optimization problems involve constraints and constraint handling has long been an area of active research. While older techniques explicitly preferred feasible solutions over infeasible ones, recent studies have uncovered some shortcomings of such strategies. There has been a growing interest in the efficient use of infeasible solutions during the course of search and this paper presents of short review of such techniques. These techniques prefer good infeasible solutions over feasible solutions during the course of search (or a part of it). The review looks at major reported works over the years and outlines how these preferences have been dealt in various stages of the solution process, viz, problem formulation, parent selection/recombination and ranking/selection. A tabular summary is then presented for easy reference to the work in this area.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Asafuddoula, M., Ray, T., Sarker, R.: A differential evolution algorithm with constraint sequencing. In: 2012 Third Global Congress on Intelligent Systems (GCIS), pp. 68–71 (2012)
Asafuddoula, M., Ray, T., Sarker, R., Alam, K.: An adaptive constraint handling approach embedded MOEA/D. In: IEEE Congress on Evolutionary Computation (CEC), pp. 1–8 (2012)
Asafuddoula, M., Ray, T., Sarker, R.: A self-adaptive differential evolution algorithm with constraint sequencing. In: Thielscher, M., Zhang, D. (eds.) AI 2012. LNCS, vol. 7691, pp. 182–193. Springer, Heidelberg (2012)
Asafuddoula, M., Ray, T., Sarker, R.: A decomposition based evolutionary algorithm for many objective optimization with systematic sampling and adaptive epsilon control. In: Purshouse, R.C., Fleming, P.J., Fonseca, C.M., Greco, S., Shaw, J. (eds.) EMO 2013. LNCS, vol. 7811, pp. 413–427. Springer, Heidelberg (2013)
Asafuddoula, M., Ray, T., Sarker, R.: Evaluate till you violate: A differential evolution algorithm based on partial evaluation of the constraint set. In: 2013 IEEE Symposium on Differential Evolution (SDE), pp. 31–37 (2013)
Coello, C.A.C.: Treating constraints as objectives for single-objective evolutionary optimization. Eng. Optimization 32(3), 275–308 (2000)
Coello, C.A.C., Zacatenco, C.S.P.: List of references on constraint-handling techniques used with evolutionary algorithms. Power 80(10), 1286–1292 (2010)
Coello, C.A.C.: Theoretical and numerical constraint-handling techniques used with evolutionary algorithms: a survey of the state of the art. Comput. Methods Appl. Mech. Eng. 191(11–12), 1245–1287 (2002)
Coello, C.A.C., Mezura-Montes, E.: Handing constraints in genetic algorithms using dominance-based tournaments. In: Proceedings of the fifth International Conference on Adaptive Computing Design and Manufacture (ACDM 2002) (2002)
Datta, R., Bittermann, M.S., Deb, K., Ciftcioglu, O.: Probabilistic constraint handling in the framework of joint evolutionary-classical optimization with engineering applications. In: IEEE Congress on Evolutionary Computation (CEC), pp. 1–8 (2012)
Datta, R., Costa, M.F.P., Deb, K., Gaspar-Cunha, A.: An evolutionary algorithm based pattern search approach for constrained optimization. In: IEEE Congress on Evolutionary Computation (CEC), pp. 1355–1362 (2013)
Datta, R., Deb, K.: An adaptive normalization based constrained handling methodology with hybrid bi-objective and penalty function approach. In: IEEE Congress on Evolutionary Computation (CEC), pp. 1–8 (2012)
Datta, R., Deb, K.: Individual penalty based constraint handling using a hybrid bi-objective and penalty function approach. In: IEEE Congress on Evolutionary Computation (CEC), pp. 2720–2727 (2013)
Datta, R., Deb, K.: 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.) EMO 2011. LNCS, vol. 6576, pp. 313–327. Springer, Heidelberg (2011)
Deb, K., Datta, R.: A fast and accurate solution of constrained optimization problems using a hybrid bi-objective and penalty function approach. In: IEEE Congress on Evolutionary Computation (CEC), pp. 1–8 (2010)
Deb, K.: An efficient constraint handling method for genetic algorithms. Comput. Methods Appl. Mech. Eng. 186(2–4), 311–338 (2000)
Deb, K., Datta, R.: A bi-objective constrained optimization algorithm using a hybrid evolutionary and penalty function approach. Eng. Optim. 45(5), 503–527 (2013)
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)
Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6(2), 182–197 (2002)
Farmani, R., Wright, J.A.: Self-adaptive fitness formulation for constrained optimization. IEEE Trans. Evol. Comput. 7(5), 445–455 (2003)
Filipiak, P., Michalak, K., Lipinski, P.: Infeasibility driven evolutionary algorithm with ARIMA-based prediction mechanism. In: Yin, H., Wang, W., Rayward-Smith, V. (eds.) IDEAL 2011. LNCS, vol. 6936, pp. 345–352. Springer, Heidelberg (2011)
Hamida, S.B., Schoenauer, M.: An adaptive algorithm for constrained optimization problems. In: Deb, K., Rudolph, G., Lutton, E., Merelo, J.J., Schoenauer, M., Schwefel, H.-P., Yao, X. (eds.) PPSN 2000. LNCS, vol. 1917, pp. 529–538. Springer, Heidelberg (2000)
Hamida, S.B., Schoenauer, M.: ASCHEA: New results using adaptive segregational constraint handling. In: Proceedings of the 2002 Congress on Evolutionary Computation, vol. 1, pp. 884–889 (2002)
Hedar, A.R., Fukushima, M.: Derivative-free filter simulated annealing method for constrained continuous global optimization. J. Global Optim. 35(4), 521–549 (2006)
Hingston, P., Barone, L., Huband, S., While, L.: Multi-level ranking for constrained multi-objective evolutionary optimisation. In: Runarsson, T.P., Beyer, H.-G., Burke, E.K., Merelo-Guervós, J.J., Whitley, L.D., Yao, X. (eds.) PPSN 2006. LNCS, vol. 4193, pp. 563–572. Springer, Heidelberg (2006)
Hinterding, R., Michalewicz, Z.: Your brains and my beauty: Parent matching for constrained optimisation. In: Proceedings of the 5th International Conference on Evolutionary Computation (CEC), pp. 810–815 (1998)
Ho, P.Y., Shimizu, K.: Evolutionary constrained optimization using an addition of ranking method and a percentage-based tolerance value adjustment scheme. Inf. Sci. 177(14), 2985–3004 (2007)
Isaacs, A., Ray, T., Smith, W.: Blessings of maintaining infeasible solutions for constrained multi-objective optimization problems. In: IEEE Congress on Evolutionary Computation (CEC), pp. 2780–2787 (2008)
Kimbrough, S.O., Lu, M., Wood, D.H., Wu, D.J.: Exploring a two-market genetic algorithm. In: Proceedings of the Genetic and Evolutionary Computation Conference (GECCO), pp. 415–421. Morgan Kaufmann (2002)
Kimbrough, S.O., Koehler, G.J., Lu, M., Wood, D.H.: On a feasible-infeasible two-population (FI-2Pop) genetic algorithm for constrained optimization: Distance tracing and no free lunch. Eur. J. Oper. Res. 190(2), 310–327 (2008)
Kimbrough, S.O., Lu, M., Wood, D.H., Wu, D.J.: Exploring a two-population genetic algorithm. In: Cantú-Paz, E., et al. (eds.) GECCO 2003. LNCS, vol. 2723, pp. 1148–1159. Springer, Heidelberg (2003)
Mezura-Montes, E., Coello, C.A.C.: A simple multimembered evolution strategy to solve constrained optimization problems. IEEE Trans. Evol. Comput. 9(1), 1–17 (2005)
Mezura-Montes, E., Velazquez-Reyes, J.,Coello, C.A.C.: Modified differential evolution for constrained optimization. In: IEEE Congress on Evolutionary Computation (CEC), pp. 25–32 (2006)
Mezura-Montes, E., Coello, C.A.C.: Useful infeasible solutions in engineering optimization with evolutionary algorithms. In: Gelbukh, A., Albornoz, Á., Terashima-Marín, H. (eds.) MICAI 2005. LNCS (LNAI), vol. 3789, pp. 652–662. Springer, Heidelberg (2005)
Mezura-Montes, E., Coello, C.A.C.: Constraint-handling in nature-inspired numerical optimization: Past, present and future. Swarm Evol. Comput. 1(4), 173–194 (2011)
Mezura-Montes, E., Coello, C.A.C.: An improved diversity mechanism for solving constrained optimization problems using a multimembered evolution strategy. In: Deb, K., Tari, Z. (eds.) GECCO 2004. LNCS, vol. 3102, pp. 700–712. Springer, Heidelberg (2004)
Michalewicz, Z.: A survey of constraint handling techniques in evolutionary computation methods. In: Proceedings of the Fourth Annual Conference on Evolutionary Programming, pp. 135–155. MIT Press, Cambridge (1995)
Powell, D., Skolnick, M.M.: Using genetic algorithms in engineering design optimization with non-linear constraints. In: Proceedings of the 5th International Conference on Genetic Algorithms, pp. 424–431. Morgan Kaufmann Publishers Inc. (1993)
Ray, T., Liew, K.M., Saini, P.: An intelligent information sharing strategy within a swarm for unconstrained and constrained optimization problems. Soft Comput. 6(1), 38–44 (2002)
Ray, T., Tai, K., Seow, K.C.: Multiobjective design optimization by an evolutionary algorithm. Eng. Optim. 33(4), 399–424 (2001)
Ray, T., Kang, T., Chye, S.K.: An evolutionary algorithm for constrained optimization. In: Genetic and Evolutionary Computation Conference (GECCO), pp. 771–777 (2000)
Ray, T., Singh, H.K., Isaacs, A., Smith, W.: Infeasibility driven evolutionary algorithm for constrained optimization. In: Mezura-Montes, E. (ed.) Constraint-Handling in Evolutionary Optimization. SCI, vol. 198, pp. 145–165. Springer, Heidelberg (2009)
Runarsson, T.P., Yao, X.: Stochastic ranking for constrained evolutionary optimization. IEEE Trans. Evol. Comput. 4(3), 284–294 (2000)
Saha, A., Ray, T.: A repair mechanism for active inequality constraint handling. In: IEEE Congress on Evolutionary Computation (CEC), pp. 1–8 (2012)
Saha, A., Ray, T.: Equality constrained multi-objective optimization. In: IEEE Congress on Evolutionary Computation (CEC), pp. 1–7 (2012)
Singh, H.K., Isaacs, A., Nguyen, T.T., Ray, T., Yao, X.: Performance of infeasibility driven evolutionary algorithm (IDEA) on constrained dynamic single objective optimization problems. In: IEEE Congress on Evolutionary Computation (CEC), pp. 3127–3134 (2009)
Singh, H.K., Isaacs, A., Ray, T., Smith, W.: A simulated annealing algorithm for constrained multi-objective optimization. In: IEEE Congress on Evolutionary Computation (CEC), pp. 1655–1662 (2008)
Singh, H.K., Ray, T., Smith, W.: Performance of infeasibility empowered memetic algorithm for CEC 2010 constrained optimization problems. In: IEEE Congress on Evolutionary Computation (CEC), pp. 1–8 (2010)
Singh, H.K., Isaacs, A., Ray, T., Smith, W.: Infeasibility driven evolutionary algorithm (IDEA) for engineering design optimization. In: Wobcke, W., Zhang, M. (eds.) AI 2008. LNCS (LNAI), vol. 5360, pp. 104–115. Springer, Heidelberg (2008)
Singh, H.K., Ray, T., Smith, W.: Performance of infeasibility empowered memetic algorithm (IEMA) on engineering design problems. In: Li, J. (ed.) AI 2010. LNCS, vol. 6464, pp. 425–434. Springer, Heidelberg (2010)
Singh, H.K., Ray, T., Sarker, R.: Optimum oil production planning using infeasibility driven evolutionary algorithm. Evol. Comput. 21(1), 65–82 (2013)
Singh, H.K., Ray, T., Smith, W.: C-PSA: Constrained pareto simulated annealing for constrained multi-objective optimization. Inf. Sci. 180(13), 2499–2513 (2010)
Surry, P.D., Radcliffe, N.J.: The COMOGA method: Constrained optimisation by multi-objective genetic algorithms. Control Cybern. 26(3), 391–412 (1997)
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)
Takahama, T., Sakai, S.: Constrained optimization by \(\epsilon \) constrained differential evolution with dynamic \(\epsilon \)-level control. In: Chakraborty, U.K. (ed.) Advances in Differential Evolution 2008. SCI, vol. 143, pp. 139–154. Springer, Heidelberg (2008)
Takahama, T., Sakai, S., Iwane, N.: Constrained optimization by the \(\epsilon \) constrained hybrid algorithm of particle swarm optimization and genetic algorithm. In: Zhang, S., Jarvis, R.A. (eds.) AI 2005. LNCS (LNAI), vol. 3809, pp. 389–400. Springer, Heidelberg (2005)
Tessema, B., Yen, G.G.: An adaptive penalty formulation for constrained evolutionary optimization. IEEE Trans. Syst. Man Cybern. Part A: Syst. Hum. 39(3), 565–578 (2009)
Vieira, D.A.G., Adriano, R., Vasconcelos, J.A., Krahenbuhl, L.: Treating constraints as objectives in multiobjective optimization problems using niched Pareto genetic algorithm. IEEE Trans. Magn. 40(2), 1188–1191 (2004)
Vieira, D.A.G., Adriano, R.L.S., Krahenbuhl, L., Vasconcelos, J.A.: Handling constraints as objectives in a multiobjective genetic based algorithm. J. Microwaves Optoelectron. 2(6), 50–58 (2002)
Wei, J., Wang, Y.: An infeasible elitist based particle swarm optimization for constrained multiobjective optimization and its convergence. Int. J. Pattern Recogn. Artif. Intell. 24(3), 381–400 (2010)
Xiao, H., Zu, J.W.: A new constrained multiobjective optimization algorithm based on artificial immune systems. In: Proceedings of the 2007 IEEE International Conference on Mechatronics and Automation, Harbin, China, pp. 3122–3127 (2007)
Yu, Y., Zhou, Z.H.: On the usefulness of infeasible solutions in evolutionary search: A theoretical study. In: IEEE Congress on Evolutionary Computation (CEC), pp. 835–840 (2008)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this paper
Cite this paper
Singh, H.K., Alam, K., Ray, T. (2016). Use of Infeasible Solutions During Constrained Evolutionary Search: A Short Survey. In: Ray, T., Sarker, R., Li, X. (eds) Artificial Life and Computational Intelligence. ACALCI 2016. Lecture Notes in Computer Science(), vol 9592. Springer, Cham. https://doi.org/10.1007/978-3-319-28270-1_17
Download citation
DOI: https://doi.org/10.1007/978-3-319-28270-1_17
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-28269-5
Online ISBN: 978-3-319-28270-1
eBook Packages: Computer ScienceComputer Science (R0)