Practical Applications in Constrained Evolutionary Multi-objective Optimization
Abstract
Constrained optimization is applicable to most real world engineering science problems. An efficient constraint handling method must be robust, reliable and computationally efficient. However, the performance of constraint handling mechanism deteriorates with the increase of multi-modality, non-linearity and non-convexity of the constraint functions. Most of the classical mathematics based optimization techniques fails to tackle these issues. Hence, researchers round the globe are putting hard effort to deal with multi-modality, non-linearity and non-convexity, as their presence in the real world problems are unavoidable. Initially, Evolutionary Algorithms (EAs) were developed for unconstrained optimization but engineering problems are always with certain type of constraints. The in-dependability of EAs to the structure of problem has led the researchers to re-think in applying the same to the problems incorporating the constraints. The constraint handling techniques have been successfully used to solve many single objective problems but there has been limited work in applying them to the multi-objective optimization problem. Since for most engineering science problems conflicting multi-objectives have to be satisfied simultaneously, multi-objective constraint handling should be one of the most active research area in engineering optimization. Hence, in this chapter authors have concentrated in explaining the constrained multi-objective optimization problem along with their applications.
Keywords
Multi-objective optimization Constraint handling Evolutionary algorithms Practical applicationsReferences
- 1.Bechikh, S., Ben Said, L., Ghédira, K.: Negotiating decision makers’ reference points for group preference-based evolutionary multi-objective optimization. In: 2011 11th International Conference on Hybrid Intelligent Systems (HIS), pp. 377–382. IEEE (2011)Google Scholar
- 2.Bechikh, S., Chaabani, A., Ben Said, L.: An efficient chemical reaction optimization algorithm for multiobjective optimization. IEEE Trans. Cybern. 45(10), 2051–2064 (2015)CrossRefGoogle Scholar
- 3.Bechikh, S., Kessentini, M., Said, L.B., Ghédira, K.: Chapter four-preference incorporation in evolutionary multiobjective optimization: a survey of the state-of-the-art. Adv. Comput. 98, 141–207 (2015)CrossRefGoogle Scholar
- 4.Azzouz, N., Bechikh, S., Ben Said, L.: Steady state ibea assisted by mlp neural networks for expensive multi-objective optimization problems. In: Proceedings of the 2014 Conference on Genetic and Evolutionary Computation, pp. 581–588. ACM (2014)Google Scholar
- 5.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)CrossRefGoogle Scholar
- 6.Courant, R., et al.: Variational methods for the solution of problems of equilibrium and vibrations. Bull. Amer. Math. Soc 49(1), 1–23 (1943)MathSciNetCrossRefMATHGoogle Scholar
- 7.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), 1245–1287 (2002)MathSciNetCrossRefMATHGoogle Scholar
- 8.Woldesenbet, Y.G., Yen, G.G., Tessema, B.G.: Constraint handling in multiobjective evolutionary optimization. IEEE Trans. Evol. Comput. 13(3), 514–525 (2009)CrossRefGoogle Scholar
- 9.Jan, M.A., Zhang, Q.: Moea/d for constrained multiobjective optimization: some preliminary experimental results. In: 2010 UK Workshop on Computational Intelligence (UKCI) (2010)Google Scholar
- 10.Li, H., Zhang, Q.: Multiobjective optimization problems with complicated pareto sets, moea/d and nsga-ii. IEEE Trans. Evol. Comput. 13(2), 284–302 (2009)CrossRefGoogle Scholar
- 11.Jan, M.A., Tairan, N., Khanum, R.A.: Threshold based dynamic and adaptive penalty functions for constrained multiobjective optimization. In: 2013 1st International Conference on Artificial Intelligence, Modelling and Simulation (AIMS), pp. 49–54. IEEE (2013)Google Scholar
- 12.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)Google Scholar
- 13.Deb, K.: An efficient constraint handling method for genetic algorithms. Comput. Methods Appl. Mech. Eng. 186(2), 311–338 (2000)CrossRefMATHGoogle Scholar
- 14.Deb, K., Agrawal, S., Pratap, A., Meyarivan, T.: A fast and elitist multi-objective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6(2), 182–197 (2002)CrossRefGoogle Scholar
- 15.Pal, S., Qu, B.Y., Das, S., Suganthan, P.N.: Optimal synthesis of linear antenna arrays with multi-objective differential evolution. Prog. Electromagn. Res. B 21, 87–111 (2010)Google Scholar
- 16.Takahama, T., Sakai, S., Iwane, N.: Constrained optimization by the \(\varepsilon \) constrained hybrid algorithm of particle swarm optimization and genetic algorithm. In: AI 2005: Advances in Artificial Intelligence, pp. 389–400 (2005)Google Scholar
- 17.Takahama, T., Sakai, S.: Constrained optimization by \(\varepsilon \) constrained differential evolution with dynamic \(\varepsilon \)-level control. In: Advances in Differential Evolution, pp.139–154. Springer (2008)Google Scholar
- 18.Zhang, Q., Li, H.: Moea/d: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans. Evol. Comput. 11(6), 712–731 (2007)CrossRefGoogle Scholar
- 19.Martínez, S.Z., Coello, C.A.C.: A multi-objective evolutionary algorithm based on decomposition for constrained multi-objective optimization, pp. 429–436 (2014)Google Scholar
- 20.Yang, Z., Cai, X., Fan, Z.: Epsilon constrained method for constrained multiobjective optimization problems: some preliminary results. In: Proceedings of the 2014 Conference Companion on Genetic and Evolutionary Computation Companion, pp. 1181–1186. ACM (2014)Google Scholar
- 21.Zhang, Q., Zhou, A., Zhao, S., Suganthan, P.N., Liu, W., Tiwari, S.: Multiobjective optimization test instances for the cec 2009 special session and competition. University of Essex, Colchester, UK and Nanyang technological University, Singapore, special session on performance assessment of multi-objective optimization algorithms, Technical report, vol. 264 (2008)Google Scholar
- 22.Jiménez, F., Gómez-Skarmeta, A.F., Sánchez, G., Deb, K.: An evolutionary algorithm for constrained multi-objective optimization. In: Proceedings of the 2002 Congress on Evolutionary Computation, 2002. CEC 2002, vol. 2, pp. 1133–1138. IEEE (2002)Google Scholar
- 23.Vieira, D.A., Adriano, R.L., Vasconcelos, J.A., Krähenbühl, L.: Treating constraints as objectives in multiobjective optimization problems using niched pareto genetic algorithm. IEEE Trans. Magn. 40(2), 1188–1191 (2004)CrossRefGoogle Scholar
- 24.Young, N.: Blended ranking to cross infeasible regions in constrainedmultiobjective problems. In: International Conference on Computational Intelligence for Modelling, Control and Automation, 2005 and International Conference on Intelligent Agents, Web Technologies and Internet Commerce, vol. 2, pp. 191–196. IEEE (2005)Google Scholar
- 25.Geng, H., Zhang, M., Huang, L., Wang, X.: Infeasible elitists and stochastic ranking selection in constrained evolutionary multi-objective optimization. In: Simulated Evolution and Learning, pp. 336–344 (2006)Google Scholar
- 26.Oyama, A., Shimoyama, K., Fujii, K.: New constraint-handling method for multi-objective and multi-constraint evolutionary optimization. Trans. Jpn. Soc. Aeronaut. Sp. Sci. 50(167), 56–62 (2007)CrossRefGoogle Scholar
- 27.Isaacs, A., Ray, T., Smith, W.: Blessings of maintaining infeasible solutions for constrained multi-objective optimization problems. In: IEEE Congress on Evolutionary Computation, 2008. CEC 2008. (IEEE World Congress on Computational Intelligence), pp. 2780–2787. IEEE (2008)Google Scholar
- 28.Ray, T., Singh, H.K., Isaacs, A., Smith, W.: Infeasibility driven evolutionary algorithm for constrained optimization. In: Constraint-Handling in Evolutionary Optimization, pp. 145–165. Springer (2009)Google Scholar
- 29.Liu, H.-L., Wang, D.: A constrained multiobjective evolutionary algorithm based decomposition and temporary register. In: 2013 IEEE Congress on Evolutionary Computation (CEC), pp. 3058–3063. IEEE (2013)Google Scholar
- 30.Datta, R., Regis, R.G.: A surrogate-assisted evolution strategy for constrained multi-objective optimization. Expert Syst. Appl. 57, 270–284 (2016)CrossRefGoogle Scholar
- 31.Michalewicz, Z., Dasgupta, D., Le Riche, R.G., Schoenauer, M.: Evolutionary algorithms for constrained engineering problems. Comput. Ind. Eng. 30(4), 851–870 (1996)CrossRefGoogle Scholar
- 32.Fonseca, C.M., Fleming, P.J.: Multiobjective optimization and multiple constraint handling with evolutionary algorithms. i. a unified formulation. IEEE Trans. Syst. Man Cybern. Part A Syst. Hum. 28(1), 26–37 (1998)CrossRefGoogle Scholar
- 33.Coello Coello, C.A., Christiansen, A.D.: Moses: a multiobjective optimization tool for engineering design. Eng. Optim. 31(3), 337–368 (1999)CrossRefGoogle Scholar
- 34.Ray, T., Tai, K., Seow, C.: An evolutionary algorithm for multiobjective optimization. Eng. Optim. 33(3), 399–424 (2001)CrossRefGoogle Scholar
- 35.Harada, K., Sakuma, J., Ono, I., Kobayashi, S.: Constraint-handling method for multi-objective function optimization: Pareto descent repair operator. In: Evolutionary Multi-Criterion Optimization, pp. 156–170, Springer (2007)Google Scholar
- 36.Asafuddoula, M., Ray, T., Sarker, R., Alam, K.: An adaptive constraint handling approach embedded moea/d. In: 2012 IEEE Congress on Evolutionary Computation (CEC), pp. 1–8. IEEE (2012)Google Scholar
- 37.Alam, K., Ray, T., Anavatti, S.G.: Design of a toy submarine using underwater vehicle design optimization framework. In: 2011 IEEE Symposium on Computational Intelligence in Vehicles and Transportation Systems (CIVTS), pp. 23–29. IEEE (2011)Google Scholar
- 38.Deb, K., Jain, H.: An evolutionary many-objective optimization algorithm using reference-point-based nondominated sorting approach, part i: Solving problems with box constraints. IEEE Trans. Evol. Comput. 18(4), 577–601 (2014)CrossRefGoogle Scholar
- 39.Jain, H., Deb, K.: An evolutionary many-objective optimization algorithm using reference-point based nondominated sorting approach, part ii: handling constraints and extending to an adaptive approach. IEEE Trans. Evol. Comput. 18(4), 602–622 (2014)CrossRefGoogle Scholar
- 40.Li, K., Deb, K., Zhang, Q., Kwong, S.: An evolutionary many-objective optimization algorithm based on dominance and decomposition. IEEE Trans. Evol. Comput. 19(5), 694–716 (2015)CrossRefGoogle Scholar
- 41.Bechikh, S., Said, L.B., Ghédira, K.: Group preference based evolutionary multi-objective optimization with nonequally important decision makers: application to the portfolio selection problem. Int. J. Comput. Inf. Syst. Ind. Manag. Appl. 5(278–288), 71 (2013)Google Scholar
- 42.Kalboussi, S., Bechikh, S., Kessentini, M., Said, L.B.: Preference-based many-objective evolutionary testing generates harder test cases for autonomous agents. In: Search Based Software Engineering, pp. 245–250. Springer (2013)Google Scholar
- 43.Bechikh, S.: Incorporating decision maker’s preference information in evolutionary multi-objective optimization. Ph.D. thesis, University of Tunis, ISG-Tunis, Tunisia (2013)Google Scholar
- 44.Kurpati, A., Azarm, S., Wu, J.: Constraint handling improvements for multiobjective genetic algorithms. Struct. Multidiscip. Optim. 23(3), 204–213 (2002)CrossRefGoogle Scholar
- 45.Aute, V.C., Radermacher, R., Naduvath, M.V.: Constrained multi-objective optimization of a condenser coil using evolutionary algorithms (2004)Google Scholar
- 46.Pinto, E.G.: Supply chain optimization using multi-objective evolutionary algorithms, vol. 15 (2004). Accessed Dec 2014Google Scholar
- 47.Sarker, R., Ray, T.: Multiobjective evolutionary algorithms for solving constrained optimization problems. In: International Conference on Computational Intelligence for Modelling, Control and Automation, 2005 and International Conference on Intelligent Agents, Web Technologies and Internet Commerce, vol. 2, pp. 197–202. IEEE (2005)Google Scholar
- 48.Chakraborty, B., Chen, T., Mitra, T., Roychoudhury, A.: Handling constraints in multi-objective ga for embedded system design. In: 19th International Conference on VLSI Design, 2006. Held Jointly with 5th International Conference on Embedded Systems and Design, 6 pp. IEEE (2006)Google Scholar
- 49.Quiza Sardiñas, R., Rivas Santana, M., Alfonso Brindis, E.: Genetic algorithm-based multi-objective optimization of cutting parameters in turning processes. Eng. Appl. Artif. Intell. 19(2), 127–133 (2006)CrossRefGoogle Scholar
- 50.Narayanan, S., Azarm, S.: On improving multiobjective genetic algorithms for design optimization. Struct. Optim. 18(2–3), 146–155 (1999)CrossRefGoogle Scholar
- 51.Jiang, H., Aute, V., Radermacher, R.: A user-friendly simulation and optimization tool for design of coils. In: Ninth International Refrigeration and Air Conditioning Conference (2002)Google Scholar
- 52.Srinivasan, N., Deb, K.: Multi-objective function optimisation using non-dominated sorting genetic algorithm. Evol. Comp. 2(3), 221–248 (1994)CrossRefGoogle Scholar
- 53.Li, L., Li, X., Yu, X.: Power generation loading optimization using a multi-objective constraint-handling method via pso algorithm. In: 6th IEEE International Conference on Industrial Informatics, 2008. INDIN 2008, pp. 1632–1637, IEEE (2008)Google Scholar
- 54.Guo, Y., Cao, X., Zhang, J.: Multiobjective evolutionary algorithm with constraint handling for aircraft landing scheduling. In: IEEE Congress on Evolutionary Computation, 2008. CEC 2008. (IEEE World Congress on Computational Intelligence), pp. 3657–3662. IEEE (2008)Google Scholar
- 55.Moser, I., Mostaghim, S.: The automotive deployment problem: a practical application for constrained multiobjective evolutionary optimisation. In: 2010 IEEE Congress on Evolutionary Computation (CEC), pp. 1–8. IEEE (2010)Google Scholar
- 56.El Ela, A.A., Abido, M., Spea, S.R.: Differential evolution algorithm for emission constrained economic power dispatch problem. Electric Power Syst. Res. 80(10), 1286–1292 (2010)CrossRefGoogle Scholar
- 57.Tripathi, V.K., Chauhan, H.M.: Multi objective optimization of planetary gear train. In: Simulated Evolution and Learning, pp. 578–582. Springer (2010)Google Scholar
- 58.Puisa, R., Streckwall, H.: Prudent constraint-handling technique for multiobjective propeller optimisation. Optim. Eng. 12(4), 657–680 (2011)CrossRefMATHGoogle Scholar
- 59.Hajabdollahi, H., Tahani, M., Fard, M.S.: CFD modeling and multi-objective optimization of compact heat exchanger using CAN method. Appl. Therm. Eng. 31(14), 2597–2604 (2011)CrossRefGoogle Scholar
- 60.Rajendra, R., Pratihar, D.: Multi-objective optimization in gait planning of biped robot using genetic algorithm and particle swarm optimization tool. J. Control Eng. Technol. 1(2), 81–94 (2011)Google Scholar
- 61.Liu, X., Bansal, R.: Integrating multi-objective optimization with computational fluid dynamics to optimize boiler combustion process of a coal fired power plant. Appl. Energy 130, 658–669 (2014)CrossRefGoogle Scholar
- 62.Wang, Y., Yin, H., Zhang, S., Yu, X.: Multi-objective optimization of aircraft design for emission and cost reductions. Chin. J. Aeronaut. 27(1), 52–58 (2014)CrossRefGoogle Scholar
- 63.Pandey, A., Datta, R., Bhattacharya, B.: Topology optimization of compliant structures and mechanisms using constructive solid geometry for 2-d and 3-d applications. Soft Comput., 1–23 (2015)Google Scholar
- 64.Sorkhabi, S.Y.D., Romero, D.A., Beck, J.C., Amon, C.H.: Constrained multi-objective wind farm layout optimization: introducing a novel constraint handling approach based on constraint programming. In: ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, pp. V02AT03A031–V02AT03A031. American Society of Mechanical Engineers (2015)Google Scholar
- 65.Droandi, G., Gibertini, G.: Aerodynamic blade design with multi-objective optimization for a tiltrotor aircraft. Aircr. Eng. Aerosp. Technol. Int. J. 87(1), 19–29 (2015)CrossRefGoogle Scholar
- 66.Datta, R., Pradhan, S., Bhattacharya, B.: Analysis and design optimization of a robotic gripper using multiobjective genetic algorithm. IEEE Trans. Syst. Man Cybern. Syst. 46(1), 16–26 (2016)CrossRefGoogle Scholar
- 67.Deb, K., Datta, R.: Hybrid evolutionary multi-objective optimization and analysis of machining operations. Eng. Optim. 44(6), 685–706 (2012)MathSciNetCrossRefGoogle Scholar
- 68.Coello, C.A.C.C., Pulido, G.T.: A micro-genetic algorithm for multiobjective optimization. In: Evolutionary Multi-Criterion Optimization, pp. 126–140. Springer (2001)Google Scholar
- 69.Lahanas, M., Milickovic, N., Baltas, D., Zamboglou, N.: Application of multiobjective evolutionary algorithms for dose optimization problems in brachytherapy. In: Evolutionary Multi-Criterion Optimization, pp. 574–587. Springer (2001)Google Scholar
- 70.Li, X., Jiang, T., Evans, D.: Medical image reconstruction using a multi-objective genetic local search algorithm. Int. J. Comput. Math. 74(3), 301–314 (2000)CrossRefMATHGoogle Scholar
- 71.Devroye, L., Györfi, L., Lugosi, G.: A Probabilistic Theory of Pattern Recognition, vol. 31. Springer Science & Business Media, New York (2013)MATHGoogle Scholar