Cohort Intelligence for Constrained Test Problems
Abstract
Any optimization algorithm requires a technique/way to handle constraints. This is important because most of the real world problems are inherently constrained problems. There are a several traditional methods available such as feasibility-based methods, gradient projection method, reduced gradient method, Lagrange multiplier method, aggregate constraint method, feasible direction based method, penalty based method, etc. (Kulkarni and Tai in Int J Comput Intell Appl 10(4):445–470, 2011 [1]). According to Vanderplaat (Numerical optimization techniques for engineering design, 1984 [2]), the penalty based methods can be referred to as generalized constraint handling methods. They can be easily incorporated into most of the unconstrained optimization methods and can be used to handle nonlinear constraints.
References
- 1.Kulkarni, A.J., Tai, K.: Solving constrained optimization problems using probability collectives and a penalty function approach. Int. J. Comput. Intell. Appl. 10(4), 445–470 (2011)CrossRefMATHGoogle Scholar
- 2.Vanderplaat, G.N.: Numerical Optimization Techniques for Engineering Design. McGraw-Hill, New York (1984)Google Scholar
- 3.Coello Coello, C.A.: Use of self-adaptive penalty approach for engineering optimization problems. Comput. Ind. 41, 113–127 (2000)CrossRefMATHGoogle Scholar
- 4.Farmani, R., Wright, J.A.: Self-adaptive fitness formulation for constrained optimization. IEEE Trans. Evol. Comput. 7(5), 445–455 (2003)CrossRefGoogle Scholar
- 5.Deb, K.: An efficient constraint handling method for genetic algorithms. Comput. Methods Appl. Mech. Eng. 186, 311–338 (2000)CrossRefMATHGoogle Scholar
- 6.Lampinen, J.: A constraint handling approach for the differential evolution algorithm. In: Proceedings of the IEEE Congress on Evolutionary Computation, vol. 2, pp. 1468–1473 (2002)Google Scholar
- 7.He, Q., Wang, L.: A hybrid particle swarm optimization with a feasibility-based rule for constrained optimization. Appl. Math. Comput. 186, 1407–1422 (2007)MathSciNetCrossRefMATHGoogle Scholar
- 8.Hu, X., Eberhart, R.: Solving constrained nonlinear optimization problems with particle swarm optimization. In: Proceedings of the 6th World Multi-conference on Systemics, Cybernetics and Informatics (2002)Google Scholar
- 9.Koziel, S., Michalewicz, Z.: Evolutionary algorithms, homomorphous mapping, and constrained parameter optimization. Evol. Comput. 7(1), 19–44 (1999)CrossRefGoogle Scholar
- 10.Coello Coello, C.A., Becerra, R.L.: Efficient evolutionary optimization through the use of a cultural algorithm. Eng. Optim. 36(2), 219–236 (2004)CrossRefGoogle Scholar
- 11.Becerra, R.L., Coello Coello, C.A.: Cultured differential evolution for constrained optimization. Comput. Methods Appl. Mech. Eng. 195, 4303–4322 (2006)Google Scholar
- 12.Chootinan, P., Chen, A.: Constraint handling in genetic algorithms using a gradient-based repair method. Comput. Oper. Res. 33, 2263–2281 (2006)CrossRefMATHGoogle Scholar
- 13.Zahara, E., Hu, C.H.: Solving constrained optimization problems with hybrid particle swarm optimization. Eng. Optim. 40(11), 1031–1049 (2008)MathSciNetCrossRefGoogle Scholar
- 14.Dong, Y., Tang, J., Xu, B., Wang, D.: An application of swarm optimization to nonlinear programming. Comput. Math. Appl. 49, 1655–1668 (2005)MathSciNetCrossRefMATHGoogle Scholar
- 15.Hedar, A.R., Fukushima, M.: Derivative-free simulated annealing method for constrained continuous global optimization. J. Global Optim. 35, 521–549 (2006)MathSciNetCrossRefMATHGoogle Scholar
- 16.Coello Coello, C.A., Montes, E.M.: Constraint-handling in genetic algorithms through the use of dominance-based tournament selection. Adv. Eng. Inform. 16, 193–203 (2002)CrossRefGoogle Scholar
- 17.Deb, K.: GeneAS: a robust optimal design technique for mechanical component design. In: Dasgupta, D., Michalewicz, Z., (eds.) Evolutionary Algorithms in Engineering Applications, pp. 497–514. Springer, New York (1997)Google Scholar
- 18.Kannan, B.K., Kramer, S.N.: An augmented lagrange multiplier based method for mixed integer discrete continuous optimization and its applications to mechanical design. ASME J. Mech. Des. 116, 405–411 (1994)CrossRefGoogle Scholar
- 19.Ragsdell, K.M., Phillips, D.T.: Optimal design of a class of welded structures using geometric programming. ASME J. Eng. Ind. Ser. B 98(3), 1021–1025 (1976)CrossRefGoogle Scholar
- 20.Sandgren, E.: Nonlinear integer and discrete programming in mechanical design. In: Proceedings of the ASME Design Technology Conference, pp. 95–105 (1988)Google Scholar
- 21.Runarsson, T.P., Yao, X.: Stochastic ranking for constrained evolutionary optimization. IEEE Trans. Evol. Comput. 4(3), 284–294 (2000)CrossRefGoogle Scholar
- 22.Hamida, S.B., Schoenauer, M.: ASCHEA: new results using adaptive segregational constraint handling. In: Fogel, D.B., et al. (eds.) Proceedings of the IEEE Congress on Evolutionary Computation, pp. 884–889 (2002)Google Scholar
- 23.Montes, E.M., Coello Coello, C.A.: A simple multimembered evolution strategy to solve constrained optimization problems. Technical Report EVOCINV-04-2003, Evolutionary Computation Group at CINVESTAV, Secciόn de Computaciόn, Departamento de Ingenierίa Eléctrica, CINVESTAV-IPN, México D.F., MéxicoGoogle Scholar
- 24.Ray, T., Tai, K., Seow, K.C.: An evolutionary algorithm for constrained optimization. In: Proceedings of the Genetic and Evolutionary Computation Conference, pp. 771–777 (2000)Google Scholar
- 25.Arora, J.S.: Introduction to Optimum Design. Elsevier Academic Press, San Diego (2004)Google Scholar
- 26.He, Q., Wang, L.: An effective co-evolutionary particle swarm optimization for constrained engineering design problems. Eng. Appl. Artif. Intell. 20, 89–99 (2006)CrossRefGoogle Scholar
- 27.Siddall, J.N.: Analytical Design-Making in Engineering Design. Prentice-Hall, Englewood Cliffs (1972)Google Scholar