Many engineering design problems can be formulated as optimization problems with constraints. In this paper we have proposed two modified variants of differential evolution (DE) for solving constrained engineering design problems. Pareto-ranking method is used to handle constrained with proposed approaches. The proposed variants named EDE-1 and EDE-2 are tested on 4 engineering design optimization problems taken from literature. Simulation results prove the efficiency of proposed approaches.

1. He, Q. and Wang, L. 2007. An effective co-evolutionary particle swarm optimization for constrained engineering design problems.Engineering Applications of Arti?cial Intelligence, pp. 89-99.
2. Esquivel, S. C. and Cagnina, L.C. 2008. Solving engineering optimization problems with the simple constrained particle swarm optimizer. Informatica 32, 319–326.
3. Storn, R. and Price, K. 1995. Differential evolution—a simple and efficient adaptive scheme for global optimization over continuous. Spaces. Berkeley, CA, Tech. Rep. TR-95-012.
4. Vesterstrom, J. and Thomsen, R. 2004. A comparative study of differential evolution, particle swarm optimization. and evolutionary algorithms on numerical benchmark problems. Congress on Evolutionary Computation, 980-987.
5. Cai, Y., Wang, J. and Yin, J. 2011. Learning enhanced differential evolution for numerical optimization. Springer-Verlag, Soft Computing . doi:10.1007/s00500-011-0744-x
6. Fan, H. and Lampinen J. 2003. A trigonometric mutation operation to differentia evolution. Journal of Global Optimization. 27, 105-129.
7. Noman, N. and Iba, H. 2008. Accelerating differential evolution using an adaptive local Search. IEEE Transaction of Evolutionary Computing. 12(1), 107–125.
8. Ali, M. and Pant, M. 2010. Improving the performance of differential evolution algorithm using cauchy mutation. Soft Computing. doi:10.1007/s00500-010-0655-2
9. Pant, M., Ali, M. and Abraham, A. 2009. Mixed mutation strategy embedded differential evolution. IEEE Congress on Evolutionary Computation, 1240-1246.
10. Liu, J. and Lampinen, J. 2005. A fuzzy adaptive differential evolution algorithm. Soft Computing Fusion Found Methodol Appl. 9(6), 448–462.
11. Brest, J., Greiner, S., Boskovic, B., Mernik, M. and Zumer, V. 2006.Self adapting control parameters in differential evolution: a comparative study on numerical benchmark problems. IEEE Transaction of Evolutionary Computing. 10(6), 646–657.
12. Rahnamayan, S., Tizhoosh, H. and Salama, M. 2008. Opposition based differential evolution. IEEE Transaction of Evolutinary Computing. 12(1), 64–79.
13. Qin, A. K., Huang, V.L.and Suganthan ,P.N. 2009. Differential evolution algorithm with strategy adaptation for global numerical optimization. IEEE Transaction of Evolutionary Computing. 13 (2), 398–417.
14. Zhang, J.and Sanderson, A. 2009. JADE: adaptive differential evolution with optional external archive. IEEE Transaction of Evolutionary Computing. 13(5), 945–958.
15. Babu, B.V. and Angira, R. 2006. Modified differential evolution (MDE) for optimization of non-linear chemical processes. Computer and Chemical Engineering. 30, 989-1002.
16. Kaelo, P. and Ali, M.M. 2006. A numerical study of some modified differential evolution algorithms. European Journal of Operational Research. 169, 1176-1184.
17. Das, S., Abraham, A., Chakraborty, U. and Konar, A. 2009. Differential evolution using a neighborhood based mutation operator. IEEE Transaction of Evolutionary Computing. 13(3), 526–553 .
18. Neri, F. and Tirronen, V. 2010. Recent advances in differential evolution: a survey and experimental analysis. ArtifIntell Rev. 33 (1–2), 61–106.
19. Das, S. and Suganthan, P.N. 2011. Differential evolution: a survey of the state-of-the-art. IEEE Transaction of Evolutionary Computing. 15(1), 4-13.
20. Kumar, P., Pant, M. and Abraham. A. 2011. Two enhanced differential evolution variants for solving global optimization problems. In Proceeding of Third World Congress on Nature and Biologically Inspired Computing (NABIC 2011) IEEE, pp. 208-213.
21. Aguirre, A. H., Zavala, A. M., Diharce, E. V. and Rionda, S. B. 2007. COPSO: Constrained optimization via PSO algorithm. Technical report No. I-07-04/22-02-2007, Center for Research in Mathematics (CIMAT).
22. Montes, E.M. and Ocana, B. H. Bacterial foraging for engineering design problems: preliminary results.
23. He, S., Prempain, E. and Wu, Q.H. 2004. An improved particle swarm optimizer for mechanical design optimization problems. Engineering Optimization, 36(5):585–605.
24. Coello, C.A.C. 2000. Use of a self-adaptive penalty approach for engineering optimization problems. Computers in Industry 41,113–127.
25. Coello, C.A.C. and Montes, E.M. 2002. Constraint-handling in genetic algorithms through the use of dominance-based tournament selection. Advanced Engineering Informatics 16, 193–203.

Differential Evolution Donor Mutation Engineering Design Optimization Constraints Handling