Abstract
Solving constrained engineering design problems via evolutionary algorithms has attracted increasing attention in the past decade. In this paper, a simple but effective differential evolution with level comparison (DELC) is proposed for constrained engineering design problems by applying the level comparison to convert the constrained optimization problem into an unconstrained one and using the differential evolution (DE) to perform a global search over the solution space. In addition, the mutation factor of DE is set to be a random number to enrich the search behavior, and the satisfaction level increases monotonously to gradually stress the feasibility. The comparison results between the DELC and five existing algorithms from the literature based on 13 widely used constrained benchmark functions show that the DELC is of better or competitive performance. Furthermore, the DELC is used to solve some typical engineering design problems. DELC is of superior searching quality on all the problems with fewer evaluation times than other algorithms. In addition, the effect of the increasing rate of satisfaction level on the performances of the DELC is investigated as well.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Barbosa HJC, Lemonge ACC (2003) A new adaptive penalty scheme for genetic algorithms. Inf Sci 156(3–4):215–251
Cai ZX, Wang Y (2006) A multiobjective optimization-based evolutionary algorithm for constrained optimization. IEEE Trans Evol Comput 10(6):658–675
Coello CAC (2002) 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
Coello CAC, Becerra RL (2004) Efficient evolutionary optimization through the use of a cultural algorithm. Eng Optim 36(2):219–236
Coello CAC, Montes EM (2002) Constraint-handling in genetic algorithms through the use of dominance-based tournament selection. Adv Eng Inf 16(3):193–203
Colaco MJ, Dulikravich GS, Sahoo D (2008) A response surface method-based hybrid optimizer. Inverse Probl Sci Eng 16(6):717–741
Deb K (2000) An efficient constraint handling method for genetic algorithms. Comput Methods Appl Mech Eng 186(2–4):311–338
Farmani R, Wright JA (2003) Self-adaptive fitness formulation for constrained optimization. IEEE Trans Evol Comput 7(5):445–455
Hamida SB, Schoenauer M (2000) An adaptive algorithm for constrained optimization problems. Lect Notes Comput Sci 1917:529–538
He Q, Wang L (2007a) An effective co-evolutionary particle swarm optimization for constrained engineering design problems. Eng Appl Artif Intell 20(1):89–99
He Q, Wang L (2007b) A hybrid particle swarm optimization with a feasibility-based rule for constrained optimization. Appl Math Comput 186(2):1407–1422
Huang FZ, Wang L, He Q (2007) An effective co-evolutionary differential evolution for constrained optimization. Appl Math Comput 186(1):340–356
Huang VL, Qin AK, Suganthan PN (2006) Self-adaptive differential evolution algorithm for constrained real-parameter optimization. In: Proceedings of the congress on evolutionary computation. IEEE Press, Vancouver, Canada, pp 17–24
Koziel S, Michalewicz Z (1999) Evolutionary algorithms, homomorphous mappings, and constrained parameter optimization. Evol Comput 7(1):19–44
Lampinen J (2002) A constraint handling approach for the differential evolution algorithm. In: Proceedings of the congress on evolutionary computation. IEEE, New York, pp 1468–1473
Liang JJ, Suganthan PN (2006) Dynamic multi-Swarm particle swarm optimizer with a novel constraint-handling mechanism. In: Proceedings of the congress on evolutionary computation. IEEE Press, Vancouver, Canada, pp 9–16
Montes EM, Coello CAC (2005) A simple multimembered evolution strategy to solve constrained optimization problems. IEEE Trans Evol Comput 9(1):1–17
Montes EM, Reyes JV, Coello CAC (2005) Promising infeasibility and multiple offspring incorporated to differential evolution for constrained optimization. In: Proceedings of the 2005 conference on genetic and evolutionary computation. ACM, New York, NY, pp 225–232
Montes EM, Coello CAC, Reyes JV (2006a) Increasing successful offspring and diversity in differential evolution for engineering design. In: Proceedings of the seventh international conference on adaptive computing in design and manufacture (ACDM 2006), pp 131–139
Montes EM, Reyes JV, Coello CAC (2006b) Modified differential evolution for constrained optimization. In: Proceedings of the congress on evolutionary computation. IEEE Press, Vancouver, Canada, pp 332–339
Poon N, Martins J (2007) An adaptive approach to constraint aggregation using adjoint sensitivity analysis. Struct Multidisc Optim 34(1):61–73
Price K, Storn RM, Lampinen JA (2005) Differential evolution: a practical approach to global optimization (natural computing series). Springer, New York
Puzzi S, Carpinteri A (2008) A double-multiplicative dynamic penalty approach for constrained evolutionary optimization. Struct Multidisc Optim 35(5):431–445
Ray T, Liew KM (2003) Society and civilization: an optimization algorithm based on the simulation of social behavior. IEEE Trans Evol Comput 7(4):386–396
Runarsson TP, Yao X (2000) Stochastic ranking for constrained evolutionary optimization. IEEE Trans Evol Comput 4(3):284–294
Runarsson TP, Yao X (2005) Search biases in constrained evolutionary optimization. IEEE Trans Syst Man Cybern Part C Appl Rev 35(2):233–243
Sinha A, Srinivasan A, Deb K (2006) A population-based, parent centric procedure for constrained real-parameter optimization. In: Proceedings of the congress on evolutionary computation. IEEE Press, Vancouver, Canada, pp 239–245
Storn RM, Price K (1997) Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11(4):341–359
Surry PD, Radcliffe NJ (1997) The COMOGA method: constrained optimisation by multi-objective genetic algorithms. Control Cybern 26(3):391–412
Takahama T, Sakai S (2005) Constrained optimization by applying the alpha constrained method to the nonlinear simplex method with mutations. IEEE Trans Evol Comput 9(5):437–451
Takahama T, Sakai S (2006) Constrained optimization by the ε constrained differential evolution with gradient-based mutation and feasible elites. In: Proceedings of the congress on evolutionary computation. IEEE Press, Vancouver, Canada, pp 1–8
Venter G, Haftka R (2009) Constrained particle swarm optimization using a bi-objective formulation. Struct Multidisc Optim. doi:10.1007/s00158-009-0380-6
Wang JH, Yin ZY (2008) A ranking selection-based particle swarm optimizer for engineering design optimization problems. Struct Multidisc Optim 37(2):131–147
Wang Y, Cai ZX, Zhou YR, Fan Z (2009) Constrained optimization based on hybrid evolutionary algorithm and adaptive constraint-handling technique. Struct Multidisc Optim 37(4):395–413
Zhang M, Luo W, Wang XF (2008) Differential evolution with dynamic stochastic selection for constrained optimization. Inf Sci 178(15):3043–3074
Acknowledgements
This research is partially supported by National Science Foundation of China (Grant No. 60774082, 70871065, 60834004) and the National 863 Program under the grant number 2007AA04Z155 as well as the Program for New Century Excellent Talents in University (NCET).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Wang, L., Li, Lp. An effective differential evolution with level comparison for constrained engineering design. Struct Multidisc Optim 41, 947–963 (2010). https://doi.org/10.1007/s00158-009-0454-5
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00158-009-0454-5