An effective differential evolution with level comparison for constrained engineering design

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.

[1]  R. Storn,et al.  Differential Evolution: A Practical Approach to Global Optimization (Natural Computing Series) , 2005 .

[2]  Aravind Srinivasan,et al.  A Population-Based, Parent Centric Procedure for Constrained Real-Parameter Optimization , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[3]  George S. Dulikravich,et al.  A response surface method-based hybrid optimizer , 2008 .

[4]  Tapabrata Ray,et al.  Society and civilization: An optimization algorithm based on the simulation of social behavior , 2003, IEEE Trans. Evol. Comput..

[5]  Xiaohui Yuan,et al.  A Modified Differential Evolution for Constrained Optimization , 2008 .

[6]  Ricardo Landa Becerra,et al.  Efficient evolutionary optimization through the use of a cultural algorithm , 2004 .

[7]  Ling Wang,et al.  A hybrid particle swarm optimization with a feasibility-based rule for constrained optimization , 2007, Appl. Math. Comput..

[8]  Xin Yao,et al.  Search biases in constrained evolutionary optimization , 2005, IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews).

[9]  R. Haftka,et al.  Constrained particle swarm optimization using a bi-objective formulation , 2009 .

[10]  J. Lampinen.  A constraint handling approach for the differential evolution algorithm , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[11]  Jinhua Wang,et al.  A ranking selection-based particle swarm optimizer for engineering design optimization problems , 2008 .

[12]  Jing J. Liang,et al.  Dynamic Multi-Swarm Particle Swarm Optimizer with a Novel Constraint-Handling Mechanism , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[13]  Jonathan A. Wright,et al.  Self-adaptive fitness formulation for constrained optimization , 2003, IEEE Trans. Evol. Comput..

[14]  Zbigniew Michalewicz,et al.  Evolutionary Algorithms, Homomorphous Mappings, and Constrained Parameter Optimization , 1999, Evolutionary Computation.

[15]  Sana Ben Hamida,et al.  An Adaptive Algorithm for Constrained Optimization Problems , 2000, PPSN.

[16]  Carlos A. Coello Coello,et al.  Modified Differential Evolution for Constrained Optimization , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[17]  Joaquim R. R. A. Martins,et al.  An adaptive approach to constraint aggregation using adjoint sensitivity analysis , 2007 .

[18]  Xin Yao,et al.  Stochastic ranking for constrained evolutionary optimization , 2000, IEEE Trans. Evol. Comput..

[19]  Carlos A. Coello Coello,et al.  Promising infeasibility and multiple offspring incorporated to differential evolution for constrained optimization , 2005, GECCO '05.

[20]  Yong Wang,et al.  A Multiobjective Optimization-Based Evolutionary Algorithm for Constrained Optimization , 2006, IEEE Transactions on Evolutionary Computation.

[21]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

[22]  Zhun Fan,et al.  Constrained optimization based on hybrid evolutionary algorithm and adaptive constraint-handling technique , 2009 .

[23]  Carlos A. Coello Coello,et al.  THEORETICAL AND NUMERICAL CONSTRAINT-HANDLING TECHNIQUES USED WITH EVOLUTIONARY ALGORITHMS: A SURVEY OF THE STATE OF THE ART , 2002 .

[24]  Tetsuyuki Takahama,et al.  Constrained Optimization by the ε Constrained Differential Evolution with Gradient-Based Mutation and Feasible Elites , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[25]  Wenjian Luo,et al.  Differential evolution with dynamic stochastic selection for constrained optimization , 2008, Inf. Sci..

[26]  Patrick D. Surry,et al.  The COMOGA Method: Constrained Optimisation by Multi-Objective Genetic Algorithms , 1997 .

[27]  Tetsuyuki Takahama,et al.  Constrained optimization by applying the /spl alpha/ constrained method to the nonlinear simplex method with mutations , 2005, IEEE Transactions on Evolutionary Computation.

[28]  Ling Wang,et al.  An effective co-evolutionary particle swarm optimization for constrained engineering design problems , 2007, Eng. Appl. Artif. Intell..

[29]  Carlos A. Coello Coello,et al.  Constraint-handling in genetic algorithms through the use of dominance-based tournament selection , 2002, Adv. Eng. Informatics.

[30]  S. Puzzi,et al.  A double-multiplicative dynamic penalty approach for constrained evolutionary optimization , 2008 .

[31]  C. Coello,et al.  Cultured differential evolution for constrained optimization , 2006 .

[32]  A. Kai Qin,et al.  Self-adaptive Differential Evolution Algorithm for Constrained Real-Parameter Optimization , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[33]  Ling Wang,et al.  An effective co-evolutionary differential evolution for constrained optimization , 2007, Appl. Math. Comput..

[34]  Helio J. C. Barbosa,et al.  A new adaptive penalty scheme for genetic algorithms , 2003, Inf. Sci..

[35]  Carlos A. Coello Coello,et al.  A simple multimembered evolution strategy to solve constrained optimization problems , 2005, IEEE Transactions on Evolutionary Computation.

[36]  K. Deb.  An Efficient Constraint Handling Method for Genetic Algorithms , 2000 .