Constrained Optimization by ε Constrained Differential Evolution with Dynamic ε-Level Control

In this chapter, the improved e constrained differential evolution (eDE) is proposed to solve constrained optimization problems with very small feasible region, such as problems with equality constraints, efficiently. The eDE is the combination of the e constrained method and differential evolution. In general, it is very difficult to solve constrained problems with very small feasible region. To solve such problems, static control schema of allowable constraint violation is often used, where solutions are searched within enlarged region specified by the allowable violation and the region is reduced to the feasible region gradually. However, the proper control depends on the initial population and searching process. In this study, the dynamic control of allowable violation is proposed to solve problems with equality constraints efficiently. In the eDE, the amount of allowable violation can be specified by the e-level. The effectiveness of the eDE with dynamic e-level control is shown by comparing with the original eDE and well known optimization method on some nonlinear constrained problems with equality constraints.

[1]  H. Kunzi,et al.  Lectu re Notes in Economics and Mathematical Systems , 1975 .

[2]  Klaus Schittkowski,et al.  More test examples for nonlinear programming codes , 1981 .

[3]  Zbigniew Michalewicz,et al.  A Survey of Constraint Handling Techniques in Evolutionary Computation Methods , 1995 .

[4]  Rainer Storn,et al.  Minimizing the real functions of the ICEC'96 contest by differential evolution , 1996, Proceedings of IEEE International Conference on Evolutionary Computation.

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

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

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

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

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

[10]  Tetsuyuki Takahama,et al.  Tuning fuzzy control rules by the ? constrained method which solves constrained nonlinear optimization problems , 2000 .

[11]  Russell C. Eberhart,et al.  Solving Constrained Nonlinear Optimization Problems with Particle Swarm Optimization , 2002 .

[12]  Tapabrata Ray,et al.  An intelligent information sharing strategy within a swarm for unconstrained and constrained optimization problems , 2002, Soft Comput..

[13]  S. Halgamuge,et al.  A comparison of constraint-handling methods for the application of particle swarm optimization to constrained nonlinear optimization problems , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

[14]  T. Takahama,et al.  Constrained Optimization by α Constrained Genetic Algorithm (αGA) , 2003 .

[15]  Tetsuyuki Takahama,et al.  Learning fuzzy control rules by alpha-constrained Simplex method , 2003, Systems and Computers in Japan.

[16]  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.

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

[18]  Shichao Zhang,et al.  AI 2005: Advances in Artificial Intelligence, 18th Australian Joint Conference on Artificial Intelligence, Sydney, Australia, December 5-9, 2005, Proceedings , 2005, Australian Conference on Artificial Intelligence.

[19]  Tetsuyuki Takahama,et al.  Constrained Optimization by epsilon Constrained Particle Swarm Optimizer with epsilon-level Control , 2005, WSTST.

[20]  Tetsuyuki Takahama,et al.  Constrained Optimization by the epsilon Constrained Hybrid Algorithm of Particle Swarm Optimization and Genetic Algorithm , 2005, Australian Conference on Artificial Intelligence.

[21]  T. Takahama,et al.  Solving Constrained Optimization Problems by the ε Constrained Particle Swarm Optimizer with Adaptive Velocity Limit Control , 2006, 2006 IEEE Conference on Cybernetics and Intelligent Systems.

[22]  Tetsuyuki Takahama,et al.  Solving Nonlinear Constrained Optimization Problems by the ε Constrained Differential Evolution , 2006, 2006 IEEE International Conference on Systems, Man and Cybernetics.

[23]  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.