A micro niche evolutionary algorithm with lower-dimensional-search crossover for optimisation problems with constraints

This paper proposes a micro niche evolutionary algorithm (MNEA) with lower-dimensional-search crossover for optimisation problems with constraints. The best individual in each niche is picked out and all those picked individuals compose the breeding pool of the evolutionary algorithm. Crossover operator of the algorithm searches a lower dimensional space which is determined by the parent points. Both the niche technique and the crossover technique are favourable to enhance the performance of the algorithm. The new algorithm has been tested by the 24 constrained benchmark problems and the results show that it works better than or competitive to any known effective algorithm. Notably, using this new algorithm to solve a well-known engineering problem (pressure vessel problem), its result is much better than that of any other known algorithm.

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

[2]  Vassilios Petridis,et al.  Varying Fitness Functions in Genetic Algorithms: Studying the Rate of Increase of the Dynamic Penalty Terms , 1998, PPSN.

[3]  Z. Michalewicz,et al.  Genocop III: a co-evolutionary algorithm for numerical optimization problems with nonlinear constraints , 1995, Proceedings of 1995 IEEE International Conference on Evolutionary Computation.

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

[5]  Carlos A. Coello Coello,et al.  Handling constraints using multiobjective optimization concepts , 2004 .

[6]  Jing J. Liang,et al.  Problem Deflnitions and Evaluation Criteria for the CEC 2006 Special Session on Constrained Real-Parameter Optimization , 2006 .

[7]  Marc Schoenauer,et al.  ASCHEA: new results using adaptive segregational constraint handling , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[8]  S. N. Kramer,et al.  An Augmented Lagrange Multiplier Based Method for Mixed Integer Discrete Continuous Optimization and Its Applications to Mechanical Design , 1994 .

[9]  T. Takahama,et al.  Learning fuzzy control rules by a constrained Powell's method , 1999, FUZZ-IEEE'99. 1999 IEEE International Fuzzy Systems. Conference Proceedings (Cat. No.99CH36315).

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

[11]  Francisco Herrera,et al.  A taxonomy for the crossover operator for real‐coded genetic algorithms: An experimental study , 2003, Int. J. Intell. Syst..

[12]  Hans-Paul Schwefel,et al.  Evolution and Optimum Seeking: The Sixth Generation , 1993 .

[13]  Colin R. Reeves,et al.  Genetic Algorithms for the Operations Researcher , 1997, INFORMS J. Comput..

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

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

[16]  Zbigniew Michalewicz,et al.  Evolutionary Algorithms for Constrained Parameter Optimization Problems , 1996, Evolutionary Computation.

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

[18]  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 .

[19]  Riccardo Poli,et al.  Particle swarm optimization , 1995, Swarm Intelligence.

[20]  X. Yao,et al.  Evolutionary search and constraint violations , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

[21]  Christopher R. Houck,et al.  On the use of non-stationary penalty functions to solve nonlinear constrained optimization problems with GA's , 1994, Proceedings of the First IEEE Conference on Evolutionary Computation. IEEE World Congress on Computational Intelligence.

[22]  Lawrence J. Fogel,et al.  Artificial Intelligence through Simulated Evolution , 1966 .

[23]  Heder S. Bernardino,et al.  A new hybrid AIS-GA for constrained optimization problems in mechanical engineering , 2008, 2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence).

[24]  Carlos A. Coello Coello,et al.  Hybridizing a genetic algorithm with an artificial immune system for global optimization , 2004 .

[25]  Gary G. Yen,et al.  A generic framework for constrained optimization using genetic algorithms , 2005, IEEE Transactions on Evolutionary Computation.

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