Evolutionary Algorithms for Global Optimization

The Chapter presents some evolutionary algorithm based methods used for solving global optimization problems. Firstly, the methods, which use proportional selection, are briefly described. Secondly, a bicriterion approach is applied for solving the constrained function minimization problem. This method transforms the constrained function minimization problem to the bicriteria optimization problem in the way that the first objective function is the sum of violated constraints and the second objective function is the one that should be minimized. Thirdly, the constraint tournament selection method is presented. The aim of the method is to reduce the number of function evaluations in the optimization process. The method is very effective while solving highly constrained single criterion optimization problems as well as the problems with the computationally expensive objective function. The method may also reduce the computation time for ordinary nonlinear programming problems as well as produce better results. Finally, the application of evolutionary algorithms to two design optimization problems is presented. The first problem deals with optimum design of concentric springs, whereas the second problem deals with the optimum design of a robot gripper. Both of these problems are considered as discrete programming problems. For problems like these the use of conventional optimization methods is very limited or even impossible. As it is shown in this Chapter evolutionary algorithm based methods can easily handle such problems.

[1]  Jerzy Montusiewicz,et al.  A Random-Search Approach to Multicriterion Discrete Optimization , 1994 .

[2]  Zbigniew Michalewicz,et al.  Genetic AlgorithmsNumerical Optimizationand Constraints , 1995, ICGA.

[3]  Abdollah Homaifar,et al.  Constrained Optimization Via Genetic Algorithms , 1994, Simul..

[4]  Erik Lund,et al.  Finite Element Based Engineering Design Sensitivity Analysis and Optimization , 1995 .

[5]  Hyun Myung,et al.  A Two-Phase Evolutionary Programming for General Constrained Optimization Problem , 1996, Evolutionary Programming.

[6]  David Mautner Himmelblau,et al.  Applied Nonlinear Programming , 1972 .

[7]  H Myung,et al.  Hybrid evolutionary programming for heavily constrained problems. , 1996, Bio Systems.

[8]  Panos M. Pardalos,et al.  Recent Advances in Global Optimization , 1991 .

[9]  Mitsuo Gen,et al.  A survey of penalty techniques in genetic algorithms , 1996, Proceedings of IEEE International Conference on Evolutionary Computation.

[10]  Kalyanmoy Deb,et al.  GeneAS: A Robust Optimal Design Technique for Mechanical Component Design , 1997 .

[11]  Ajg Bert Schoofs.  Experimental Design and Structural Optimization , 1988 .

[12]  Keigo Watanabe,et al.  Evolutionary Optimization of Constrained Problems , 2004 .

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

[14]  K. Stanislaw,et al.  A new constraint tournament selection method for multicriteria optimization using genetic algorithm , 2000, Proceedings of the 2000 Congress on Evolutionary Computation. CEC00 (Cat. No.00TH8512).

[15]  Mitsuo Gen,et al.  Genetic algorithms and engineering design , 1997 .

[16]  Byoung-Tak Zhang,et al.  Comparison of Selection Methods for Evolutionary Optimization , 2000 .

[17]  Lawrence Davis,et al.  Using a genetic algorithm to optimize problems with feasibility constraints , 1994, Proceedings of the First IEEE Conference on Evolutionary Computation. IEEE World Congress on Computational Intelligence.

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

[19]  C. G. Broyden,et al.  A smooth sequential penalty function method for solving nonlinear programming problems , 1984 .

[20]  A. Osyczka,et al.  Computer aided multicriterion optimization system for computationally expensive functions , 1994 .

[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]  J. P. Karidis,et al.  Efficient Optimization of Computationally Expensive Objective Functions , 1986 .