Extensive Experiments on Genetic Algorithms for the Optimization of Piezoelectric Actuator Locations

Abstract

For shape control of smart structures, we have developed a series of micro-genetic-algorithms for optimal placement of a large number of piezoelectric actuators. Here, we investigate the effect on the solution quality of 1) different random seed generators; 2) restart criteria in micro-genetic-algorithms, specifically the two parameters, the number of generations used for the inner loop and the level of diversity in the population; and 3) different numbers of actuators. We also report a comparison of our genetic algorithms with two heuristic integer programming algorithms: worst-out-best-in and exhaustive single point substitution proposed by Haftka and Adelman (Selection of Actuator Locations for Static Shape Control of Large Space Structures by Heuristic Integer Programming, Computers and Structures, Vol. 20, 1985, pp. 572-582). Using current genetic algorithms, we not only get better layouts of actuators than reported in our previous publications, but we also find that the most distinct nature of genetic algorithms is randomness and robustness. The best parameter setting of genetic algorithms is dependent on both the number of evaluations used for termination and the seed generator used. Moreover, the best parameter setting of genetic algorithms varies as the number of actuators changes. To get the highest quality of solutions, multiple runs using different random seed generators are necessary. The time of investigation can be significantly reduced using a coarse grain parallel computing. Comparison of our genetic algorithms with the worst-out-best-in and exhaustive single point substitution shows that for a group of runs our genetic algorithms usually converge faster in the first few thousand evaluations and are more likely to find better solutions than the worst-out-best-in and exhaustive single point substitution algorithms.