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

Abstract

To investigate the shape control of smart structures, we have developed a series of genetic algorithms ( GAs ) for an optimal placement of a large number of the piezoelectric actuators. Here we report results from extensive numerical experiments on the GAs, conducted using a coarse-grain parallel computing. We look at how GAs work, what their most distinct properties are, what their robustness means, and how to choose appropriate parameters in applying the micro-GAs. We address the following topics through a thorough comparison of solution quality as obtained by our latest micro-GAs version 3, running on a high performance Sun machine with 17 processors: (i) What is the effect of different random number seeds on the solution quality, specifically a comparison between the results obtained using a small seed and a large seed? (ii) What is the effect of restart criteria in micro-GAs, specifically the two parameters --- number of generations used for the inner loop and the level of diversity in the population on the solution quality? (iii) What is the effect on the solution quality as the number of actuators changes from 30 and 121 to 15, 60, and 90? Through these extended studies, we not only get better layouts of piezoelectric actuators in each of the cases than those reported in our previous publications, but also find that the most distinct natures of genetic algorithms are random and robust. By the random nature of GAs, we mean that we can not precisely predict the performance of genetic algorithms on future evaluations based on their performance on previous evaluations. By the robustness of GAs, we mean that although genetic algorithms have their random nature the range of their results are usually small from their different runs after a certain number of evaluations and they are capable of finding a very good solution by simply adjusting the parameter setting or using another random seed generator. To get high quality solutions in the design of complex adaptive structures using finite element analysis and genetic algorithm optimization, the multiple runs including different random seed generators are necessary. The time of the investigation can be significantly reduced using a very coarse grain parallel computing. We also find that although the RMS error reduces with the number of actuators, the reduction of RMS error may not be worth the effort of increasing the number of actuators. Overall, the methodology of using finite element analysis and genetic algorithm optimization is a very good approach and the GA version 3 is efficient, reliable and robust optimization tool for the challenging problem.