Comparison of Genetic Algorithms and Heuristic Integer Programming on the Optimization of Piezoelectric Actuator Locations

Abstract

Optimal placement of actuators has been studied for more than 20 years. The typical optimization methods for the problem, including heuristic integer programming, tabu search, simulated annealing, and genetic algorithms, have been developed over the years. However, the comparison of various methods has not been addressed. This paper compares two heuristic integer programming algorithms: Worst-Out-Best-In (WOBI) and Exhaustive Single Point Substitution (ESPS) proposed by Haftka and Adelman in early 1980s with Genetic Algorithms (GAs) developed most recently by present authors. The problems considered here are the large-scale optimization of N piezoelectric strip actuator location from a set of M possible locations on the back surface of a hexagonal spherical mirror for thermal deformation control. The number of candidate placements for these problems are too large to use an exhaustive method. The comparison of GAs with WOBI and ESPS are made on two types of optimization problems: (i) to find the optimal locations and optimal voltages suitable for only a single type of thermal loads at a given time, and (ii) to determine just one set of actuator locations which will be good for all the four types of thermal loads considered in this study. Although both these problems are large, difficult and computationally intensive, combinatorial and continuous optimization problems, the latter is a more challenging, multi-criterion optimization problem. Several interesting results are observed. For example, the results show that both WOBI and ESPS usually converge to local optima and that the rate of the convergence of ESPS is much lower than that of WOBI and GAs and that the number of evaluations required for ESPS convergence might be too large to accept for large-scale optimization. As for the quality of final solutions they find in a group of runs, GAs are usually better than ESPS, and WOBI is the worst. Also, the paper explores reasonable use of these algorithms. For example, considering the fast rate of convergence in the early stage of the GA optimization and the fact that it is hard, if not impossible, to say whether GAs have reached the global optima using limited runs, the paper recommends that WOBI and ESPS might be used to check whether GAs have reached the optima in the sense of WOBI and ESPS. This check is not necessary if GAs are allowed to run enough time. Because the number of evaluations for ESPS convergence is quite large, the effect of the fast reanalysis by neglecting the stiffness effect of actuators is also investigated in the paper.