Adaptive Fuzzy Fitness Granulation in Structural Optimization Problems

Abstract

Computational complexity is a prohibitive factor in evolutionary optimization of sufficiently large and/or complex problems. Much of this computational complexity is due to the fitness function evaluation that may either not exist or be computationally very expensive. Here, we investigate the use of fitness granulation via an adaptive fuzzy similarity analysis as applied to two different hardware design problems that are evaluated using finite element analysis. The first design problem is a relatively simpler 2-D truss frame design with 36 parameters while the second problem is piezoelectric voltage and pattern arrangement design for static shape control in which 200 parameters are optimized. In comparison with standard application of evolutionary algorithms, statistical analysis reveals that the proposed method significantly decreases the number of fitness function evaluations while finding equally good or better solutions. Additionally, this more improvement is indicated with higher problem complexity.