Adaptive fuzzy fitness granulation for evolutionary optimization

Abstract

Nature may have been the original inspiration for evolutionary algorithms, but unlike artificially designed systems, nature has an abundance of resources and time. For man-made systems, computational complexity is a prohibitive factor in sufficiently large and complex problems of today. Much of this computational complexity is due to the fitness function evaluation that may either not exist or be computationally very expensive. But, an exact computation of fitness may not be really necessary as long as a proper rank is approximately preserved in the evolution’s scheme of the survival of the fittest. Here, we aim to exploit this feature of evolution and to investigate the use of fitness granulation via an adaptive fuzzy similarity analysis in order to reduce the number of fitness evaluations. In the proposed algorithm, an individual’s fitness is only computed if it has insufficient similarity to a pool of fuzzy granules whose fitness has already been computed. If an individual is sufficiently similar to a known fuzzy granule, then that granule’s fitness is used instead as a crude estimate. Otherwise, that individual is added to the pool as the core of a new fuzzy granule. Each granule’s radius of influence is adaptive and will grow/shrink depending on the population fitness. The proposed technique is applied to two sets of problems. First is a set of several numerical benchmark problems with various optimization characteristics. Second is a set of four hardware design problems that are evaluated via finite element analysis. Performance of the proposed algorithm is compared with several other competing algorithms, i.e. a fast evolutionary strategy (FES), a GA-NN, as well as a simple GA, in terms of both computational efficiency and accuracy. Statistical analysis reveals that the proposed method significantly decreases the number of fitness function evaluations while finding equally good or better solutions. Moreover, application to the hardware design problems reveals better structural designs more consistently with better computational efficiency.