Multiobjective cellular genetic algorithm with adaptive fuzzy fitness granulation

Computational complexity is a major challenge in evolutionary algorithms due to their need for repeated fitness function evaluations. In the context of multiobjective evolutionary algorithms, there are a few attentions to the computational complexity of this kind of algorithms. Here, we aim to reduce number of fitness function evaluations in multiobjective cellular genetic algorithms by the use of fitness granulation via an adaptive fuzzy similarity analysis. In the proposed algorithm, an individual´s fitness is only computed if it has insufficient similarity to a queue 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 queue as a new fuzzy granule. The queue size as well as each granule´s radius of influence is adaptive and will grow/shrink depending on the population fitness and the number of dissimilar granules. The proposed method is applied to a set of 6 test problems. In comparison with two well-known multiobjective evolutionary algorithms, NSGA-II, and MoCell, computational results show that the proposed method is competitive with these algorithms.