Surrogate modeling based on an adaptive network and granular computing

Reducing the number of evaluations of expensive fitness functions is one of the main concerns in evolutionary algorithms, especially when working with instances of contemporary engineering problems. As an alternative to this efficiency constraint, surrogate-based methods are grounded in the construction of approximate models that estimate the solutions’ fitness by modeling the relationships between solution variables and their performance. This paper proposes a methodology based on granular computing for the construction of surrogate models for evolutionary algorithms. Under the proposed method, granules are associated with representative solutions of the problem under analysis. New solutions are evaluated with the expensive (original) fitness function only if they are not already covered by an existing granule. The parameters defining granules are periodically adapted as the search goes on using a neuro-fuzzy network that does not only reduce the number of fitness function evaluations, but also provides better convergence capabilities. The proposed method is evaluated on classical benchmark functions and on a recent benchmark created to test large-scale optimization models. Our results show that the proposed method considerably reduces the actual number of fitness function evaluations without significantly degrading the quality of solutions.