An efficient multi-objective evolutionary fuzzy system for regression problems

During the last years, multi-objective evolutionary algorithms (MOEAs) have been extensively employed as optimization tools for generating fuzzy rule-based systems (FRBSs) with different trade-offs between accuracy and interpretability from data. Since the size of the search space and the computational cost of the fitness evaluation depend on the number of input variables and instances, respectively, managing high-dimensional and large datasets is a critical issue.In this paper, we focus on MOEAs applied to learn concurrently the rule base and the data base of Mamdani FRBSs and propose to tackle the issue by exploiting the synergy between two different techniques. The first technique is based on a novel method which reduces the search space by learning rules not from scratch, but rather from a heuristically generated rule base. The second technique performs an instance selection by exploiting a co-evolutionary approach where cyclically a genetic algorithm evolves a reduced training set which is used in the evolution of the MOEA.The effectiveness of the synergy has been tested on twelve datasets. Using non-parametric statistical tests we show that, although achieving statistically equivalent solutions, the adoption of this synergy allows saving up to 97.38% of the execution time with respect to a state-of-the-art multi-objective evolutionary approach which learns rules from scratch.