A study on fuzzy cognitive map optimization using metaheuristics

Abstract

Fuzzy Cognitive Maps (FCMs) are a framework based on weighted directed graphs which can be used for system modeling. The relationships between the concepts are stored in graph edges and they are expressed as real numbers from the [−1, 1] interval (called weights). Our goal was to evaluate the effectiveness of non-deterministic optimization algorithms which can calculate weight matrices (i.e. collections of all weights) of FCMs for synthetic and real-world time series data sets. The best results were reported for Differential Evolution (DE) with recombination based on 3 random individuals, as well as Particle Swarm Optimization (PSO) where each particle is guided by its neighbors and the best particle. The choice of the algorithm was not crucial for maps of size roughly up to 10 nodes, however, the difference in performance was substantial (in the orders of magnitude) for bigger matrices.