Stationary Fuzzy Fokker–Planck Learning for Derivative-Free Optimization

Stationary fuzzy Fokker-Planck learning (SFFPL) is a recently introduced computational method that applies fuzzy modeling to solve optimization problems. This study develops a concept of applying SFFPL-based computations for nonlinear constrained optimization. We consider the development of SFFPL-based optimization algorithms which do not require derivatives of the objective function and of the constraints. The sequential penalty approach was used to handle the inequality constraints. It was proved under some standard assumptions that the carefully designed SFFPL-based algorithms converge asymptotically to the stationary points. The convergence proofs follow a simple mathematical approach and invoke mean-value theorem. The algorithms were evaluated on the test problems with the number of variables up to 50. The performance comparison of the proposed algorithms with some of the standard optimization algorithms further justifies our approach. The SFFPL-based optimization approach, due to its novelty, could possibly be extended to several research directions.