A Study on Evolutionary Multi-Objective Optimization with Fuzzy Approximation for Computational Expensive Problems

Recent progress in the development of Evolutionary Algorithms made them one of the most powerful and flexible optimization tools for dealing with Multi-Objective Optimization problems. Nowadays one challenge in applying MOEAs to real-world applications is that they usually need a large number of fitness evaluations before a satisfying result can be obtained. Several methods have been presented to tackle this problem and among these the use of approximate models within MOEA-based optimization methods proved to be beneficial whenever dealing with problems that need computationally expensive objective evaluations. In this paper we present a study on a general approach based on an inexpensive fuzzy function approximation strategy, that uses data collected during the evolution to build and refine an approximate model. When the model becomes reliable it is used to select only promising candidate solutions for real evaluation. Our approach is integrated with popular MOEAs and their performance are assessed by means of benchmark test problems. Numerical experiments, with a low budget of fitness evaluations, show improvement in efficiency while maintaining a good quality of solutions.