Optimization test function synthesis with generative adversarial networks and adaptive neuro-fuzzy systems

This paper presents an approach to synthesizing optimization test functions that couples generative adversarial networks and adaptive neuro-fuzzy systems. A generative adversarial network produces optimization landscapes from a database of known optimization test functions, and an adaptive neuro-fuzzy system performs regression on the generated landscapes to provide closed-form expressions. These expressions can be implemented as fuzzy basis function expansions. Eight databases of two-dimensional optimization landscapes reported in the literature are used to train the generative network. Exploratory landscape analysis over the generated samples reveals that the network can lead to new optimization landscapes with features of interest. In addition, fuzzy basis function expansions provide the best approximation results when compared against two symbolic regression frameworks over several selected landscapes. Examples are used to illustrate the ability of these functions to model complex surface artifacts such as plateaus. The proposed approach can be used as a mathematical collaboration tool that couples generative artificial and computational intelligence techniques to formulate high-dimensional optimization test problems from two-dimensional synthesized functions.