Combining Grammatical Evolution with Modal Interval Analysis: An Application to Solve Problems with Uncertainty

Abstract

Complex systems are usually affected by various sources of uncertainty, and it is essential to account for mechanisms that ensure the proper management of such disturbances. This paper introduces a novel approach to solve symbolic regression problems, which combines the potential of Grammatical Evolution to obtain solutions by describing the search space with context-free grammars, and the ability of Modal Interval Analysis (MIA) to handle quantified uncertainty. The presented methodology uses an MIA solver to evaluate the fitness function, which represents a novel method to manage uncertainty by means of interval-based prediction models. This paper first introduces the theory that establishes the basis of the proposed methodology, and follows with a description of the system architecture and implementation details. Then, we present an illustrative application example which consists of determining the outer and inner approximations of the mean velocity of the water current of a river stretch. Finally, the interpretation of the obtained results and the limitations of the proposed methodology are discussed.

Keywords

• modal interval analysis
• machine learning
• interval arithmetic
• grammatical evolution
• data science
• uncertainty modelling