Management of categorical variables using probability features in a genetic algorithm for expensive black-box optimization

Various real-life applications combine continuous and categorical variables. For instance, in mechanical design, components can be characterized by real-valued geometrical parameters (e.g. spring lengths, plate thicknesses, hole diameters), in addition to variables defining a material type or a configuration option. Challenges arise for optimization methods when dealing with nominal categorical variables without any natural ordering. In this work, we propose strategies based on ‘probability features’ to improve their management inside genetic algorithms, in particular within a surrogate-based optimization context. These probability features aim to represent the likelihood of the non-numerical ‘values’, namely attributes, of a categorical variable to be selected during the optimization process. The proposed strategies are applied on a set of test problems coming from structural, mechanical and thermal engineering design. The numerical experiments have been performed based on the genetic algorithm provided by Minamo, Cenaero's in-house multi-disciplinary optimization platform, showing promising results when categorical variables bring a high level of complexity to the search space.