Hidden-genes multi-dimensional archive of phenotypic elites: a quality-diversity algorithm for conditional search-space problems

Abstract The preliminary design and optimization of engineering systems requires to make architectural and technological choices that can be represented by design variables called conditional variables. They are acting on the structure of the optimization problem (e.g., number of design variables and constraints) along the iterations. In the early design phases, the decision makers may be interested in obtaining a set of valuable solutions presenting a diversity of characteristics. Quality-Diversity (QD) is an optimization paradigm tailored for providing optimal solutions with respect to an objective function and diversified with respect to feature functions. Multi-dimensional Archive of Phenotypic Elites (MAP-Elites) is a popular QD algorithm which explores the design space using evolutionary operations. This work extends the MAP-Elites algorithm to deal with conditional variables by developing an adapted mutation mechanism. The performance of the proposed method is assessed on four test-cases of increasing complexity. Three of them are analytical and the last one is an engineering representative problem dealing with the design of a sounding rocket.