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In complex, expensive optimization domains we often narrowly focus on finding high performing solutions, instead of expanding our understanding of the domain itself. But what if we could quickly understand the complex behaviors that can emerge in said domains instead? We introduce surrogate-assisted phenotypic niching, a quality diversity algorithm which allows to discover a large, diverse set of behaviors by using computationally expensive phenotypic features. In this work we discover the types of air flow in a 2D fluid dynamics optimization problem. A fast GPU-based fluid dynamics solver is used in conjunction with surrogate models to accurately predict fluid characteristics from the shapes that produce the air flow. We show that these features can be modeled in a data-driven way while sampling to improve performance, rather than explicitly sampling to improve feature models. Our method can reduce the need to run an infeasibly large set of simulations while still being able to design a large diversity of air flows and the shapes that cause them. Discovering diversity of behaviors helps engineers to better understand expensive domains and their solutions.
In optimization methods that return diverse solution sets, three interpretations of diversity can be distinguished: multi-objective optimization which searches diversity in objective space, multimodal optimization which tries spreading out the solutions in genetic space, and quality diversity which performs diversity maintenance in phenotypic space. We introduce niching methods that provide more flexibility to the analysis of diversity and a simple domain to compare and provide insights about the paradigms. We show that multiobjective optimization does not always produce much diversity, quality diversity is not sensitive to genetic neutrality and creates the most diverse set of solutions, and multimodal optimization produces higher fitness solutions. An autoencoder is used to discover phenotypic features automatically, producing an even more diverse solution set. Finally, we make recommendations about when to use which approach.