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The encoding of solutions in black-box optimization is a delicate, handcrafted balance between expressiveness and domain knowledge between exploring a wide variety of solutions, and ensuring that those solutions are useful. Our main insight is that this process can be automated by generating a dataset of high-performing solutions with a quality diversity algorithm (here, MAP-Elites), then learning a representation with a generative model (here, a Varia-tional Autoencoder) from that dataset. Our second insight is that this representation can be used to scale quality diversity optimization to higher dimensions-but only if we carefully mix solutions generated with the learned representation and those generated with traditional variation operators. We demonstrate these capabilities by learning an low-dimensional encoding for the inverse kinemat-ics of a thousand joint planar arm. The results show that learned representations make it possible to solve high-dimensional problems with orders of magnitude fewer evaluations than the standard MAP-Elites, and that, once solved, the produced encoding can be used for rapid optimization of novel, but similar, tasks. The presented techniques not only scale up quality diversity algorithms to high dimensions, but show that black-box optimization encodings can be automatically learned, rather than hand designed.
Optimization plays an essential role in industrial design, but is not limited to minimization of a simple function, such as cost or strength. These tools are also used in conceptual phases, to better understand what is possible. To support this exploration we focus on Quality Diversity (QD) algorithms, which produce sets of varied, high performing solutions. These techniques often require the evaluation of millions of solutions -- making them impractical in design cases. In this thesis we propose methods to radically improve the data-efficiency of QD with machine learning, enabling its application to design. In our first contribution, we develop a method of modeling the performance of evolved neural networks used for control and design. The structures of these networks grow and change, making them difficult to model -- but with a new method we are able to estimate their performance based on their heredity, improving data-efficiency by several times. In our second contribution we combine model-based optimization with MAP-Elites, a QD algorithm. A model of performance is created from known designs, and MAP-Elites creates a new set of designs using this approximation. A subset of these designs are the evaluated to improve the model, and the process repeats. We show that this approach improves the efficiency of MAP-Elites by orders of magnitude. Our third contribution integrates generative models into MAP-Elites to learn domain specific encodings. A variational autoencoder is trained on the solutions produced by MAP-Elites, capturing the common “recipe” for high performance. This learned encoding can then be reused by other algorithms for rapid optimization, including MAP-Elites. Throughout this thesis, though the focus of our vision is design, we examine applications in other fields, such as robotics. These advances are not exclusive to design, but serve as foundational work on the integration of QD and machine learning.
The way solutions are represented, or encoded, is usually the result of domain knowledge and experience. In this work, we combine MAP-Elites with Variational Autoencoders to learn a Data-Driven Encoding (DDE) that captures the essence of the highest-performing solutions while still able to encode a wide array of solutions. Our approach learns this data-driven encoding during optimization by balancing between exploiting the DDE to generalize the knowledge contained in the current archive of elites and exploring new representations that are not yet captured by the DDE. Learning representation during optimization allows the algorithm to solve high-dimensional problems, and provides a low-dimensional representation which can be then be re-used. We evaluate the DDE approach by evolving solutions for inverse kinematics of a planar arm (200 joint angles) and for gaits of a 6-legged robot in action space (a sequence of 60 positions for each of the 12 joints). We show that the DDE approach not only accelerates and improves optimization, but produces a powerful encoding that captures a bias for high performance while expressing a variety of solutions.
AErOmAt Abschlussbericht
(2020)
Das Projekt AErOmAt hatte zum Ziel, neue Methoden zu entwickeln, um einen erheblichen Teil aerodynamischer Simulationen bei rechenaufwändigen Optimierungsdomänen einzusparen. Die Hochschule Bonn-Rhein-Sieg (H-BRS) hat auf diesem Weg einen gesellschaftlich relevanten und gleichzeitig wirtschaftlich verwertbaren Beitrag zur Energieeffizienzforschung geleistet. Das Projekt führte außerdem zu einer schnelleren Integration der neuberufenen Antragsteller in die vorhandenen Forschungsstrukturen.