text: The optimization of functions to find the best solution according to one or several objectives has a central role in many engineering and research fields. Recently, a new family of optimization algorithms, named Quality-Diversity optimization, has been introduced, and contrasts with classic algorithms. Instead of searching for a single solution, Quality-Diversity algorithms are searching for a large collection of both diverse and high-performing solutions. The role of this collection is to cover the range of possible solution types as much as possible, and to contain the best solution for each type. The contribution of this paper is threefold. Firstly, we present a unifying framework of Quality-Diversity optimization algorithms that covers the two main algorithms of this family (Multi-dimensional Archive of Phenotypic Elites and the Novelty Search with Local Competition), and that highlights the large variety of variants that can be investigated within this family. Secondly, we propose algorithms with a new selection mechanism for Quality-Diversity algorithms that outperforms all the algorithms tested in this paper. Lastly, we present a new collection management that overcomes the erosion issues observed when using unstructured collections. These three contributions are supported by extensive experimental comparisons of Quality-Diversity algorithms on three different experimental scenarios.
  @cite_5: Numerous algorithms have been proposed to allow legged robots to learn to walk. However, most of these algorithms are devised to learn walking in a straight line, which is not sufficient to accomplish any real-world mission. Here we introduce the Transferability-based Behavioral Repertoire Evolution algorithm TBR-Evolution, a novel evolutionary algorithm that simultaneously discovers several hundreds of simple walking controllers, one for each possible direction. By taking advantage of solutions that are usually discarded by evolutionary processes, TBR-Evolution is substantially faster than independently evolving each controller. Our technique relies on two methods: 1 novelty search with local competition, which searches for both high-performing and diverse solutions, and 2 the transferability approach, which combines simulations and real tests to evolve controllers for a physical robot. We evaluate this new technique on a hexapod robot. Results show that with only a few dozen short experiments performed on the robot, the algorithm learns a repertoire of controllers that allows the robot to reach every point in its reachable space. Overall, TBR-Evolution introduced a new kind of learning algorithm that simultaneously optimizes all the achievable behaviors of a robot.
summary: While this definition is shared with the existing literature, we also stress the importance of the coverage regularity of the produced collections. In the vast majority of the applications presented previously, not only is the coverage of importance but its uniformity is as well. For example, in the locomotion tasks, an even coverage of all possible turning abilities of the robot is required to allow the execution of arbitrary trajectories @cite_5 .