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_28: This paper presents a machine learning approach to optimizing a quadrupedal trot gait for forward speed. Given a parameterized walk designed for a specific robot, we propose using a form of policy gradient reinforcement learning to automatically search the set of possible parameters with the goal of finding the fastest possible walk. We implement and test our approach on a commercially available quadrupedal robot platform, namely the Sony Aibo robot. After about three hours of learning, all on the physical robots and with no human intervention other than to change the batteries, the robots achieved a gait faster than any previously known gait known for the Aibo, significantly outperforming a variety of existing hand-coded and learned solutions.
  @cite_42: An ambitious challenge in artificial life is to craft an evolutionary process that discovers a wide diversity of well-adapted virtual creatures within a single run. Unlike in nature, evolving creatures in virtual worlds tend to converge to a single morphology because selection therein greedily rewards the morphology that is easiest to exploit. However, novelty search, a technique that explicitly rewards diverging, can potentially mitigate such convergence. Thus in this paper an existing creature evolution platform is extended with multi-objective search that balances drives for both novelty and performance. However, there are different ways to combine performance-driven search and novelty search. The suggested approach is to provide evolution with both a novelty objective that encourages diverse morphologies and a local competition objective that rewards individuals outperforming those most similar in morphology. The results in an experiment evolving locomoting virtual creatures show that novelty search with local competition discovers more functional morphological diversity within a single run than models with global competition, which are more predisposed to converge. The conclusions are that novelty search with local competition may complement recent advances in evolving virtual creatures and may in general be a principled approach to combining novelty search with pressure to achieve.
summary: The authors of Novelty Search also introduced the Novelty Search with Local Competition'' algorithm (NSLC) @cite_42 , in which the exploration focuses on solutions that are both novel (according to the novelty score) and locally high-performing. The main insight consists of comparing the performance of a solution only to those that are close in the descriptor space. This is achieved with a local quality score'' that is defined as the number of the k-nearest neighboring solutions in the novelty archive with a lower performance (e.g., slower walking speed @cite_42 ) than the considered solution. The exploration is then achieved with a multi-objective optimization algorithm (e.g., NSGA-II @cite_28 ) that optimizes both the novelty and local quality scores of the solutions. However, the local quality score does not influence the threshold used to select whether an individual is added to the novelty archive. The final result of NSLC is the population of the optimization algorithm, which contains solutions that are both novel and high-performing compared to other local solutions. In other words, the population gathers solutions that are both different from those saved in the novelty archive, and high-performing when compared to similar types of solutions.