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_35: A challenge in evolutionary computation is to create representations as evolvable as those in natural evolution. This paper hypothesizes that extinction events, i.e. mass extinctions, can significantly increase evolvability, but only when combined with a divergent search algorithm, i.e. a search driven towards diversity (instead of optimality). Extinctions amplify diversity-generation by creating unpredictable evolutionary bottlenecks. Persisting through multiple such bottlenecks is more likely for lineages that diversify across many niches, resulting in indirect selection pressure for the capacity to evolve. This hypothesis is tested through experiments in two evolutionary robotics domains. The results show that combining extinction events with divergent search increases evolvability, while combining them with convergent search offers no similar benefit. The conclusion is that extinction events may provide a simple and effective mechanism to enhance performance of divergent search algorithms.
  @cite_17: We conceived a novel notion of a signature to characterize evolvability.We conducted an extensive comparison of approaches to evolve robot gaits.A better evolvability signature corresponds to faster adaption time in new scenarios.Our evolvability measure is an analysis tool, beyond standard performance benchmarks. Evolutionary robotics is a promising approach to autonomously synthesize machines with abilities that resemble those of animals, but the field suffers from a lack of strong foundations. In particular, evolutionary systems are currently assessed solely by the fitness score their evolved artifacts can achieve for a specific task, whereas such fitness-based comparisons provide limited insights about how the same system would evaluate on different tasks, and its adaptive capabilities to respond to changes in fitness (e.g., from damages to the machine, or in new situations). To counter these limitations, we introduce the concept of "evolvability signatures", which picture the post-mutation statistical distribution of both behavior diversity (how different are the robot behaviors after a mutation?) and fitness values (how different is the fitness after a mutation?). We tested the relevance of this concept by evolving controllers for hexapod robot locomotion using five different genotype-to-phenotype mappings (direct encoding, generative encoding of open-loop and closed-loop central pattern generators, generative encoding of neural networks, and single-unit pattern generators (SUPG)). We observed a predictive relationship between the evolvability signature of each encoding and the number of generations required by hexapods to adapt from incurred damages. Our study also reveals that, across the five investigated encodings, the SUPG scheme achieved the best evolvability signature, and was always foremost in recovering an effective gait following robot damages. Overall, our evolvability signatures neatly complement existing task-performance benchmarks, and pave the way for stronger foundations for research in evolutionary robotics.
summary: In addition to direct applications, several other works focus on studying the properties of QD-algorithms. For example, @cite_35 revealed that extinction events (i.e., erasing a significant part of the collection) increases the evolvability of the solutions @cite_17 and allow the process to find higher-performing solutions afterwards. For example, with MAP-Elites, erasing the entire collection except 10 solutions every 100 000 generations increases the number of filled cells by $20 setups @cite_35 .