{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/using-centroidal-voronoi-tessellations-to","title":"Using Centroidal Voronoi Tessellations to Scale Up the Multi-dimensional Archive of Phenotypic Elites Algorithm","arxiv_id":"1610.05729","date":"2016-10-18","proceeding":null,"authors":["Vassilis Vassiliades","Konstantinos Chatzilygeroudis","Jean-Baptiste Mouret"],"abstract":"The recently introduced Multi-dimensional Archive of Phenotypic Elites\n(MAP-Elites) is an evolutionary algorithm capable of producing a large archive\nof diverse, high-performing solutions in a single run. It works by discretizing\na continuous feature space into unique regions according to the desired\ndiscretization per dimension. While simple, this algorithm has a main drawback:\nit cannot scale to high-dimensional feature spaces since the number of regions\nincrease exponentially with the number of dimensions. In this paper, we address\nthis limitation by introducing a simple extension of MAP-Elites that has a\nconstant, pre-defined number of regions irrespective of the dimensionality of\nthe feature space. Our main insight is that methods from computational geometry\ncould partition a high-dimensional space into well-spread geometric regions. In\nparticular, our algorithm uses a centroidal Voronoi tessellation (CVT) to\ndivide the feature space into a desired number of regions; it then places every\ngenerated individual in its closest region, replacing a less fit one if the\nregion is already occupied. We demonstrate the effectiveness of the new\n\"CVT-MAP-Elites\" algorithm in high-dimensional feature spaces through\ncomparisons against MAP-Elites in maze navigation and hexapod locomotion tasks.","url_abs":"http://arxiv.org/abs/1610.05729v2","url_pdf":"http://arxiv.org/pdf/1610.05729v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"using-centroidal-voronoi-tessellations-to","repo_url":"https://github.com/resibots/vassiliades_2017_cvt_map_elites","is_official":0,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok"}},{"paper_slug":"using-centroidal-voronoi-tessellations-to","repo_url":"https://github.com/adaptive-intelligent-robotics/dcg-map-elites","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"jax","reach":{"status":"ok","spdx":"MIT"}},{"paper_slug":"using-centroidal-voronoi-tessellations-to","repo_url":"https://github.com/ollenilsson19/MAP-Elites-GAPG","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}},{"paper_slug":"using-centroidal-voronoi-tessellations-to","repo_url":"https://github.com/ollenilsson19/PGA-MAP-Elites","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}},{"paper_slug":"using-centroidal-voronoi-tessellations-to","repo_url":"https://github.com/sferes2/cvt_map_elites","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=1610.05729","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}