{"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/reinvestigating-the-r2-indicator-achieving","title":"Reinvestigating the R2 Indicator: Achieving Pareto Compliance by Integration","arxiv_id":"2407.01504","date":"2024-07-01","proceeding":null,"authors":["Lennart Schäpermeier","Pascal Kerschke"],"abstract":"In multi-objective optimization, set-based quality indicators are a cornerstone of benchmarking and performance assessment. They capture the quality of a set of trade-off solutions by reducing it to a scalar number. One of the most commonly used set-based metrics is the R2 indicator, which describes the expected utility of a solution set to a decision-maker under a distribution of utility functions. Typically, this indicator is applied by discretizing this distribution of utility functions, yielding a weakly Pareto-compliant indicator. In consequence, adding a nondominated or dominating solution to a solution set may - but does not have to - improve the indicator's value. In this paper, we reinvestigate the R2 indicator under the premise that we have a continuous, uniform distribution of (Tchebycheff) utility functions. We analyze its properties in detail, demonstrating that this continuous variant is indeed Pareto-compliant - that is, any beneficial solution will improve the metric's value. Additionally, we provide an efficient computational procedure to compute this metric for bi-objective problems in $\\mathcal O (N \\log N)$. As a result, this work contributes to the state-of-the-art Pareto-compliant unary performance metrics, such as the hypervolume indicator, offering an efficient and promising alternative.","url_abs":"https://arxiv.org/abs/2407.01504v1","url_pdf":"https://arxiv.org/pdf/2407.01504v1.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":"reinvestigating-the-r2-indicator-achieving","repo_url":"https://github.com/schaepermeier/r2-revisited","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"benchmarking","task_name":"Benchmarking"}],"methods":[{"method_slug":"set","method_name":"SET"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}