{"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/an-approach-to-ordering-objectives-and-pareto","title":"An Approach to Ordering Objectives and Pareto Efficient Solutions","arxiv_id":"2205.15291","date":"2022-05-30","proceeding":null,"authors":["Sebastian Hönel","Welf Löwe"],"abstract":"Solutions to multi-objective optimization problems can generally not be compared or ordered, due to the lack of orderability of the single objectives. Furthermore, decision-makers are often made to believe that scaled objectives can be compared. This is a fallacy, as the space of solutions is in practice inhomogeneous without linear trade-offs. We present a method that uses the probability integral transform in order to map the objectives of a problem into scores that all share the same range. In the score space, we can learn which trade-offs are actually possible and develop methods for mapping the desired trade-off back into the preference space. Our results demonstrate that Pareto efficient solutions can be ordered using a low- or no-preference aggregation of the single objectives. When using scores instead of raw objectives during optimization, the process allows for obtaining trade-offs significantly closer to the expressed preference. Using a non-linear mapping for transforming a desired solution in the score space to the required preference for optimization improves this even more drastically.","url_abs":"https://arxiv.org/abs/2205.15291v1","url_pdf":"https://arxiv.org/pdf/2205.15291v1.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":"an-approach-to-ordering-objectives-and-pareto","repo_url":"https://github.com/MrShoenel/precondition-moop","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"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}