{"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/learning-to-approximate-auto-direction-vector","title":"Learning to Approximate: Auto Direction Vector Set Generation for Hypervolume Contribution Approximation","arxiv_id":"2201.06707","date":"2022-01-18","proceeding":null,"authors":["Ke Shang","Tianye Shu","Hisao Ishibuchi"],"abstract":"Hypervolume contribution is an important concept in evolutionary multi-objective optimization (EMO). It involves in hypervolume-based EMO algorithms and hypervolume subset selection algorithms. Its main drawback is that it is computationally expensive in high-dimensional spaces, which limits its applicability to many-objective optimization. Recently, an R2 indicator variant (i.e., $R_2^{\\text{HVC}}$ indicator) is proposed to approximate the hypervolume contribution. The $R_2^{\\text{HVC}}$ indicator uses line segments along a number of direction vectors for hypervolume contribution approximation. It has been shown that different direction vector sets lead to different approximation quality. In this paper, we propose \\textit{Learning to Approximate (LtA)}, a direction vector set generation method for the $R_2^{\\text{HVC}}$ indicator. The direction vector set is automatically learned from training data. The learned direction vector set can then be used in the $R_2^{\\text{HVC}}$ indicator to improve its approximation quality. The usefulness of the proposed LtA method is examined by comparing it with other commonly-used direction vector set generation methods for the $R_2^{\\text{HVC}}$ indicator. Experimental results suggest the superiority of LtA over the other methods for generating high quality direction vector sets.","url_abs":"https://arxiv.org/abs/2201.06707v1","url_pdf":"https://arxiv.org/pdf/2201.06707v1.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":"learning-to-approximate-auto-direction-vector","repo_url":"https://github.com/hisaolabsustc/lta","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}