{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,3]],"date-time":"2025-12-03T17:48:07Z","timestamp":1764784087746},"reference-count":48,"publisher":"MIT Press","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Evolutionary Computation"],"published-print":{"date-parts":[[2019,6]]},"abstract":"<jats:p>For a many-objective optimization problem with redundant objectives, we propose two novel objective reduction algorithms for linearly and, nonlinearly degenerate Pareto fronts. They are called LHA and NLHA respectively. The main idea of the proposed algorithms is to use a hyperplane with non-negative sparse coefficients to roughly approximate the structure of the PF. This approach is quite different from the previous objective reduction algorithms that are based on correlation or dominance structure. Especially in NLHA, in order to reduce the approximation error, we transform a nonlinearly degenerate Pareto front into a nearly linearly degenerate Pareto front via a power transformation. In addition, an objective reduction framework integrating a magnitude adjustment mechanism and a performance metric [Formula: see text] are also proposed here. Finally, to demonstrate the performance of the proposed algorithms, comparative experiments are done with two correlation-based algorithms, LPCA and NLMVUPCA, and with two dominance-structure-based algorithms, PCSEA and greedy [Formula: see text]MOSS, on three benchmark problems: DTLZ5(I,M), MAOP(I,M), and WFG3(I,M). Experimental results show that the proposed algorithms are more effective.<\/jats:p>","DOI":"10.1162\/evco_a_00223","type":"journal-article","created":{"date-parts":[[2018,5,1]],"date-time":"2018-05-01T13:55:58Z","timestamp":1525182958000},"page":"313-344","source":"Crossref","is-referenced-by-count":13,"title":["Hyperplane-Approximation-Based Method for Many-Objective Optimization Problems with Redundant Objectives"],"prefix":"10.1162","volume":"27","author":[{"given":"Yifan","family":"Li","sequence":"first","affiliation":[{"name":"School of Applied Mathematics, Guangdong University of Technology, Guangzhou, 510520, China"}]},{"given":"Hai-Lin","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Applied Mathematics, Guangdong University of Technology, Guangzhou, 510520, China"}]},{"given":"E. D.","family":"Goodman","sequence":"additional","affiliation":[{"name":"BEACON Center for the Study of Evolution in Action (NSF DBI-0939454), Michigan State University, East Lansing, MI 48824, USA"}]}],"member":"281","reference":[{"key":"B1","doi-asserted-by":"publisher","DOI":"10.1162\/EVCO_a_00009"},{"key":"B2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-19893-9_6"},{"key":"B3","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejor.2006.08.008"},{"key":"B4","doi-asserted-by":"publisher","DOI":"10.1109\/TEVC.2003.810761"},{"key":"B5","doi-asserted-by":"publisher","DOI":"10.1007\/11844297_54"},{"key":"B6","doi-asserted-by":"publisher","DOI":"10.1162\/evco.2009.17.2.135"},{"key":"B7","doi-asserted-by":"publisher","DOI":"10.1109\/CEC.2014.6900548"},{"key":"B8","doi-asserted-by":"publisher","DOI":"10.1109\/TEVC.2016.2519758"},{"issue":"4","key":"B9","first-page":"1040","volume":"6","author":"Coleman T. F.","year":"1996","journal-title":"Society for Industrial and Applied Mathematics, Journal on Optimization"},{"key":"B10","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-45356-3_82"},{"key":"B11","doi-asserted-by":"publisher","DOI":"10.1109\/TEVC.2013.2281535"},{"key":"B12","doi-asserted-by":"publisher","DOI":"10.1162\/106365605774666895"},{"key":"B13","doi-asserted-by":"publisher","DOI":"10.1109\/4235.996017"},{"key":"B14","author":"Deb K.","year":"2005","journal-title":"On finding Pareto-optimal solutions through dimensionality reduction for certain large-dimensional multi-objective optimization problems"},{"key":"B15","doi-asserted-by":"publisher","DOI":"10.1016\/S0377-2217(99)00139-3"},{"key":"B16","first-page":"282:363","author":"Giagkiozis I.","year":"2014","journal-title":"Information Sciences"},{"key":"B17","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-003-0487-2"},{"key":"B18","doi-asserted-by":"publisher","DOI":"10.1109\/CEC.2015.7257243"},{"key":"B19","doi-asserted-by":"publisher","DOI":"10.1109\/TEVC.2015.2433266"},{"key":"B20","doi-asserted-by":"publisher","DOI":"10.1162\/evco.2007.15.4.493"},{"key":"B21","doi-asserted-by":"publisher","DOI":"10.1109\/TEVC.2005.861417"},{"key":"B22","doi-asserted-by":"publisher","DOI":"10.1109\/CEC.2001.934293"},{"key":"B23","doi-asserted-by":"publisher","DOI":"10.1109\/TEVC.2015.2505784"},{"key":"B24","first-page":"2419","author":"Ishibuchi H.","year":"2008","journal-title":"Evolutionary Computation"},{"key":"B25","doi-asserted-by":"publisher","DOI":"10.1109\/TEVC.2016.2587749"},{"key":"B26","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-01020-0_34"},{"key":"B27","doi-asserted-by":"publisher","DOI":"10.1109\/TEVC.2002.802873"},{"key":"B28","first-page":"727","volume-title":"Proceedings of Evolutionary Multi-Criterion Optimization, 4th International Conference","author":"K\u00f6ppen M.","year":"2006"},{"key":"B29","doi-asserted-by":"publisher","DOI":"10.1162\/106365602760234108"},{"key":"B30","doi-asserted-by":"publisher","DOI":"10.1109\/TEVC.2008.925798"},{"key":"B31","doi-asserted-by":"publisher","DOI":"10.1109\/TEVC.2014.2373386"},{"key":"B32","doi-asserted-by":"publisher","DOI":"10.1109\/TCYB.2014.2365354"},{"issue":"6","key":"B33","first-page":"1264","volume":"49","author":"Liu H.","year":"2012","journal-title":"Journal of Computer Research and Development"},{"key":"B34","doi-asserted-by":"publisher","DOI":"10.1109\/MCI.2013.2291690"},{"key":"B35","doi-asserted-by":"publisher","DOI":"10.1109\/TEVC.2013.2281533"},{"issue":"99","key":"B36","author":"Luo J.","year":"2015","journal-title":"IEEE Transactions on Evolutionary Computation"},{"key":"B37","doi-asserted-by":"publisher","DOI":"10.1109\/CEC.2003.1299927"},{"key":"B38","doi-asserted-by":"publisher","DOI":"10.1109\/TCYB.2014.2334632"},{"key":"B39","doi-asserted-by":"publisher","DOI":"10.1109\/TEVC.2012.2185847"},{"key":"B40","doi-asserted-by":"publisher","DOI":"10.1109\/TEVC.2010.2093579"},{"key":"B41","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-89694-4_41"},{"key":"B42","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-89694-4_41"},{"issue":"1","key":"B43","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1111\/j.2517-6161.1996.tb02080.x","volume":"58","author":"Tibshirani R","year":"1996","journal-title":"Journal of the Royal Statistical Society"},{"key":"B44","doi-asserted-by":"publisher","DOI":"10.1109\/TEVC.2012.2227145"},{"key":"B45","doi-asserted-by":"publisher","DOI":"10.1109\/TEVC.2007.892759"},{"key":"B46","doi-asserted-by":"publisher","DOI":"10.1109\/TEVC.2015.2457245"},{"key":"B47","first-page":"3242:832","author":"Zitzler E.","year":"2004","journal-title":"Lecture Notes in Computer Science"},{"key":"B48","first-page":"95","volume-title":"Proceedings of Evolutionary Methods for Design Optimization and Control with Applications to Industrial Problems","author":"Zitzler E.","year":"2001"}],"container-title":["Evolutionary Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mitpressjournals.org\/doi\/pdf\/10.1162\/evco_a_00223","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,7,6]],"date-time":"2024-07-06T12:01:40Z","timestamp":1720267300000},"score":1,"resource":{"primary":{"URL":"https:\/\/direct.mit.edu\/evco\/article\/27\/2\/313-344\/1090"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,6]]},"references-count":48,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2019,6]]}},"alternative-id":["10.1162\/evco_a_00223"],"URL":"https:\/\/doi.org\/10.1162\/evco_a_00223","relation":{},"ISSN":["1063-6560","1530-9304"],"issn-type":[{"value":"1063-6560","type":"print"},{"value":"1530-9304","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,6]]}}}