{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,11]],"date-time":"2026-07-11T06:01:30Z","timestamp":1783749690264,"version":"3.55.0"},"reference-count":29,"publisher":"MIT Press - Journals","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Evolutionary Computation"],"published-print":{"date-parts":[[2015,9]]},"abstract":"<jats:p> In multiobjective optimization, set-based performance indicators are commonly used to assess the quality of a Pareto front approximation. Based on the scalarization obtained by these indicators, a performance comparison of multiobjective optimization algorithms becomes possible. The [Formula: see text] and the hypervolume (HV) indicator represent two recommended approaches which have shown a correlated behavior in recent empirical studies. Whereas the HV indicator has been comprehensively analyzed in the last years, almost no studies on the [Formula: see text] indicator exist. In this extended version of our previous conference paper, we thus perform a comprehensive investigation of the properties of the [Formula: see text] indicator in a theoretical and empirical way. The influence of the number and distribution of the weight vectors on the optimal distribution of [Formula: see text] solutions is analyzed. Based on a comparative analysis, specific characteristics and differences of the [Formula: see text] and HV indicator are presented. Furthermore, the [Formula: see text] indicator is integrated into an indicator-based steady-state evolutionary multiobjective optimization algorithm (EMOA). It is shown that the so-called [Formula: see text]-EMOA can accurately approximate the optimal distribution of [Formula: see text] solutions regarding [Formula: see text]. <\/jats:p>","DOI":"10.1162\/evco_a_00135","type":"journal-article","created":{"date-parts":[[2014,7,1]],"date-time":"2014-07-01T19:13:26Z","timestamp":1404242006000},"page":"369-395","source":"Crossref","is-referenced-by-count":84,"title":["2 Indicator-Based Multiobjective Search"],"prefix":"10.1162","volume":"23","author":[{"given":"Dimo","family":"Brockhoff","sequence":"first","affiliation":[{"name":"DOLPHIN Team, INRIA Lille, Nord Europe, 59650 Villeneuve d\u2019Ascq, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tobias","family":"Wagner","sequence":"additional","affiliation":[{"name":"Institute of Machining Technology, TU Dortmund University, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Heike","family":"Trautmann","sequence":"additional","affiliation":[{"name":"Information Systems and Statistics, M\u00fcnster University, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"281","reference":[{"key":"B1","doi-asserted-by":"publisher","DOI":"10.1145\/1569901.1569980"},{"key":"B2","doi-asserted-by":"publisher","DOI":"10.1145\/1527125.1527138"},{"key":"B3","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2011.03.012"},{"key":"B4","doi-asserted-by":"publisher","DOI":"10.1162\/EVCO_a_00009"},{"key":"B6","doi-asserted-by":"publisher","DOI":"10.1109\/TEVC.2009.2015575"},{"key":"B7","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejor.2006.08.008"},{"key":"B8","first-page":"207","volume-title":"Mathematical Foundations of Computer Science","author":"Bringmann K.","year":"2012"},{"key":"B9","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-92182-0_40"},{"key":"B10","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-01020-0_6"},{"key":"B11","doi-asserted-by":"publisher","DOI":"10.1145\/2330163.2330230"},{"key":"B12","doi-asserted-by":"publisher","DOI":"10.1109\/FOCS.2013.51"},{"key":"B14","doi-asserted-by":"publisher","DOI":"10.1109\/CEC.2002.1007032"},{"key":"B16","doi-asserted-by":"publisher","DOI":"10.1162\/106365601750190398"},{"key":"B18","doi-asserted-by":"publisher","DOI":"10.1162\/evco.2007.15.1.1"},{"key":"B19","doi-asserted-by":"publisher","DOI":"10.1109\/CEC.2009.4982991"},{"key":"B20","doi-asserted-by":"publisher","DOI":"10.1145\/1830483.1830578"},{"key":"B22","volume-title":"Statistical methods","author":"Snedecor G. 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