{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,2]],"date-time":"2026-06-02T06:51:26Z","timestamp":1780383086765,"version":"3.54.1"},"reference-count":54,"publisher":"MIT Press","issue":"3","content-domain":{"domain":["direct.mit.edu"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2022,9,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>The most relevant property that a quality indicator (QI) is expected to have is Pareto compliance, which means that every time an approximation set strictly dominates another in a Pareto sense, the indicator must reflect this. The hypervolume indicator and its variants are the only unary QIs known to be Pareto-compliant but there are many commonly used weakly Pareto-compliant indicators such as R2, IGD+, and \u03b5+. Currently, an open research area is related to finding new Pareto-compliant indicators whose preferences are different from those of the hypervolume indicator. In this article, we propose a theoretical basis to combine existing weakly Pareto-compliant indicators with at least one being Pareto-compliant, such that the resulting combined indicator is Pareto-compliant as well. Most importantly, we show that the combination of Pareto-compliant QIs with weakly Pareto-compliant indicators leads to indicators that inherit properties of the weakly compliant indicators in terms of optimal point distributions. The consequences of these new combined indicators are threefold: (1) to increase the variety of available Pareto-compliant QIs by correcting weakly Pareto-compliant indicators, (2) to introduce a general framework for the combination of QIs, and (3) to generate new selection mechanisms for multiobjective evolutionary algorithms where it is possible to achieve\/adjust desired distributions on the Pareto front.<\/jats:p>","DOI":"10.1162\/evco_a_00307","type":"journal-article","created":{"date-parts":[[2022,2,18]],"date-time":"2022-02-18T21:09:11Z","timestamp":1645218551000},"page":"381-408","update-policy":"https:\/\/doi.org\/10.1162\/mitpressjournals.corrections.policy","source":"Crossref","is-referenced-by-count":13,"title":["On the Construction of Pareto-Compliant Combined Indicators"],"prefix":"10.1162","volume":"30","author":[{"given":"J. G.","family":"Falc\u00f3n-Cardona","sequence":"first","affiliation":[{"name":"Computer Science Department, CINVESTAV-IPN, Mexico City, 07360, Mexico jfalcon@computacion.cs.cinvestav.mx"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"M. T. M.","family":"Emmerich","sequence":"additional","affiliation":[{"name":"LIACS, Leiden University, Leiden, 2333, The Netherlands m.t.m.emmerich@liacs.leidenuniv.nl"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"C. A. 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