{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,8]],"date-time":"2026-04-08T11:44:42Z","timestamp":1775648682694,"version":"3.50.1"},"reference-count":20,"publisher":"MIT Press - Journals","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Evolutionary Computation"],"published-print":{"date-parts":[[2018,3]]},"abstract":"<jats:p> Non-dominated sorting is a technique often used in evolutionary algorithms to determine the quality of solutions in a population. The most common algorithm is the Fast Non-dominated Sort (FNS). This algorithm, however, has the drawback that its performance deteriorates when the population size grows. The same drawback applies also to other non-dominating sorting algorithms such as the Efficient Non-dominated Sort with Binary Strategy (ENS-BS). An algorithm suggested to overcome this drawback is the Divide-and-Conquer Non-dominated Sort (DCNS) which works well on a limited number of objectives but deteriorates when the number of objectives grows. This article presents a new, more efficient algorithm called the Efficient Non-dominated Sort with Non-Dominated Tree (ENS-NDT). ENS-NDT is an extension of the ENS-BS algorithm and uses a novel Non-Dominated Tree (NDTree) to speed up the non-dominated sorting. ENS-NDT is able to handle large population sizes and a large number of objectives more efficiently than existing algorithms for non-dominated sorting. In the article, it is shown that with ENS-NDT the runtime of multi-objective optimization algorithms such as the Non-Dominated Sorting Genetic Algorithm II (NSGA-II) can be substantially reduced. <\/jats:p>","DOI":"10.1162\/evco_a_00204","type":"journal-article","created":{"date-parts":[[2017,1,19]],"date-time":"2017-01-19T20:09:05Z","timestamp":1484856545000},"page":"89-116","source":"Crossref","is-referenced-by-count":51,"title":["A New Algorithm Using the Non-Dominated Tree to Improve Non-Dominated Sorting"],"prefix":"10.1162","volume":"26","author":[{"given":"Patrik","family":"Gustavsson","sequence":"first","affiliation":[{"name":"School of Engineering, University of Sk\u00f6vde, Sk\u00f6vde, 54134, Sweden"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Anna","family":"Syberfeldt","sequence":"additional","affiliation":[{"name":"School of Engineering, University of Sk\u00f6vde, Sk\u00f6vde, 54134, Sweden"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"281","reference":[{"key":"B1","doi-asserted-by":"publisher","DOI":"10.1145\/361002.361007"},{"key":"B2","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-0000(73)80033-9"},{"issue":"1","key":"B3","first-page":"50","volume":"4","author":"Brown R. 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