{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,29]],"date-time":"2025-09-29T15:49:46Z","timestamp":1759160986362},"reference-count":3,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2008,10,6]],"date-time":"2008-10-06T00:00:00Z","timestamp":1223251200000},"content-version":"vor","delay-in-days":310,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Proc Appl Math and Mech"],"published-print":{"date-parts":[[2007,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In multiobjective optimization there is often the problem of the existence of a large number of objectives. For more than two objectives there is a difficulty with the representation and visualization of the solutions in the objective space. Therefore, it is not clear for the decision maker the trade\u2010off between the different alternative solutions. Thus, this creates enormous difficulties when choosing a solution from the Pareto\u2010optimal set and constitutes a central question in the process of decision making. Based on statistical methods as Principle Component Analysis and Cluster Analysis, the problem of reduction of the number of objectives is addressed. Several test examples with different number of objectives have been studied in order to evaluate the process of decision making through these methods. Preliminary results indicate that this statistical approach can be a valuable tool on decision making in multiobjective optimization. (\u00a9 2008 WILEY\u2010VCH Verlag GmbH &amp; Co. KGaA, Weinheim)<\/jats:p>","DOI":"10.1002\/pamm.200700561","type":"journal-article","created":{"date-parts":[[2008,10,6]],"date-time":"2008-10-06T10:56:38Z","timestamp":1223290598000},"page":"2060047-2060048","source":"Crossref","is-referenced-by-count":6,"title":["Dimension reduction in multiobjective optimization"],"prefix":"10.1002","volume":"7","author":[{"given":"Lino","family":"Costa","sequence":"first","affiliation":[]},{"given":"Pedro","family":"Oliveira","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2008,10,6]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1162\/106365603322519297"},{"key":"e_1_2_1_3_2","unstructured":"J.D.Schaffer:Multiple objective optimization with vector evaluated genetic algorithms. Proceedings of the First International Conference on Genetic Algorithms (J.J Grefensttete Ed. Hillsdale 1985) 93\u2013100."},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1162\/106365600568202"}],"container-title":["PAMM"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fpamm.200700561","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/pamm.200700561","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,2]],"date-time":"2023-09-02T23:44:23Z","timestamp":1693698263000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/pamm.200700561"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,12]]},"references-count":3,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2007,12]]}},"alternative-id":["10.1002\/pamm.200700561"],"URL":"https:\/\/doi.org\/10.1002\/pamm.200700561","archive":["Portico"],"relation":{},"ISSN":["1617-7061","1617-7061"],"issn-type":[{"value":"1617-7061","type":"print"},{"value":"1617-7061","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,12]]}}}