{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,22]],"date-time":"2026-06-22T21:22:23Z","timestamp":1782163343768,"version":"3.54.5"},"reference-count":38,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2017,11,28]],"date-time":"2017-11-28T00:00:00Z","timestamp":1511827200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>Portfolio optimization is a serious challenge for financial engineering and has pulled down special attention among investors. It has two objectives: to maximize the reward that is calculated by expected return and to minimize the risk. Variance has been considered as a risk measure. There are many constraints in the world that ultimately lead to a non\u2013convex search space such as cardinality constraint. In conclusion, parametric quadratic programming could not be applied and it seems essential to apply multi-objective evolutionary algorithm (MOEA). In this paper, a new efficient multi-objective portfolio optimization algorithm called 2-phase NSGA II algorithm is developed and the results of this algorithm are compared with the NSGA II algorithm. It was found that 2-phase NSGA II significantly outperformed NSGA II algorithm.<\/jats:p>","DOI":"10.3390\/a10040130","type":"journal-article","created":{"date-parts":[[2017,11,28]],"date-time":"2017-11-28T11:23:50Z","timestamp":1511868230000},"page":"130","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":20,"title":["2-Phase NSGA II: An Optimized Reward and Risk Measurements Algorithm in Portfolio Optimization"],"prefix":"10.3390","volume":"10","author":[{"given":"Seyedeh","family":"Eftekharian","sequence":"first","affiliation":[{"name":"Department of Financial Engineering, Raja University of Qazvin, Qazvin 341451177, Iran"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mohammad","family":"Shojafar","sequence":"additional","affiliation":[{"name":"Department of Information Engineering, Electronics and Telecommunications, University of Rome Sapienza, Via Eudossiana 18, 00184 Rome, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6605-498X","authenticated-orcid":false,"given":"Shahaboddin","family":"Shamshirband","sequence":"additional","affiliation":[{"name":"Department for Management of Science and Technology Development, Ton Duc Thang University, Ho Chi Minh City, Vietnam"},{"name":"Faculty of Information Technology, Ton Duc Thang University, Ho Chi Minh City, Vietnam"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2017,11,28]]},"reference":[{"key":"ref_1","first-page":"77","article-title":"Portfolio selection","volume":"7","author":"Markowitz","year":"1952","journal-title":"J. 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