{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,26]],"date-time":"2026-03-26T12:47:44Z","timestamp":1774529264737,"version":"3.50.1"},"reference-count":28,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2017,8,25]],"date-time":"2017-08-25T00:00:00Z","timestamp":1503619200000},"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>The portfolio optimization problem is the central problem of modern economics and decision theory; there is the Mean-Variance Model and Stochastic Dominance Model for solving this problem. In this paper, based on the second order stochastic dominance constraints, we propose the improved biogeography-based optimization algorithm to optimize the portfolio, which we called    \u03b5   BBO. In order to test the computing power of    \u03b5   BBO, we carry out two numerical experiments in several kinds of constraints. In experiment 1, comparing the Stochastic Approximation (SA) method with the Level Function (LF) algorithm and Genetic Algorithm (GA), we get a similar optimal solution by    \u03b5   BBO in     [ 0 , 0 . 6 ]     and     [ 0 , 1 ]     constraints with the return of 1.174% and 1.178%. In     [ - 1 , 2 ]     constraint, we get the optimal return of 1.3043% by    \u03b5   BBO, while the return of SA and LF is 1.23% and 1.26%. In experiment 2, we get the optimal return of 0.1325% and 0.3197% by    \u03b5   BBO in     [ 0 , 0 . 1 ]     and     [ - 0 . 05 , 0 . 15 ]     constraints. As a comparison, the return of FTSE100 Index portfolio is 0.0937%. The results prove that    \u03b5   BBO algorithm has great potential in the field of financial decision-making, it also shows that    \u03b5   BBO algorithm has a better performance in optimization problem.<\/jats:p>","DOI":"10.3390\/a10030100","type":"journal-article","created":{"date-parts":[[2017,8,25]],"date-time":"2017-08-25T11:03:17Z","timestamp":1503658997000},"page":"100","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Biogeography-Based Optimization of the Portfolio Optimization Problem with Second Order Stochastic Dominance Constraints"],"prefix":"10.3390","volume":"10","author":[{"given":"Tao","family":"Ye","sequence":"first","affiliation":[{"name":"School of economic and management, Hainan University, No. 58 Renmin Avenue, Haikou 570228, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ziqiang","family":"Yang","sequence":"additional","affiliation":[{"name":"College of Information Science & Technology, Hainan University, No. 58 Renmin Avenue, Haikou 570228, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Siling","family":"Feng","sequence":"additional","affiliation":[{"name":"College of Information Science & Technology, Hainan University, No. 58 Renmin Avenue, Haikou 570228, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,8,25]]},"reference":[{"key":"ref_1","first-page":"77","article-title":"Portfolio Selection","volume":"7","author":"Markowitz","year":"1952","journal-title":"J. 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