Genetic algorithm designed for solving portfolio optimization problems subjected to cardinality constraint

In the present study, a new algorithm named BEXPM-RM is proposed which require no constraint handling techniques to solve portfolio optimization problems subjected to budget, cardinality, and lower/upper bound constraints. The algorithm presented combines the BEX-PM (Thakur et al. in Appl Math Comput 235:292–317, 2014) genetic algorithm (GA) together with repair mechanism (RM) proposed by Chang et al. (Comput Oper Res 27(13):1271–1302, 2000). BEXPM GA tries to efficiently explore the search space whereas repair method suggested by Chang et al. (2000) ensures that a solution string is always feasible subject to the budget, cardinality, and lower/upper bound constraints. To analyze the performance of BEXPM-RM, six portfolio optimization problems are considered from the literature (Chang et al. 2000; Barak et al. in Eur J Oper Res 228(1):141–147, 2013). Among these one problem uses fuzzy set theory and others used probability theory to quantify attributes of a portfolio. In addition to these problems, a new portfolio model is formulated in fuzzy environment to analyze the effect of providing different sets of lower or/and upper bound to an asset. © 2017, The Society for Reliability Engineering, Quality and Operations Management (SREQOM), India and The Division of Operation and Maintenance, Lulea University of Technology, Sweden.