An Efficient Local Search Algorithm For Constrained Portfolio Selection Problems

Portfolio selection problem is a common problem in financial economics.Portfolio selection problem aims to get a solution about the selection of assets and the share of investment in each asset.Portfolio provides investors with the minimum return as well as the minimum risk.To solve this problem,Markowitz proposed the mean-variance model of portfolio in 1952.Although the basic portfolio problem can be solved by linear programming or quadratic programming,its more practical and realistic variants which include a variety of constraints and objectives,often need to be solved by heuristics.In this paper,we study the constrained portfolio optimization problem and design an efficient local search algorithm based on Markowitz mean-variance model.Two constraints are added to the Markowitz MV model in order to form the CMV model:the cardinality constraint and the quantity constraint.The cardinality constraint limits the number of assets,and the quantity constraint limits the upper and lower limits of assets.A hybrid solution technique based on local search and genetic algorithm is used to solve the solution.Using genetic algorithm to select the assets first,selecting a potential advantage combination from varieties of alternative combinations.Local search is used to conduct in-depth search to adjust the num and proportion of assets,and three different neighborhood moves are combined to solve the problem.Besides,a combination of randomization and adaptive method is used to simplify the setting of key parameters,which can not only preserves the excellent structure of understanding,but also simplifies the solving process.By using this efficient local search technique to solve the constrained portfolio problem,a set of feasible allocation schemes can be obtained to balance the risks and benefits.Compared with the results of different algorithms,our heuristic algorithm is tested on the common benchmark example sets,and the results show that the heuristic algorithm has high efficiency and good solution performance.