A Hybrid Quadratic Programming And Heuristic Algorithm For Portfolio Selection Problem

The Portfolio Selection Problem is to select a number of assets in a given set of assets and determine the fraction of each selected asset,and to minimize the risk of investment as long as the minimum return requirement of the investor is met.This problem is aimed at solving the problem of portfolio selection problem in finance and economics,which has important practical significance.Although the basic formula of the problem can be effectively solved by linear or quadratic programming,its more practical and realistic changes,its more practical and realistic variants(including various constraints and goals)need to be solved by heuristics in many cases.Algorithms that efficiently solve portfolio optimization problems can be widely applied in finance and economics,and provide effective decisions for investors when choosing investment assets.A hybrid heuristic algorithm combining tabu search and quadratic programming solver is proposed for Portfolio Selection Problem.The original problem is decomposed into two independent sub-problems: the choice of assets and the determination of the fraction of selected assets.The sub-problem of asset selection is a discrete optimization problem,and the determination of the fraction of selected assets is a continuous optimization problem.The first sub-problem will be solved with tabu search algorithm which is more effective.Considering the cost of calling the solver,this algorithm proposes an evaluation system to speed up the iteration of local search by quickly evaluating the actions of different neighborhoods.The second subproblem will be solved using the quadratic programming solver.Since heuristic method is difficult to determine if the optimal solution has been found,but the exact algorithm used by the solver can make sure that.And the calculations show that in this case,using the solver to solve this subproblem is fast enough.By comparing the results of the complete mathematical model with the solver on the public case set,the results show that the efficiency and solution performance of the hybrid heuristic algorithm can reach a very high level.