A reactive greedy randomized adaptive search procedure for a mixed integer portfolio optimization problem

Purpose – The purpose of this paper is to present a procedure for finding the efficient frontier, i.e. a non‐decreasing curve representing the set of Pareto‐optimal or non‐dominated portfolios, when the standard Markowitz' classical mean‐variance model is enriched with additional constraints. Design/methodology/approach – The mean‐variance portfolio optimization model is extended to include integer constraints that limit a portfolio to have a specified number of assets, and to impose limits on the proportion of the portfolio held in a given asset. Optimization‐based procedures run into difficulties in this framework and this motivates the investigation of heuristic algorithms to find acceptable solutions. Findings – The problem is solved by a greedy randomized adaptive search procedure (GRASP), enhanced by a learning mechanism and a bias function for determining the next element to be introduced in the solution. Originality/value – This is believed to be the first time, a GRASP for finding the efficient frontier for this class of portfolio selection problems is used.