A multiobjective genetic algorithm for portofolio selection with integer constraints

Abstract

In this paper we develop a computational procedure in order to find the efficient frontier, i.e.
a non-decreasing curve representing the set of Pareto-optimal or non-dominated portfolios, for
the standard Markowitz mean-variance model enriched with integer constraints. These constraints
limit both the portfolio to contain a predetermined number of assets and the proportion of the
portfolio held in a given asset. The problem is solved by adapting the multiobjective algorithm
NSGA (Non-dominated Sorting Genetic Algorithm) that ranks the solutions of each generation
in layers based on Pareto non-domination. The algorithm was applied in 60 assets of ATHEX
and a comparison with a single genetic algorithm was realized. The computational results indicate
that the procedure is promising for this class of problems.