The Effect of Local Search on the Constrained Portfolio Selection Problem

Abstract

The portfolio selection problem is a prominent example for multi-objective optimization in financial engineering. While for some problem instances of the portfolio selection problem there are efficient optimization algorithms, other problem instances can only be addressed by means of meta-heuristics like evolutionary algorithms. These more complicated problem instances include portfolio selection with multiple quadratic objectives or with non-linear constraints, like cardinality constraints. Evolutionary algorithms allow hybridization with local search heuristics, resulting in so called memetic algorithms. Such memetic approaches to the portfolio selection problem seem to be an interesting alternative. Unfortunately, the interaction between the evolutionary global search and the local search heuristic is complicated and difficult to understand. In this paper we evaluate the hybridization of a multi-objective evolutionary algorithm and a quadratic programming local search on multiple instances of the constrained and unconstrained portfolio selection problem using a problem specific representation. This multi-objective memetic algorithm proves to be a two-edged approach: On the one hand it improves the convergence rate for some problem instances. While on other hand problem instances the local search causes a neutral search space and eventually premature convergence. This paper investigates this behavior more closely, offers a plausible explanation and also outlines a possible remedy.