Novel multiobjective evolutionary algorithm approaches with application in the constrained portfolio optimization

Abstract

Multiobjective optimization (MO) is the problem of simultaneously optimizing two or more conflicting objectives subject to certain constraints. Many real-world problems involve simultaneous optimization of several often conflicting objectives. The portfolio optimization problem belongs to this category of problems. According to Markowitz’s Mean - Variance model (MV) an investor attempts to maximize portfolio expected return for a given amount of portfolio risk or minimize portfolio risk for a given level of expected return. The portfolio optimization problem involves two conflicting objectives (i.e. expected return and portfolio risk) and thus belongs to the family of multiobjective problems. With the assistance of scalarization techniques a multiple objective problem can be converted into a single objective problem. However, the drawbacks to these conventional approaches lead to the development of alternative techniques that yield a set of Pareto optimal solutions rather than only a single solution. The problem becomes much more complicated when we incorporate to the portfolio model some real world constraints. These additional constraints made the portfolio optimization problem difficult to be solved with exact methods. In the last decade several metaheuristic optimization techniques have been developed to address the challenges imposed by complex multiobjective optimization problems. Due to the intrinsic multiobjective nature of the portfolio optimization problem, multiobjective approaches, particularly multiobjective evolutionary algorithms (MOEAs) are suitable in handling the difficulties imposed by this type of problems. Especially in the presence of multiple constraints the portfolio optimization problem becomes very complicate and efficient solution needs to be found.Furthermore, the existing multiobjective evolutionary algorithms (MOEAs) techniques cannot be used directly to solve the constrained portfolio optimization problem as a number of configuration issues related to the application of MOEAs for solving the constrained portfolio optimization problem must be addressed. The successful implementation of the constrained portfolio optimization problem by the MOEAs requires the development of novel algorithmic and technical approaches. In particular new multiobjective evolutionary approaches are needed to efficiently solve the constrained portfolio optimization problem. In this thesis we address these issues by examining a number of configuration issues related to the application of MOEAs for solving the constrained portfolio optimization problem. Furthermore we introduce a new multiobjective evolutionary algorithm (MOEA) that incorporates a novel representation scheme and specially designed genetic operators for the solution of the constrained portfolio optimization problem. These issues have been addressed in this thesis and a set of efficient solutions is found for each of the examined test problems. In this thesis we develop a methodological framework for conducting a comprehensive literature study based on the papers published in MOEAs for the Portfolio Management over a long time span across various disciplines. This framework is being used to gain an understanding of the current state of the MOEAs for the Portfolio Management research field. Based on the literature study, we identify potential areas of concern in regard to MOEAs for the Portfolio Management. Based on the examination of the state-of-the art we present the best practices from a technical and algorithmic point of view for dealing with the complexities of the constrained portfolio optimization problem. We introduce new genetic operators to enhance algorithms’ performance. We propose a novel representation scheme for the solution of the constrained portfolio optimization problem. Finally, we introduce a novel MOEA for the solution of the constrained portfolio optimization problem. The experimental results applied to the constrained portfolio optimization problem, indicate that the proposed approach generates solutions that lie on the true efficient frontier (TEF) for all of the examined cases for a fraction of time required by exact approaches.