Collaborative Neurodynamic Approaches to Multiobjective Optimization and Their Applications in Portfolio Selection


Student thesis: Doctoral Thesis

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Award date29 Jul 2019


Multiobjective optimization is an important area in both academic research and engineering applications. It is concerned with optimizing two or more objective functions simultaneously, subject to a set of constraints. In contrast to a single-objective optimization problem, the aim of optimizing a multiobjective optimization problem is to obtain a set of Pareto-optimal solutions instead of just one unique solution. A major challenge of optimizing a multiobjective optimization problem lies in the generation of Pareto-optimal solutions with both convergence and diversity, especially when the optimization problem is nonconvex.

Neurodynamic optimization is a continuous-time approach for solving optimization problems based on neural networks. In the past few decades, numerous approaches are proposed for solving various single-objective optimization problems. This thesis focuses on neurodynamic approaches to multiobjective optimization, and their applications in portfolio selection problems.

In the first part, collaborative neurodynamic approaches are presented for linear and nonlinear multiobjective optimization. Multiple neural networks are used to generate Pareto-optimal solutions and a weight optimization based on particle swarm optimizer is used to diversify the solutions. When a multiobjective optimization problem is nonconvex, the states of the neural networks will be reinitialized.

Portfolio selection is of great interest for financial investments from academic and economic points of view. The Markowitz’s ground-breaking work on mean-variance analysis provides a formal framework for portfolio optimization with quantified investment returns and risks. A typical portfolio optimization problem aims to maximize the expected return and minimize the risk of a portfolio simultaneously. Despite its theoretical importance, the mean-variance theory is not perfect, as some of its assumptions are unrealistic. In the second part, various portfolio optimization problems are considered, and they are solved by using various collaborative neurodynamic approaches. Besides, a collaborative neurodynamic approach is also presented to solve portfolio optimization problems with binary variables.