Variable Division and Optimization for Constrained Multiobjective Portfolio Problems

TL;DR

This paper introduces a variable division and optimization approach within a multiobjective evolutionary algorithm to effectively solve constrained portfolio problems, demonstrating superior performance on large-scale instances.

Contribution

It develops a formal elitist partial variable selection method for multiobjective problems and integrates it into a decomposition-based EA for portfolio optimization.

Findings

Outperforms existing methods on large-scale portfolio problems.

Maintains good diversity and convergence in solutions.

Effective on both single- and multi-objective problems.

Abstract

Variable division and optimization (D\&O) is a frequently utilized algorithm design paradigm in Evolutionary Algorithms (EAs). A D\&O EA divides a variable into partial variables and then optimize them respectively. A complicated problem is thus divided into simple subtasks. For example, a variable of portfolio problem can be divided into two partial variables, i.e. the selection of assets and the allocation of capital. Thereby, we optimize these two partial variables respectively. There is no formal discussion about how are the partial variables iteratively optimized and why can it work for both single- and multi-objective problems in D\&O. In this paper, this gap is filled. According to the discussion, an elitist selection method for partial variables in multiobjective problems is developed. Then this method is incorporated into the Decomposition-Based Multiobjective Evolutionary Algorithm (D\&O-MOEA/D). With the help of a mathematical programming optimizer, it is achieved on the constrained multiobjective portfolio problems. In the empirical study, D\&O-MOEA/D is implemented for 20 instances and recent Chinese stock markets. The results show the superiority and versatility of D\&O-MOEA/D on large-scale instances while the performance of it on small-scale problems is also not bad. The former targets convergence towards the Pareto front and the latter helps promote diversity among the non-dominated solutions during the search process.