Variable Division and Optimization for Constrained Multiobjective Portfolio Problems
This work addresses a gap in algorithm design for evolutionary optimization in portfolio management, though it appears incremental as it builds on existing D&O and MOEA/D frameworks.
The paper tackles the lack of formal discussion on how partial variables are iteratively optimized in variable division and optimization for evolutionary algorithms, developing an elitist selection method for multiobjective problems and incorporating it into D&O-MOEA/D, with results showing superiority and versatility on large-scale constrained multiobjective portfolio instances.
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.