# Variable Division and Optimization for Constrained Multiobjective Portfolio Problems

arXiv: https://arxiv.org/abs/2101.08552 · HTML: https://mlsanity.com/paper/2101.08552/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 47 references that are in the map.
- First posted on arXiv 21 Jan 2021.

## Builds on (most cited first, 5 of 5)

- [A Review on Bilevel Optimization: From Classical to Evolutionary Approaches and Applications](https://mlsanity.com/paper/1705.06270/) (2017)
- [NSGANetV2: Evolutionary Multi-Objective Surrogate-Assisted Neural Architecture Search](https://mlsanity.com/paper/2007.10396/) (2020)
- [PlatEMO: A MATLAB Platform for Evolutionary Multi-Objective Optimization](https://mlsanity.com/paper/1701.00879/) (2017)
- [High-dimensional Black-box Optimization via Divide and Approximate Conquer](https://mlsanity.com/paper/1603.03518/) (2016)
- [Evolving Unsupervised Deep Neural Networks for Learning Meaningful Representations](https://mlsanity.com/paper/1712.05043/) (2017)

## Abstract (arXiv)

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.