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.

翻译：在进化算法(EAs)中,变量的区分和优化(D ⁇ O)是一种常用的算法设计范式。 D ⁇ O EA将一个变量分为部分变量,然后加以优化。因此,一个复杂的问题被分成简单的子任务。例如,组合问题的一个变量可以分为两个部分变量,即资产选择和资本分配。因此,我们分别优化这两个部分变量。没有正式讨论部分变量是如何迭接优化的,为什么它能同时处理D ⁇ O的单一和多目标问题。在本文中,这一空白被填补。根据讨论,为多目标问题中部分变量开发了精英选择方法。随后,该方法可以分为两个部分变量,即资产选择资产和资本分配。因此,我们优化了这两个部分变量。在数学编程优化的帮助下,在受限制的多目标组合问题上,它得到了实现。D ⁇ O-MOEA/D在20个实例中和最近的中国股票市场搜索过程中,没有执行D ⁇ -MO-在前期的大规模市场中,结果显示前级的优势和前等业绩。