用MOEA/D和Levy Flight求解投资组合优化问题
Solving Portfolio Optimization Problems Using MOEA/D and Levy Flight
摘要：
投资组合优化是一项金融任务，它要求在一组金融资产上分配资本，以实现收益和风险之间的更好权衡。为了解决这个问题，最近的研究应用多目标进化算法（MOEAs）的自然双目标结构。本文提出了一种将基于分布的变异方法Lévy Flight注入到基于分解的MOEA/D中的方法。该算法相比，三个MOEA/D类算法，NSGA-II，和其他基于分布的变异方法在5个投资组合优化基准大小从31到225在OR库无约束，评估与6个指标。数值结果和统计检验表明，在大多数情况下，该方法的性能优于比较方法。我们分析了Levy Flight如何通过在优化的早期促进全局搜索来实现这一改进。我们通过考虑变异方法和问题性质之间的相互作用来解释这种改进。
英文摘要：
Portfolio optimization is a financial task which requires the allocation of capital on a set of financial assets to achieve a better trade-off between return and risk. To solve this problem, recent studies applied multi-objective evolutionary algorithms (MOEAs) for its natural bi-objective structure. This paper presents a method injecting a distribution-based mutation method named Lévy Flight into a decomposition based MOEA named MOEA/D. The proposed algorithm is compared with three MOEA/D-like algorithms, NSGA-II, and other distribution-based mutation methods on five portfolio optimization benchmarks sized from 31 to 225 in OR library without constraints, assessing with six metrics. Numerical results and statistical test indicate that this method can outperform comparison methods in most cases. We analyze how Levy Flight contributes to this improvement by promoting global search early in the optimization. We explain this improvement by considering the interaction between mutation method and the property of the problem.
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