A mapping-based constraint-handling technique for evolutionary algorithms with its applications to portfolio optimization problems
A mapping-based constraint-handling technique for evolutionary algorithms with its applications to portfolio optimization problems
复制标题
一种基于映射的进化算法约束处理技术及其在投资组合优化问题中的应用
DOI：
10.1080/18824889.2022.2040268
复制
发表时间：
2022
期刊：
影响因子：
--
通讯作者：
Orito Yukiko
中科院分区：
文献类型：
--
作者：
Tagawa Kiyoharu;Orito Yukiko
提出了一种新的用于求解约束优化问题的进化算法约束处理技术。假设约束优化问题的可行域由多个顶点的凸包定义。另一方面，不失一般性，EA的搜索空间是由一个超立方体。该算法将进化算法搜索空间中的真实的向量转化为可行域中的解。它还证明了CHM执行一个满射映射从搜索空间的EA的可行域。虽然建议的CHM可以应用于任何EA，最新的EA之一，或自适应差分进化（ADE），在本文中使用。通过使用ADE，CHM与传统的CHTs在现实世界中的金融领域的优化问题，即投资组合优化问题进行了比较。投资组合优化是根据一定的目标确定不同资产的最佳投资比例的过程。具体而言，揭示CHM的特性取决于上述顶点的数量，三种不同的配方的投资组合优化问题，以评估使用CHM的ADE的性能。数值实验表明，CHM在大多数情况下优于传统的CHTs。此外，CHM与传统CHT相结合的混合方法优于原始CHT。
A novel Constraint-Handling Technique (CHT) for Evolutionary Algorithms (EAs) applied to constrained optimization problems is proposed. It is assumed that the feasible region of the constrained optimization problem is defined by a convex-hull of multiple vertices. On the other hand, without loss of generality, the search space of EA is given by a hyper-cube. The proposed CHT called Convex-Hull Mapping (CHM) transforms the real vector in the search space of EA into the solution in the feasible region. It is also proven that CHM performs a surjective mapping from the search space of EA to the feasible region. Although the proposed CHM can be applied to any EAs, one of the latest EAs, or Adaptive Differential Evolution (ADE), is used in this paper. By using ADE, CHM is compared with conventional CHTs in a real-world optimization problem in the field of finance, namely the portfolio optimization problem. Portfolio optimization is the process of determining the best proportion of investment in different assets according to some objective. Specifically, to reveal the characteristic of CHM depending on the number of the above vertices, three different formulations of the portfolio optimization problem are employed to evaluate the performance of ADE using CHM. Numerical experiments show that CHM is better than conventional CHTs in most cases. Moreover, the hybrid method combining CHM with a conventional CHT outperforms the original CHT.