用神经网络求解不确定分布下的几何联合概率约束优化问题。
Distributionally Robust Geometric Joint Chance-Constrained Optimization: Neurodynamic Approaches
- 设计双时标神经动力学方法，基于投影方程求解
- 在三种分布不确定性集下实现概率收敛至全局最优
- 适用于形状优化与通信系统等实际问题
本文提出一种双时标神经动力学双层方法，用于求解分布鲁棒性几何联合机会约束优化问题。行向量的概率分布事先未知，属于特定的分布不确定性集。研究中考虑了三种不确定性集。神经动力学双层结构基于三个投影方程构建。主要贡献在于提出一种基于神经网络的方法，可在不依赖主流求解方法的情况下，以概率收敛到全局最优解。实验表明，该方法可高效求解多个实例。数值实验中，应用于形状优化和电信问题。
原文摘要 · Abstract (English)
This paper proposes a two-time scale neurodynamic duplex approach to solve distributionally robust geometric joint chance-constrained optimization problems. The probability distributions of the row vectors are not known in advance and belong to a certain distributional uncertainty set. In our paper, we study three uncertainty sets for the unknown distributions. The neurodynamic duplex is designed based on three projection equations. The main contribution of our work is to propose a neural network-based method to solve distributionally robust joint chance-constrained optimization problems that converges in probability to the global optimum without the use of standard state-of-the-art solving methods. We show that neural networks can be used to solve multiple instances of a problem. In the numerical experiments, we apply the proposed approach to solve a problem of shape optimisation and a telecommunication problem.
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