基于概率模型降维和随机动力系统的演化优化理论与模型

This project aims to systematically study the theories and methods of evolutionary algorithms by means of discovering suitable techniques from the field of statistical machine learning, model predictive control and stochastic dynamical system. For this purpose, we put forward a new framework to design and analysis evolutionary algorithm from a comprehensive perspective: Controllable and Learning Evolution Optimization Models (CLEOM). The main research focuses on the following: firstly, the iterative process of the evolutionary algorithm is described by stochastic dynamical system, and then the related technologies and methods from the field of statistical machine learning and automatic control are explores to design new operators and propose new strategies for adaptive parameter adjustment of evolutionary algorithms to solve complex optimization problems. Finally, we use some related theories, such as Lyapunov's second theorem, Doob 's martingale convergence theorem, to construct the theories of evolution algorithms. The innovations are as follows: (1) To construct the convergence theory by random dynamic system model, and then analysis the stability and moment estimation theorem of intelligent algorithm via building it as Ornstein–Uhlenbeck process; (2) To setup new learning and control strategies for intelligent algorithm, some Controllable & Learnable methods is used to predict and control intelligent algorithm;(3) To Explore new areas of application, some new optimization problems are proposed and studied, such as, super high dimension optimization problems (whose dimensionality is larger than 10,000), the evolution of river bed topography under water and channel of automatic programming and other fields. The above three innovations can conclude as: (1) New theoretical is used to guide the design of intelligent algorithm design; (2) new methodology of algorithm design can simulate new theory, and new application fields can verify the algorithm efficiency.

项目旨在结合统计机器学习、模型预测控制及随机动力系统等领域的理论与方法，从全新视角提出一种演化算法的设计和分析框架：可控、可学习的演化优化模型框架。项目研究的内容是首先把演化算法的迭代过程用随机动力学系统来刻画，继而挖掘统计机器学习和自动控制中的相关技术和方法应用于智能算法的算子设计和参数自适应调整上，最后利用李亚普诺夫第二定理、Doob’s 鞅收敛性定理来构建演化算法相关理论。项目创新点有：构建随机动力系统模型来刻画一类演化算法的行为；利用统计机器学习中的概率模型、元模型到隐空间降维和模型预测控制等方法来设计算法算子和参数自适应控制；针对大于1万维的超高维优化问题，提出利用隐空间降维技术来提升一类演化算法的性能；将智能算法应用于河床地形演变预测和航道自动规划等领域。实现上述内容，就解决了如下科学问题：如何结合随机系统、预测控制及统计学习中的方法研究高度自适应的优化算法及其理论构成要素。

项目旨在结合系统论、控制论及机器学习等领域的方法，从全新的视角提出一种智能算法的计算和分析框架：可控、可学习的演化优化模型（CLEOM）。该模型致力于研究将随机动力系统、机器学习和自动控制的相关理论与方法集成到智能算法中。研究的核心内容是将机器学习和自动控制中的相关技术和方法用于智能算法的控制，其目的是自动调整智能算法的搜索过程，提高智能算法在求解复杂优化问题时的性能。项目创新点有：构建随机动力系统模型，并用稳定性和矩估计定理来构建收敛性、收敛速度的理论；提出利用机器学习和预测控制的方法开指导智能算法的搜索过程，相关技术从学习问题的概率模型、元模型到隐空间技术，再到预测控制技术；首次提出求解超高维优化问题，并将智能算法应用于河床水下地形演变预测和航道自动规划等领域。上述三个创新点自成体系，理论指导算法设计、算法设计可以促进理论的提升、应用领域可以验证算法效能。研究成果主要是发表论文，一共发表了期刊论文14篇，会议论文3篇。另外，研究成果已经应用于本人做的无人驾驶项目中，取得了不错的效果。