A New Placement Scheme of Distributed Generation in Power Grid

Smart grid gets more and more popular today. Distributed generation is one of the key technologies, and especially, the integration problem of the distributed generation is an important issue. Especially, the location and capacity of the distributed generation play an important role for the performance of the distribution network. In this paper, an optimization model to minimize the loss cost of the unsatisfied demand is given. This model is based on a reliability computing method which avoiding power flow calculation in a previous work. Then the model is used on the IEEE-123 nodes experiment network and a result of five distributed generation placement is got.

An Energy-Based Centrality for Electrical Networks

We present an energy-based method to estimate centrality in electrical networks. Here the energy between a pair of vertices denotes by the effective resistance between them. If there is only one generation and one load, then the centrality of an edge in our method is the difference between the energy of network after deleting the edge and that of the original network. Compared with the local current-flow betweenness on the IEEE 14-bus system, we have an interesting discovery that our proposed centrality is closely related to it in the sense of that the significance of edges under the two measures are very similar.

NeuroPrim:An attention-based model for solving NP-hard spanning tree problems

Spanning tree problems with specialized constraints can be difficult to solve in real-world scenarios,often requiring intricate algorithmic design and exponential time.Recently,there has been growing interest in end-to-end deep neural networks for solving routing problems.However,such methods typically produce sequences of vertices,which make it difficult to apply them to general combinatorial optimization problems where the solution set consists of edges,as in various spanning tree problems.In this paper,we propose NeuroPrim,a novel framework for solving various spanning tree problems by defining a Markov decision process for general combinatorial optimization problems on graphs.Our approach reduces the action and state space using Prim's algorithm and trains the resulting model using REINFORCE.We apply our framework to three difficult problems on the Euclidean space:the degree-constrained minimum spanning tree problem,the minimum routing cost spanning tree problem and the Steiner tree problem in graphs.Experimental results on literature instances demonstrate that our model outperforms strong heuristics and achieves small optimality gaps of up to 250 vertices.Additionally,we find that our model has strong generalization ability with no significant degradation observed on problem instances as large as 1,000.Our results suggest that our framework can be effective for solving a wide range of combinatorial optimization problems beyond spanning tree problems.

Optimal pivot path of the simplex method for linear programming based on reinforcement learning

Based on the existing pivot rules,the simplex method for linear programming is not polynomial in the worst case.Therefore,the optimal pivot of the simplex method is crucial.In this paper,we propose the optimal rule to find all the shortest pivot paths of the simplex method for linear programming problems based on Monte Carlo tree search.Specifically,we first propose the SimplexPseudoTree to transfer the simplex method into tree search mode while avoiding repeated basis variables.Secondly,we propose four reinforcement learning models with two actions and two rewards to make the Monte Carlo tree search suitable for the simplex method.Thirdly,we set a new action selection criterion to ameliorate the inaccurate evaluation in the initial exploration.It is proved that when the number of vertices in the feasible region is C_(n)^(m),our method can generate all the shortest pivot paths,which is the polynomial of the number of variables.In addition,we experimentally validate that the proposed schedule can avoid unnecessary search and provide the optimal pivot path.Furthermore,this method can provide the best pivot labels for all kinds of supervised learning methods to solve linear programming problems.

Preface

Optimization stands as a foundational research discipline,permeating various domains such as engineering,and management,and beyond,where many problems inherently entail optimization.The development of algorithms tailored to solve optimization problems not only holds significant theoretical implications but also promises substantial practical applications.

逐层数据再表达的前后端融合学习的理论及其模型和算法

基于学习的两个主要研究内容,本文提出了学习的二元分层模式,给出了前端学习、后端学习、前后端组合学习和前后端融合学习的概念,构建了前后端融合学习的理论框架与最优化模型;针对前端学习,模拟大脑的分级工作机制,提出了数据与模型混合驱动的逐层数据再表达的方法;最后,以视觉(图像)学习为例,本文给出了一种数据与模型混合驱动的逐层数据再表达的具体方法.

一类随机方差缩减算法的分析与改进

近年来,随机方差缩减类算法在求解机器学习中的大规模优化问题时得到了广泛应用.但是如何选择此类算法的合适步长依然是值得研究的问题.受启发于结合Barzilai-Borwein步长的随机方差缩减梯度(stochastic variance reduced gradient with Barzilai-Borwein step size,SVRG-BB)算法,本文针对方差缩减类算法提出基于局部Lipschitz常数估计的自适应步长,并通过构建一个极小极大化问题给出该步长应用于不同算法时的参数选取方法.然后将该步长与随机递归梯度算法(stochastic recursive gradient algorithm,SARAH)和随机方差缩减(stochastic variance reduced gradient,SVRG)算法相结合,分别提出结合自适应步长的随机递归梯度(SARAH with adaptive step size,SARAH-AS)方法和结合自适应步长的随机方差缩减梯度(SVRG with adaptive step size,SVRG-AS)算法,并且在强凸假设下证明以上算法点距离序列的线性收敛性质.此外,本文还提供一个新颖的视角揭示为什么SARAH+算法是有效的.在公开数据集上的数值实验结果表明本文提出的自适应步长在方差缩减类算法中表现良好.

人工智能机理解释与数学方法探讨

人工智能是一门交叉学科,融合了脑认知科学、心理学、数学(包括统计学)、信息科学、计算机科学等诸多学科.目前,以大数据驱动的深度学习为代表的人工智能发展迅速,在许多领域有广泛的应用.但是,人工智能现在最大的缺陷是没有理论,基本上还处于实验科学阶段.探讨人工智能的机理,进行其理论研究,对人工智能的进一步发展至关重要.为了揭示人工智能的本质,进一步促进人工智能的理论研究,本文从认知生物学和认知心理学两个层面,探讨现有的三个主要的人工智能学派—联结主义、符号主义和行为主义—所蕴含的机理和具体实现的数学理论和方法,试图解释人工智能的本质,给出未来可解释的和具有创造性的人工智能的一些可能的基础研究方法和研究方向.