Hopfield神经网络在机组组合问题中的应用

提出利用多层Hopfield神经网络求解机组组合优化问题。通过构造合适的能量函数使得单层Hopfield神经网络可以解决某一时刻的机组出力问题,与之相对应的多层神经网络可以解决任意时间段的机组出力问题。多层Hopfield神经网络的层数由所需求解问题的时间段确定。给出单层及多层神经网络的能量函数及求解算法,能量函数考虑到机组升降功率和出力上下限的约束。通过对已有文献的算例进行计算比对,所得结果和遗传算法基本一致,但Hopfield神经网络通过解微分方程组来确定最优解,计算时间相对较少。     

基于离散Hopfield神经网络的数字识别实现

介绍了离散Hopfield神经网络的基本概念;以MATLAB为工具,根据Hopfield神经网络的相关知识,设计了一个具有联想记忆功能的离散型Hopfield神经网络,并给出了设计思路、设计步骤和测试结果。实验结果表明,通过联想记忆,对于带有一定噪声的数字点阵,Hopfield网络可以正确地进行识别,且当噪声强度为0．1时的识别效果较好。     

电力系统经济负荷分配的混合粒子群优化算法

为解决电力系统中的经济负荷分配问题,提出一种将约束优化与粒子群优化算法相结合的混合算法,同时引入直接搜索方法。使得混合后的粒子群优化算法不但具有高效的全局搜索能力,而且具有较强的局部搜索能力,避免陷入局部最优,提高求解精度。对两个实例进行测试,与其他智能算法的结果比较,证明提出的算法可以有效找到可行解,避免陷入局部最优,实现问题的快速求解。     

Hopfield神经网络在有限元求解中的应用

计算机本身固有的计算与存储之间是一对很难解决的矛盾,许多工程力学问题因计算规模大等原因还没有突破性进展,因此,需要发展新的理论与计算方法。通过对有限元求解方法和Hopfield神经网络的深入研究,在对Hopfield神经网络适当改造后,得到了有限元的神经网络计算方法,在电路实现中避免了采用高增益传递函数的假设,进而在理论上实现了有限元神经网络计算的无误差求解。     

Solving non-convex/non-smooth economic load dispatch problems via an enhanced particle swarm optimization

Economic load dispatch (ELD) problems have been an important issue in optimal operation and planning of power system. Characterized by non-convex/non-smooth properties and various practical constraints, the ELD problems are difficult to solve using conventional optimization techniques. In this paper, an improved orthogonal design particle swarm optimization (IODPSO) algorithm is presented for solving the single-area and multi-area ELD problems with nonlinear characteristics of the generators, such as valve-point effects, prohibited operating zones, ramp rate limits and multiple fuels. In the IODPSO algorithm, an orthogonal designed method is used to construct a promising exemplar. Multiple auxiliary vector generating strategies are proposed to enhance the efficiency and effectiveness of orthogonal design operations. A tent chaotic map is employed for the adaptation of the acceleration coefficients, thus improving the proposed algorithm's robustness and global search capabilities. In addition, we designed a repair method to handle the practical constraints. Six cases of ELD problems with different characteristics are utilized to benchmark the proposed algorithm. Experimental results demonstrate that IODPSO algorithm is a promising approach for solving the non-convex/non-smooth ELD problems.     

基于Hopfield 神经网络的污水处理过程优化控制

针对前置反硝化污水处理过程的优化控制问题,提出一种基于拉格朗日乘子法的Hofield神经网络优化方法.构造了污水处理过程约束优化问题的数学表达式,通过Hopfield神经网络优化计算生化池第5分区溶解氧浓度和第2分区硝态氮浓度的设定值,并采用PID控制器实现底层的跟踪控制.基于国际标准的Benchmark基准仿真平台进行仿真实验,结果表明污水处理系统在出水关键水质达标的基础上,能够显著降低能耗.     

Mutation Hopfield neural network and its applications

In this paper, a new operator is proposed to optimize the traditional Hopfield neural network (HNN). The key idea is to incorporate the global search capability of the Estimation of Distribution Algorithms (EDAs) into the HNN, which typically has a powerful local search capability and fast operation. On account of this property of the EDA, our proposed algorithm also exhibits a powerful global search capability. In addition, the possible infeasible solutions generated during the re-sampling period of the EDA are eliminated by the HNN. Therefore, the merits of both these methods are combined in a unified framework. The proposed model is tested on a numerical example, the max-cut problem. The new and optimized model yielded a better performance than certain traditional intelligent optimization methods, such as HNN, genetic algorithm (GA). The proposed mutation Hopfield neural network (MHNN) is also used to solve a practical problem, aircraft landing scheduling (ALS). Compared with first-come-first-served sequence, MHNN sequence reduces both total landing time and total delay.     

A shortest path routing algorithm using Hopfield neural network with an improved energy function

A shortest path routing algorithm using the Hopfield neural network with a modified Lyapunov function is proposed. The modified version of the Lyapunov energy function for an optimal routing problem is proposed for determining routing order for a source and multiple destinations. The proposed energy function mainly prevents the solution path from having loops and partitions. Experiments are performed on 3000 networks of up to 50 nodes with randomly selected link costs. The performance of the proposed algorithm is compared with several conventional algorithms including Ali and Kamoun's, Park and Choi's, and Ahn and Ramakrishna's algorithms in terms of the route optimality and convergence rate. The results show that the proposed algorithm outperforms conventional methods in all cases of experiments. The proposed algorithm particularly shows significant improvements on the route optimality and convergence rate over conventional algorithms when the size of the network approaches 50 nodes.     

模糊Hopfield网络的收敛性与鲁棒性分析

收敛性与鲁棒性是模糊神经网络的两个重要性质。对带阈值的Max-T模糊Hopfield神经网络（记为Max-T-C FHNN）的收敛性及在训练模式小幅摄动情况下的鲁棒性进行了分析,从理论上给出了严格的证明。发现了采用最大权值矩阵学习算法时,Max-T-C FHNN具有良好的收敛性,同时当T模及其蕴含算子满足Lipschitz条件时,Max-T-C FHNN对训练模式摄动全局拥有好的鲁棒性,用自联想实验验证了理论的有效性。     

Agriculture satellite image segmentation using a modified artificial Hopfield neural network

Beekeeping plays an important role in increasing and diversifying the incomes of many rural communities in Kingdom of Saudi Arabia. However, despite the region’s relatively good rainfall, which results in better forage conditions, bees and beekeepers are greatly affected by seasonal shortages of bee forage. Because of these shortages, beekeepers must continually move their colonies in search of better forage. The aim of this paper is to determine the actual bee forage areas with specific characteristics like population density, ecological distribution, flowering phenology based on color satellite image segmentation. Satellite images are currently used as an efficient tool for agricultural management and monitoring. It is also one of the most difficult image segmentation problems due to factors like environmental conditions, poor resolution and poor illumination. Pixel clustering is a popular way of determining the homogeneous image regions, corresponding to the different land cover types, based on their spectral properties. In this paper Hopfield neural network (HNN) is introduced as Pixel clustering based segmentation method for agriculture satellite images.     

自适应差分进化算法及对动态环境经济调度问题应用

为了应对动态环境经济调度(DEED)问题的高维性和大规模约束性,提出了一种自适应多目标差分进化算法(ADEA)。设计自适应差分交叉模块,提出改进的current to best/1交叉策略提高种群的多样性,有效地提高传统进化算法的探索与开采能力,提出一种修补策略处理功率平衡约束和爬坡率约束。为了验证该方法的有效性,数值仿真将ADEA应用于10机系统进行测试,并与同类算法展开比较,仿真结果表明ADEA具有较好的收敛能力,获得的Pareto前沿具有较好的均匀性和延展性,通过模糊决策获得的最好折中解能为电力系统调度人员提供较为合理的调度方案。     

Nonconvex/nonsmooth economic load dispatch using modified time‐varying particle swarm optimization

In this paper, a modified time‐varying particle swarm optimization (MTVPSO) is proposed for solving nonconvex economic load dispatch problems. It is a variant of the traditional particle swarm optimization (PSO) algorithm. In an MTVPSO, novel acceleration coefficients for cognitive and social components are presented as linear time‐varying parameters in the velocity update equation of the PSO algorithm. In the early stages of the optimization process, it improves the global search capability of particles and directs the global optima at the end stage. Additionally, a linearly decreased inertia weight is introduced in an MTVPSO, instead of a fixed constant value, which helps improve the diversity of the population. Through this modification mechanism in PSO, the proposed algorithm has a higher probability of avoiding local optima, and it is likely to find global optima more quickly. Six complex benchmark functions have been used to validate the effectiveness of the proposed algorithm. Furthermore, to demonstrate its efficiency, feasibility, and fastness, six different cases (3‐, 6‐, 13‐, 15‐, and 40‐unit systems and one large‐scale Korean power 140‐unit system) of the economic load dispatch problem are solved by an MTVPSO. The results of the proposed algorithm have been compared with state‐of‐the‐art algorithms. It was found that the proposed MTVPSO can deliver better results in terms of solution quality, convergence characteristics, and robustness.     

基于连续Hopfield网络求解TSP的新方法

当连续Hopfield网络及其能量函数同时具有自反馈或不具有自反馈时,称之为一致连续Hopfield网络．在分析了一致连续Hopfield网络能量稳定性的基础上,进一步研究了当网络有自反馈,而其能量函数无自反馈的情况下,网络能量变化的性质,分别给出了使能量函数上升、下降和不变的条件．利用这一理论,可以克服由于梯度下降法所导致的网络能量函数总是下降,从而使网络陷入局部极小值或不可行解的现象．最后在这个理论的基础上我们给出了一种新的求解TSP(traveling salesman problem)的方法,仿真研究表明此方法对于求解TSP问题是很有效的．     

基于蚁群算法的Hopfield神经网络在多空间站路径规划的应用研究*

空间机器人每次携带的燃料有限,提高空间机器人的工作效率以及延长其在轨寿命研究具有重要意义,分析了空间机器人多空间站访问问题。为了弥补传统路径规划方法容易陷入局部极小点的问题,提出利用基于蚁群算法的Hopfield神经网络来解决空间机器人多空间站访问问题。仿真实验结果表明,基于蚁群算法的Hopfiled神经网络用于多空间站访问问题,收敛速度要比Hopfield神经网络快,且比Hopfield神经网络易于跳出局部极点,该算法有利于解决多空间站路径规划问题。     

电力系统经济负荷分配的族群优化方法

经济负荷分配（Economic Load Dispatch,ELD）是电力系统中一种重要的优化问题,它可归为一类高维、离散、非线性的多约束函数优化问题。针对这类问题,提出了一种基于线性截取策略的改进族群进化算法——EGEA/LT,并使用EGEA/LT对IEEE的3机、6机和15机3个仿真系统进行了优化实验,将实验结果与其他典型算法优化结果进行比较,说明了EGEA/LT是一种求解ELD问题的有效方法。     

Solution of economic load dispatch using hybrid chemical reaction optimization approach

In this paper, a new and efficient optimization technique based on hybridization of chemical reaction optimization (CRO) with differential evolution (DE) is developed and demonstrated to solve the ELD problem with thermal cost function having valve point loading effect together with and without multiple fuel options and with and without considering prohibited operating zone and ramp rate constraint. When valve-point effects, multi-fuel operations and the constraints of prohibited operating zone and ramp rate are taken into account, ELD problem become more complex than conventional ELD problem. To show the priority of the proposed algorithm, it is implemented on six different test systems for solving ELD problems. Comparative studies are carried out to examine the effectiveness of the proposed HCRO-DE approach with conventional DE, CRO and the other algorithms reported in the literature. The simulation results show that the proposed HCRO-DE method is capable of obtaining better quality solutions than DE, CRO and the other well popular optimization techniques.     

用改进的差分式Hopfield网络实现线性二次型最优控制

为解决差分式Hopfield网络能量函数的局部极小问题,本文对之改进得到一种具有迭代学习功能的线性差分式Hopfield网络.理论分析表明,该网络具有稳定性,且稳定状态使其能量函数达到唯一极小值.基于线性差分式Hopfield网络稳定性与其能量函数收敛特性的关系,本文将该网络用于求解多变量时变系统的线性二次型最优控制问题.网络的理论设计方法表明,网络的稳态输出就是欲求的最优控制向量.数字仿真取得了与理论分析一致的实验结果.     

A hill-jump algorithm of Hopfield neural network for shortest path problem in communication network

In this paper, we present a hill-jump algorithm of the Hopfield neural network for the shortest path problem in communication networks, where the goal is to find the shortest path from a starting node to an ending node. The method is intended to provide a near-optimum parallel algorithm for solving the shortest path problem. To do this, first the method uses the Hopfield neural network to get a path. Because the neural network always falls into a local minimum, the found path is usually not a shortest path. To search the shortest path, the method then helps the neural network jump from local minima of energy function by using another neural network built from a part of energy function of the problem. The method is tested through simulating some randomly generated communication networks, with the simulation results showing that the solution found by the proposed method is superior to that of the best existing neural network based algorithm.     

一种基于免疫和Hopfield神经网络的多峰值优化算法

分析了免疫算法和Hopfield神经网络的优缺点,提出了一种解决多峰值函数优化问题的混合算法。Hopfield神经网络易于硬件实现,具有简单、快速的优点,但是对初始值具有依赖性以及容易陷入局部极值。免疫算法具有识别多样性的特点,但搜索效率和精度不高。将两算法结合起来,优势互补。首先用免疫算法寻优,然后对所得具有全局多样性的解进行聚类分析,所得聚类中心作为Hopfield神经网络的初始搜索点,最后利用Hopfield神经网络逐个寻优。实验表明,该算法是一种有效的求解多峰函数优化问题的方法,与免疫算法相比,搜索效率和精度都较高。     

Chaotic electromagnetism-like mechanism algorithm for economic load dispatch of power system

Chaotic electromagnetism-like mechanism algorithm (CEMA) is first proposed in this paper, which is the integration of electromagnetism-like mechanism algorithm (EMA) and chaos theory. EMA simulates the attraction and repulsion mechanism for particles in the electromagnetic field. Every solution is a charged particle, and it moves to optimum solution according to certain criteria which need several steps. To enrich the searching behaviour and to avoid being trapped into local optimum, chaotic dynamics is incorporated into EMA. CEMA possesses excellent global optimal performance, simple programming realisation and good convergence, and it is used in economic load dispatch of power systems. Through performance comparison, it is obvious that the solution is superior to other optimisation algorithms. It can be applied to other research problems in power systems.