优化高速网络收敛：FC-Africa算法提升TCP性能

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论文研究-DCDG-EA: Dynamic Convergence-Diversity Guided Evolutionary Algorithm for Many-Objective Optimization.pdf

在DCDG-EA算法中，作者设计了基于收敛性和多样性算子选择（Convergence and Diversity based Operator Selection, CDOS）策略和基于收敛性和多样性个体选择（Convergence and Diversity based Individual Selection,...

Networkers2009：BRKIPM-3363 - Advanced Fast Routing Convergence: Network Availability and Simplicity

从给定的文件信息来看，该内容主要围绕网络高级快速路由收敛、网络可用性和简化设计进行探讨，由思科系统公司于2009年的Networkers会议中的BRKIPM-3363演讲所提供。以下是对关键知识点的详细解析： ### 知识点一：...

解释：def conjugate_gradient(fun, grad, x0, iterations, tol): """ Minimization of scalar function of one or more variables using the conjugate gradient algorithm. Parameters ---------- fun : function Objective function. grad : function Gradient function of objective function. x0 : numpy.array, size=9 Initial value of the parameters to be estimated. iterations : int Maximum iterations of optimization algorithms. tol : float Tolerance of optimization algorithms. Returns ------- xk : numpy.array, size=9 Parameters wstimated by optimization algorithms. fval : float Objective function value at xk. grad_val : float Gradient value of objective function at xk. grad_log : numpy.array The record of gradient of objective function of each iteration. """ fval = None grad_val = None x_log = [] y_log = [] grad_log = [] x0 = asarray(x0).flatten() # iterations = len(x0) * 200 old_fval = fun(x0) gfk = grad(x0) k = 0 xk = x0 # Sets the initial step guess to dx ~ 1 old_old_fval = old_fval + np.linalg.norm(gfk) / 2 pk = -gfk x_log = np.append(x_log, xk.T) y_log = np.append(y_log, fun(xk)) grad_log = np.append(grad_log, np.linalg.norm(xk - x_log[-1:])) gnorm = np.amax(np.abs(gfk)) sigma_3 = 0.01 while (gnorm > tol) and (k < iterations): deltak = np.dot(gfk, gfk) cached_step = [None] def polak_ribiere_powell_step(alpha, gfkp1=None): xkp1 = xk + alpha * pk if gfkp1 is None: gfkp1 = grad(xkp1) yk = gfkp1 - gfk beta_k = max(0, np.dot(yk, gfkp1) / deltak) pkp1 = -gfkp1 + beta_k * pk gnorm = np.amax(np.abs(gfkp1)) return (alpha, xkp1, pkp1, gfkp1, gnorm) def descent_condition(alpha, xkp1, fp1, gfkp1): # Polak-Ribiere+ needs an explicit check of a sufficient # descent condition, which is not guaranteed by strong Wolfe. # # See Gilbert & Nocedal, "Global convergence properties of # conjugate gradient methods for optimization", # SIAM J. Optimization 2, 21 (1992). cached_step[:] = polak_ribiere_powell_step(alpha, gfkp1) alpha, xk, pk, gfk, gnorm = cached_step # Accept step if it leads to convergence. if gnorm <= tol: return True # Accept step if sufficient descent condition applies. return np.dot(pk, gfk) <= -sigma_3 * np.dot(gfk, gfk) try: alpha_k, fc, gc, old_fval, old_old_fval, gfkp1 = \ _line_search_wolfe12(fun, grad, xk, pk, gfk, old_fval, old_old_fval, c2=0.4, amin=1e-100, amax=1e100, extra_condition=descent_condition) except _LineSearchError: break # Reuse already computed results if possible if alpha_k == cached_step[0]: alpha_k, xk, pk, gfk, gnorm = cached_step else: alpha_k, xk, pk, gfk, gnorm = polak_ribiere_powell_step(alpha_k, gfkp1) k += 1 grad_log = np.append(grad_log, np.linalg.norm(xk - x_log[-1:])) x_log = np.append(x_log, xk.T) y_log = np.append(y_log, fun(xk)) fval = old_fval grad_val = grad_log[-1] return xk, fval, grad_val, x_log, y_log, grad_log

返回值包括参数的估计值，目标函数在该点的值，目标函数在该点的梯度值以及每次迭代中目标函数梯度的记录。这个算法使用了Polak-Ribiere共轭梯度法，并且在每次迭代中使用了Wolfe条件进行线搜索。算法的大致步骤是：...

二维TE波FDTD方法引入高斯源作图，显示收敛阶matlab实现

### 回答1：二维TE波的FDTD方法中，我们可以通过引入高斯源来激发电磁波的传播。而FDTD方法的收敛阶则用于评估算法的精度...以上是通过在二维TE波的FDTD方法中引入高斯源并进行作图，以显示其收敛阶的Matlab实现方法。

use" the m-step of the em algorithm: min_{affine, translation, variance} 1/(2variance) sum_{m,n} p(y_m | x_n) ||x_n - affine y_m - translation||_2^2" to optimizing the previous code: def em_for_alignment(xs: np.ndarray, ys: np.ndarray, num_iter: int = 100) -> Tuple[np.ndarray, np.ndarray]: """ The em algorithm for aligning two point clouds based on affine transformation :param xs: a set of points with size (N, D), N is the number of samples, D is the dimension of points :param ys: a set of points with size (M, D), M is the number of samples, D is the dimension of points :param num_iter: the number of EM iterations :return: ys_new: the aligned points: ys_new = ys @ affine + translation responsibility: the responsibility matrix P=[p(y_m | x_n)] with size (N, M), whose elements indicating the correspondence between the points """ # TODO: implement the EM algorithm of GMM below for point cloud alignment return

4. Repeat steps 2-3 for num_iter iterations or until convergence. Here's the updated code: ```python def em_for_alignment(xs: np.ndarray, ys: np.ndarray, num_iter: int = 100) -> Tuple[np.ndarray, np...

生成雅可比迭代python代码

很高兴为您服务！以下是生成雅可比迭代Python代码的示例： ``` def jacobi(A, b, x0, tol=1e-8, ... raise ValueError("No convergence after {} iterations".format(maxiter)) ``` 希望这能帮助您回答您的问题！

model.fit(initial_learning_rate=0.01, learning_rate_decay=1.5, convergence_epochs=5, batch_size=32, maximum_epochs=100, learning_rate_minimum=1e-4, training_split=0.8)

- `convergence_epochs`：收敛周期数，指定当模型在连续多少个周期内没有显著改善时，训练过程将被提前终止。这有助于防止模型过拟合或者在训练过程中浪费时间。 - `batch_size`：批次大小，指定每次迭代中用于更新...

clc; clear; % 设定方阵大小和数量 n = 5; % 方阵大小 m = 10; % 方阵数量 variances = zeros(1, m); % 每个方阵的各列方差 convergence_times = zeros(1, m); % 每个方阵的收敛次数 for i = 1:m % 逐个生成方阵 % 随机生成方阵，每行元素之和为1 A = rand(n); A = A./sum(A,2); % 计算各列方差，并存储 variances(i) = var(A); % 进行迭代，直到收敛 prev_A = A; curr_A = A; iter = 0; while max(abs(curr_A(:)-prev_A(:))) > 1e-6 prev_A = curr_A; curr_A = A*prev_A; iter = iter + 1; end convergence_times(i) = iter; end % 输出平均各列方差和平均收敛次数 avg_variance = mean(variances); avg_convergence_time = mean(convergence_times); fprintf('Average variance: %.4f\n', avg_variance); fprintf('Average convergence time: %d\n', avg_convergence_time); % 绘制方差与收敛次数关系图 figure; scatter(convergence_times, variances); xlabel('Convergence Times'); ylabel('Column Variances'); title('Relationship between Convergence Times and Column Variances');matlab对这段代码报错，无法赋值，因为左侧和右侧的元素数目不同，应该怎么修改

修改后代码中，`variances`和`convergence_times`的定义中，分别将`zeros(1, m)`修改为`zeros(m, 1)`，表示创建m行1列的全零数组，用于存储每个方阵的各列方差和收敛次数。这样就可以避免左右元素数目不同的错误了。

代码解释：format long; close all; clear ; clc tic global B0 bh B1 B2 M N pd=8; %问题维度(决策变量的数量) N=100; % 群 (鲸鱼) 规模 readfile HPpos=chushihua; tmax=300; % 最大迭代次数 (tmax） Wzj=fdifference(HPpos); Convergence_curve = zeros(1,tmax); B = 0.1; for t=1:tmax for i=1:size(HPpos,1)%对每一个个体地多维度进行循环运算 % 更新位置和记忆 % j1=(HPpos(i,:)>=B1);j2=(HPpos(i,:)<=B2); % if (j1+j2)==16 % HPpos(i,:)=HPpos(i,:); %%%%有问题，原算法改正&改进算法映射规则 % else % %HPpos(i,:)=B0+bh.(ones(1,8)(-1)+rand(1,8)2);%产生范围内的随机数更新鲸鱼位置 % HPpos(i,:)=rand(1,8).(B2-B1)+B1; % end HPposFitness=Wzj(:,2M+1); end [~,indx] = min(HPposFitness); Target = HPpos(indx,:); % Target HPO TargetScore =HPposFitness(indx); % Convergence_curve(1)=TargetScore; % Convergence_curve(1)=TargetScore; %nfe = zeros(1,MaxIt); %end % for t=2:tmax c = 1 - t((0.98)/tmax); % Update C Parameter kbest=round(Nc); % Update kbest一种递减机制 % for i = 1:N r1=rand(1,pd)<c; r2=rand; r3=rand(1,pd); idx=(r1==0); z=r2.idx+r3.~idx; % r11=rand(1,dim)<c; % r22=rand; % r33=rand(1,dim); % idx=(r11==0); % z2=r22.idx+r33.~idx; if rand<B xi=mean(HPpos); dist = pdist2(xi,HPpos);%欧几里得距离 [~,idxsortdist]=sort(dist); SI=HPpos(idxsortdist(kbest),:);%距离位置平均值最大的搜索代理被视为猎物 HPpos(i,:) =HPpos(i,:)+0.5((2*(c)z.SI-HPpos(i,:))+(2(1-c)z.xi-HPpos(i,:))); else for j=1:pd rr=-1+2z(j); HPpos(i,j)= 2z(j)cos(2pirr)(Target(j)-HPpos(i,j))+Target(j); end end HPposFitness=Wzj(:,2M+1); % % Update Target if HPposFitness(i)<TargetScore Target = HPpos(i,:); TargetScore = HPposFitness(i); end Convergence_curve(t)=TargetScore; disp(['Iteration: ',num2str(t),' Best Fitness = ',num2str(TargetScore)]); end

这段代码是一个使用鲸鱼优化算法来解决多维优化问题的程序。该算法模拟了鲸鱼群体寻找猎物的过程，通过不断更新每个鲸鱼的位置来...最后，程序会将每次迭代后的最优解存储在Convergence_curve变量中，以便后续分析。

% Define the input matrices A_matrix and B A = [0 0 -1 3 -1 0; 0 1/2 0 -1 3 -1; 1/2 0 0 0 -1 3; 3 -1 0 0 0 1.2; -1 3 -1 0 1/2 0; 0 -1 3 -1 0 0]; B = [1; 3/2; 5/2; 5/2; 3/2; 1]; % Define the Gauss-Seidel function function [X] = GaussSeidel(A, b, tol, max_iter) % Get the dimensions of A and initialize the output vector [n, ~] = size(A); X = zeros(n, 1); X_new = X; tolerance = 1e-3; max_iterations = 1000; X1 = GaussSeidel(A_matrix, B, tolerance, max_iterations); disp(X1); % Iterate through the Gauss-Seidel method for iter = 1:max_iter for i = 1:n X_new(i) = (b(i) - A(i, 1:i-1) * X_new(1:i-1) - A(i, i+1:end) * X(i+1:end)) / A(i, i); end % Check for convergence if norm(X_new - X) < tol break; end % Update the approximation X = X_new; tolerance = 1e-3; max_iterations = 1000; X1 = GaussSeidel(A_matrix, B, tolerance, max_iterations); disp(X1); end end % Set the tolerance and maximum number of iterations; % Call the Gauss-Seidel function with the input matrices and parameters % Display the output

At each iteration, it updates the approximation using the formula for Gauss-Seidel, and then checks for convergence. Finally, it returns the approximation `X`. The code then calls the `GaussSeidel` ...

Multisim报错------ Checking SPICE netlist for Design1 - 2023年5月30日, 22:59:18 ------ ======= SPICE Netlist check completed, 0 error(s), 0 warning(s) ======= Error: Unable to converge during transient analysis. Consider increasing the ABSTOL, VNTOL, and RELTOL options. Simulation canceled See convergence help for more information

建议尝试增加ABSTOL、VNTOL和RELTOL选项的值，以提高收敛性。您可以在Multisim的仿真选项中找到这些选项，并逐个增加它们的值，直到您的仿真可以成功收敛。另外，您可以尝试使用更高级的仿真器，如PSPICE或LTSpice，...

class LogisticRegression(object): def init(self, input_size, output_size, eta, max_epoch, eps):

eps: float - convergence threshold """ self.input_size = input_size self.output_size = output_size self.eta = eta self.max_epoch = max_epoch self.eps = eps self.weights = np.zeros((input_size,...

import numpy as np def sigmoid(z): return 1 / (1 + np.exp(-z)) def cost_function(theta, X, y): m = len(y) h = sigmoid(X @ theta) J = -(1/m) * (y.T @ np.log(h) + (1-y).T @ np.log(1-h)) grad = (1/m) * X.T @ (h - y) return J, grad def trust_region_newton_method(X, y, max_iter=100, eta=0.05, delta=0.1): n = X.shape[1] theta = np.zeros((n,1)) J, grad = cost_function(theta, X, y) H = np.eye(n) for i in range(max_iter): # solve trust region subproblem p = np.linalg.solve(H, -grad) if np.linalg.norm(p) <= delta: d = p else: d = delta * p / np.linalg.norm(p) # compute actual reduction and predicted reduction J_new, grad_new = cost_function(theta+d, X, y) actual_reduction = J - J_new predicted_reduction = -grad.T @ d - 0.5 * d.T @ H @ d # update trust region radius rho = actual_reduction / predicted_reduction if rho < 0.25: delta = 0.25 elif rho > 0.75 and np.abs(np.linalg.norm(d) - delta) < 1e-8: delta = min(2delta, eta*np.linalg.norm(theta)) # update parameters if rho > 0: theta += d J, grad = J_new, grad_new H += (grad_new - grad) @ (grad_new - grad).T / ((grad_new - grad).T @ d) # check convergence if np.linalg.norm(grad) < 1e-5: break return theta 修改此代码，让他运行出来

# check convergence if np.linalg.norm(grad) < 1e-5: break return theta ``` 在这个修改中，我们对输入的X和y进行了检查，并且将n的值从函数内部计算改为了从X的shape中获取。我们还修改了代码中的一些细节...

admm-lasso分位数回归代码

# check convergence if np.linalg.norm(z - z_old) < tol: break return z ``` 其中，输入参数为： - `X`：一个 m x n 的矩阵，表示 m 个样本的 n 个特征。 - `y`：长度为 m 的向量，表示 m 个样本的标签。...

import numpy as np def sigmoid(z): return 1 / (1 + np.exp(-z)) def cost_function(theta, X, y): m = len(y) h = sigmoid(X @ theta) J = -(1/m) * (y.T @ np.log(h) + (1-y).T @ np.log(1-h)) grad = (1/m) * X.T @ (h - y) return J, grad def trust_region_newton_method(X, y, max_iter=100, eta=0.05, delta=0.1): n = X.shape[1] theta = np.zeros((n,1)) J, grad = cost_function(theta, X, y) H = np.eye(n) for i in range(max_iter): # solve trust region subproblem p = np.linalg.solve(H, -grad) if np.linalg.norm(p) <= delta: d = p else: d = delta * p / np.linalg.norm(p) # compute actual reduction and predicted reduction J_new, grad_new = cost_function(theta+d, X, y) actual_reduction = J - J_new predicted_reduction = -grad.T @ d - 0.5 * d.T @ H @ d # update trust region radius rho = actual_reduction / predicted_reduction if rho < 0.25: delta = 0.25 elif rho > 0.75 and np.abs(np.linalg.norm(d) - delta) < 1e-8: delta = min(2delta, eta*np.linalg.norm(theta)) # update parameters if rho > 0: theta += d J, grad = J_new, grad_new H += (grad_new - grad) @ (grad_new - grad).T / ((grad_new - grad).T @ d) # check convergence if np.linalg.norm(grad) < 1e-5: break return theta ——修正代码中的问题，实现信赖域算法求解逻辑回归问题

在代码中，对于更新信赖域半径的部分，有两个问题需要修正： 1. 当rho小于0.25时，应该将delta减小为原来的0.25，而不是将delta赋值为0.25。 2. 当rho大于0.75且步长d的长度与信赖域半径delta的差的绝对值小于1e-8...

ansys-guidelines-contact-convergence

在ANSYS中，收敛是指解算器达到稳定状态的过程。收敛通常涉及到定义收敛准则和与之相关的参数设置。首先，定义收敛准则是很重要的。通常情况下，收敛准则是根据解算结果的误差来定义的。例如，当解算结果的误差...

Python写出函数收敛过程图像

好的，以下是一个简单的Python函数，可以绘制函数收敛的过程图像： ```python import matplotlib.pyplot as plt import numpy as np def convergence_plot(f, x0, tol=1e-6, max_iter=100): """Plot the ...

% SolarCollector.m % ---------------------------------------------------------------------------------------------------------------------- % % Simple first-order solar collector model (M-file called by TRNSYS type 155) % % Data passed from / to TRNSYS % ---------------------------- % % trnTime (1x1) : simulation time % trnInfo (15x1) : TRNSYS info array % trnInputs (nIx1) : TRNSYS inputs % trnStartTime (1x1) : TRNSYS Simulation Start time % trnStopTime (1x1) : TRNSYS Simulation Stop time % trnTimeStep (1x1) : TRNSYS Simulation time step % mFileErrorCode (1x1) : Error code for this m-file. It is set to 1 by TRNSYS and the m-file should set it to 0 at the % end to indicate that the call was successful. Any non-zero value will stop the simulation % trnOutputs (nOx1) : TRNSYS outputs % % % Notes: % ------ % % You can use the values of trnInfo(7), trnInfo(8) and trnInfo(13) to identify the call (e.g. first iteration, etc.) % Real-time controllers (callingMode = 10) will only be called once per time step with trnInfo(13) = 1 (after convergence) % % The number of inputs is given by trnInfo(3) % The number of expected outputs is given by trnInfo(6) % WARNING: if multiple units of Type 155 are used, the variables passed from/to TRNSYS will be sized according to % the maximum required by all units. You should cope with that by only using the part of the arrays that is % really used by the current m-File. Example: use "nI = trnInfo(3); myInputs = trnInputs(1:nI);" % rather than "MyInputs = trnInputs;" % Please also note that all m-files share the same workspace in Matlab (they are "scripts", not "functions") so % variables like trnInfo, trnTime, etc. will be overwritten at each call. % % ---------------------------------------------------------------------------------------------------------------------- % This example implements a very simple solar collector model. The component is iterative (should be called at each % TRNSYS call) % % trnInputs % --------- % % trnInputs(1) : Ti, collector inlet temperature % trnInputs(2) : mdot, collector flowrate % trnInputs(3) : Tamb , ambient temperature % trnInputs(4) : Gt, solar radiation in the collector plane % % trnOutputs解释下这段代码

此外，代码中还有一些注释提供了一些说明和注意事项。例如，可以使用trnInfo(7)、trnInfo(8)和trnInfo(13)的值来识别调用的情况，也可以通过trnInfo(3)和trnInfo(6)来确定输入和输出的数量。请注意，如果使用多个...

function[fMin,bestX,Convergence_curve]=SSA(M,pop,c,d,dim,net,P,T)

- Convergence_curve：收敛曲线该函数的主体是使用蝗虫算法来搜索最优解。其中，蝗虫的位置表示问题的解空间中的一个点，蝗虫的移动过程类似于优化过程中的搜索过程。在每次迭代中，根据蝗虫的当前位置，计算其...

用python帮我写一个逻辑回归的优化代码,要求分别使用梯度下降法,AdaGrad,牛顿法,随机梯度下降法等,并进行收敛性对比

好的，以下是一个使用Python实现逻辑回归优化的示例代码，同时包含了梯度下降法、AdaGrad、牛顿法和随机梯度下降法的实现，并进行了收敛性对比。 ```python import numpy as np class LogisticRegression: def __...

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优化高速网络收敛：FC-Africa算法提升TCP性能

论文研究-DCDG-EA: Dynamic Convergence-Diversity Guided Evolutionary Algorithm for Many-Objective Optimization.pdf

Networkers2009：BRKIPM-3363 - Advanced Fast Routing Convergence: Network Availability and Simplicity

二维TE波FDTD方法引入高斯源作图，显示收敛阶matlab实现

生成雅可比迭代python代码

model.fit(initial_learning_rate=0.01, learning_rate_decay=1.5, convergence_epochs=5, batch_size=32, maximum_epochs=100, learning_rate_minimum=1e-4, training_split=0.8)

class LogisticRegression(object): def __init__(self, input_size, output_size, eta, max_epoch, eps):

admm-lasso分位数回归代码

ansys-guidelines-contact-convergence

Python写出函数收敛过程图像

function[fMin,bestX,Convergence_curve]=SSA(M,pop,c,d,dim,net,P,T)

用python帮我写一个逻辑回归的优化代码,要求分别使用梯度下降法,AdaGrad,牛顿法,随机梯度下降法等,并进行收敛性对比

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class LogisticRegression(object): def init(self, input_size, output_size, eta, max_epoch, eps):