算法改进

⑴ Floyd算法的改进

判断连通可以在输入时作一下预处理
Floyd已经是DP的思想了.
可以有些小优化.但求一个图中任意两点的最短路径目前只有o(n^3)的算法

⑵ 对算法进行改进是因为不能实现还是因为实现的效果不好

1、你需要理解世界上没有完美的算法，永远存在可以改进的空间。
2、改进的原因，一般来说不能实现很少。因为不能实现，这个算法就根本没完成，还谈不上改进。
3、一般来说，实现效果不好倒是个多见的原因。更多原因是需求调整，性能优化，模型优化等等。
4、希望对你有帮助。

⑶ 鲍威尔方法的基本算法与改进算法的区别

鲍威尔基本算法的问题在于，可能发生退化问题，具体而言就是可能在某一环迭代中出现基本方向组线性相关的情况，这种情况下按新方向替代第一个方向的方法进行替换，就会导致搜索在降维的空间中进行，无法得到原本n维空间的函数极小值，计算将失败。

而改进的方法和原来方法本质区别在于替换方向的规则不同。改进的方法，能够保证每轮迭代中搜索方向都线性无关，而且随着迭代的延续，共轭的程度会逐渐增加。

具体展开比较复杂，简单来说就是每次产生了新生方向，都要判断一下这个方向好不好，如果不好就不换进来；如果觉得这个方向好，就看一下旧方向中哪个函数下降量最大，把这个下降量最大的方向替换掉。

⑷ 如何改进算法，提高程序效率

从根本上了解算法是怎么执行的，这样可以做到一通百通。

一般来说，降低时间复杂度是比较好的方法。 有时候，占用更多的内存可以帮助程序更快的运行。还有就是选用效率高的语言，例如C。

⑸ 如何改进此算法，使得算法效率提高

voidDeletaz(ElemTypex)
{
inti=0,j;
while(i<length&&elem[i]<x)i++;
if(i==length)cout<<”X不存在”<<endl;
else{
while(elem[i]==x)
{n++;i++;}//关键在这里
for(j=i;j<length-1;j++)
elem[j-n]=elem[j];
length=length-n;
}
}

解析：这里用了一个变量n，可以更好的解决连续出现x的情况，你可以想一下，假设数据是{1,2，x,x,x,3,3,3},按照原先的代码，连续的3个x需要连续3次运行

for(j=I;j<length;j++)elem[j]=elem[j+1];
length--;

而此处则仅需要一次，相对而言提高了效率，但是这也不是绝对的，比如：如果所有的x都不是连续出现的，那么这两个代码没什么区别！

⑹ A*算法如何改进

十万火急：此改进的模糊C-此函数实现遗传算法，用于模糊C－均值聚类 %% A=farm(:,Ser(1)); B=farm(:,Ser(2)); P0=unidrnd(M-1); a=[

⑺ 如何改进SVM算法，最好是自己的改进方法，别引用那些前人改进的算法

楼主对于这种问题的答案完全可以上SCI了，知道答案的人都在写论文中，所以我可以给几个改进方向给你提示一下：
1 SVM是分类器对于它的准确性还有过拟合性都有很成熟的改进，所以采用数学方法来改进感觉很难了，但是它的应用很广泛 SVMRank貌似就是netflix电影推荐系统的核心算法，你可以了解下
2 与其他算法的联合，boosting是一种集成算法，你可以考虑SVM作为一种弱学习器在其框架中提升学习的准确率
SVM的本身算法真有好的改进完全可以在最高等级杂志上发论文，我上面说的两个方面虽然很简单但如果你有实验数据证明，在国内发表核心期刊完全没问题，本人也在论文纠结中。。

⑻ BP算法及其改进

传统的BP算法及其改进算法的一个很大缺点是：由于其误差目标函数对于待学习的连接权值来说非凸的，存在局部最小点，对网络进行训练时，这些算法的权值一旦落入权值空间的局部最小点就很难跳出，因而无法达到全局最小点(即最优点)而使得网络训练失败。针对这些缺陷，根据凸函数及其共轭的性质，利用Fenchel不等式，使用约束优化理论中的罚函数方法构造出了带有惩罚项的新误差目标函数。

用新的目标函数对前馈神经网络进行优化训练时，隐层输出也作为被优化变量。这个目标函数的主要特点有：
1.固定隐层输出，该目标函数对连接权值来说是凸的；固定连接权值，对隐层输出来说是凸的。这样在对连接权值和隐层输出进行交替优化时，它们所面对的目标函数都是凸函数，不存在局部最小的问题，算法对于初始权值的敏感性降低；
2.由于惩罚因子是逐渐增大的，使得权值的搜索空间变得比较大，从而对于大规模的网络也能够训练，在一定程度上降低了训练过程陷入局部最小的可能性。

这些特性能够在很大程度上有效地克服以往前馈网络的训练算法易于陷入局部最小而使网络训练失败的重大缺陷，也为利用凸优化理论研究前馈神经网络的学习算法开创了一个新思路。在网络训练时，可以对连接权值和隐层输出进行交替优化。把这种新算法应用到前馈神经网络训练学习中，在学习速度、泛化能力、网络训练成功率等多方面均优于传统训练算法，如经典的BP算法。数值试验也表明了这一新算法的有效性。

本文通过典型的BP算法与新算法的比较，得到了二者之间相互关系的初步结论。从理论上证明了当惩罚因子趋于正无穷大时新算法就是BP算法，并且用数值试验说明了惩罚因子在网络训练算法中的作用和意义。对于三层前馈神经网络来说，惩罚因子较小时，隐层神经元局部梯度的可变范围大，有利于连接权值的更新；惩罚因子较大时，隐层神经元局部梯度的可变范围小，不利于连接权值的更新，但能提高网络训练精度。这说明了在网络训练过程中惩罚因子为何从小到大变化的原因,也说明了新算法的可行性而BP算法则时有无法更新连接权值的重大缺陷。

矿体预测在矿床地质中占有重要地位，由于输入样本量大，用以往前馈网络算法进行矿体预测效果不佳。本文把前馈网络新算法应用到矿体预测中，取得了良好的预期效果。

本文最后指出了新算法的优点，并指出了有待改进的地方。

关键词：前馈神经网络，凸优化理论，训练算法，矿体预测，应用

Feed forward Neural Networks Training Algorithm Based on Convex Optimization and Its Application in Deposit Forcasting
JIA Wen-chen (Computer Application)
Directed by YE Shi-wei

Abstract

The paper studies primarily the application of convex optimization theory and algorithm for feed forward neural networks’ training and convergence performance.

It reviews the history of feed forward neural networks, points out that the training of feed forward neural networks is essentially a non-linear problem and introces BP algorithm, its advantages as well as disadvantages and previous improvements for it. One of the big disadvantages of BP algorithm and its improvement algorithms is: because its error target function is non-convex in the weight values between neurons in different layers and exists local minimum point, thus, if the weight values enter local minimum point in weight values space when network is trained, it is difficult to skip local minimum point and reach the global minimum point (i.e. the most optimal point).If this happening, the training of networks will be unsuccessful. To overcome these essential disadvantages, the paper constructs a new error target function including restriction item according to convex function, Fenchel inequality in the conjugate of convex function and punishment function method in restriction optimization theory.
When feed forward neural networks based on the new target function is being trained, hidden layers’ outputs are seen as optimization variables. The main characteristics of the new target function are as follows:

1.With fixed hidden layers’ outputs, the new target function is convex in connecting weight variables; with fixed connecting weight values, the new target function is convex in hidden layers’ outputs. Thus, when connecting weight values and hidden layers’ outputs are optimized alternately, the new target function is convex in them, doesn’t exist local minimum point, and the algorithm’s sensitiveness is reced for original weight values .
2.Because the punishment factor is increased graally, weight values ’ searching space gets much bigger, so big networks can be trained and the possibility of entering local minimum point can be reced to a certain extent in network training process.

Using these characteristics can overcome efficiently in the former feed forward neural networks’ training algorithms the big disadvantage that networks training enters local minimum point easily. This creats a new idea for feed forward neural networks’ learning algorithms by using convex optimization theory .In networks training, connecting weight variables and hidden layer outputs can be optimized alternately. The new algorithm is much better than traditional algorithms for feed forward neural networks. The numerical experiments show that the new algorithm is successful.

By comparing the new algorithm with the traditional ones, a primary conclusion of their relationship is reached. It is proved theoretically that when the punishment factor nears infinity, the new algorithm is BP algorithm yet. The meaning and function of the punishment factor are also explained by numerical experiments. For three-layer feed forward neural networks, when the punishment factor is smaller, hidden layer outputs’ variable range is bigger and this is in favor to updating of the connecting weights values, when the punishment factor is bigger, hidden layer outputs’ variable range is smaller and this is not in favor to updating of the connecting weights values but it can improve precision of networks. This explains the reason that the punishment factor should be increased graally in networks training process. It also explains feasibility of the new algorithm and BP algorithm’s disadvantage that connecting weigh values can not be updated sometimes.

Deposit forecasting is very important in deposit geology. The previous algorithms’ effect is not good in deposit forecasting because of much more input samples. The paper applies the new algorithm to deposit forecasting and expectant result is reached.
The paper points out the new algorithm’s strongpoint as well as to-be-improved places in the end.

Keywords: feed forward neural networks, convex optimization theory, training algorithm, deposit forecasting, application

传统的BP算法及其改进算法的一个很大缺点是：由于其误差目标函数对于待学习的连接权值来说非凸的，存在局部最小点，对网络进行训练时，这些算法的权值一旦落入权值空间的局部最小点就很难跳出，因而无法达到全局最小点(即最优点)而使得网络训练失败。针对这些缺陷，根据凸函数及其共轭的性质，利用Fenchel不等式，使用约束优化理论中的罚函数方法构造出了带有惩罚项的新误差目标函数。

用新的目标函数对前馈神经网络进行优化训练时，隐层输出也作为被优化变量。这个目标函数的主要特点有：
1.固定隐层输出，该目标函数对连接权值来说是凸的；固定连接权值，对隐层输出来说是凸的。这样在对连接权值和隐层输出进行交替优化时，它们所面对的目标函数都是凸函数，不存在局部最小的问题，算法对于初始权值的敏感性降低；
2.由于惩罚因子是逐渐增大的，使得权值的搜索空间变得比较大，从而对于大规模的网络也能够训练，在一定程度上降低了训练过程陷入局部最小的可能性。

这些特性能够在很大程度上有效地克服以往前馈网络的训练算法易于陷入局部最小而使网络训练失败的重大缺陷，也为利用凸优化理论研究前馈神经网络的学习算法开创了一个新思路。在网络训练时，可以对连接权值和隐层输出进行交替优化。把这种新算法应用到前馈神经网络训练学习中，在学习速度、泛化能力、网络训练成功率等多方面均优于传统训练算法，如经典的BP算法。数值试验也表明了这一新算法的有效性。

本文通过典型的BP算法与新算法的比较，得到了二者之间相互关系的初步结论。从理论上证明了当惩罚因子趋于正无穷大时新算法就是BP算法，并且用数值试验说明了惩罚因子在网络训练算法中的作用和意义。对于三层前馈神经网络来说，惩罚因子较小时，隐层神经元局部梯度的可变范围大，有利于连接权值的更新；惩罚因子较大时，隐层神经元局部梯度的可变范围小，不利于连接权值的更新，但能提高网络训练精度。这说明了在网络训练过程中惩罚因子为何从小到大变化的原因,也说明了新算法的可行性而BP算法则时有无法更新连接权值的重大缺陷。

矿体预测在矿床地质中占有重要地位，由于输入样本量大，用以往前馈网络算法进行矿体预测效果不佳。本文把前馈网络新算法应用到矿体预测中，取得了良好的预期效果。

本文最后指出了新算法的优点，并指出了有待改进的地方。

关键词：前馈神经网络，凸优化理论，训练算法，矿体预测，应用

Feed forward Neural Networks Training Algorithm Based on Convex Optimization and Its Application in Deposit Forcasting
JIA Wen-chen (Computer Application)
Directed by YE Shi-wei

Abstract

The paper studies primarily the application of convex optimization theory and algorithm for feed forward neural networks’ training and convergence performance.

It reviews the history of feed forward neural networks, points out that the training of feed forward neural networks is essentially a non-linear problem and introces BP algorithm, its advantages as well as disadvantages and previous improvements for it. One of the big disadvantages of BP algorithm and its improvement algorithms is: because its error target function is non-convex in the weight values between neurons in different layers and exists local minimum point, thus, if the weight values enter local minimum point in weight values space when network is trained, it is difficult to skip local minimum point and reach the global minimum point (i.e. the most optimal point).If this happening, the training of networks will be unsuccessful. To overcome these essential disadvantages, the paper constructs a new error target function including restriction item according to convex function, Fenchel inequality in the conjugate of convex function and punishment function method in restriction optimization theory.
When feed forward neural networks based on the new target function is being trained, hidden layers’ outputs are seen as optimization variables. The main characteristics of the new target function are as follows:

1.With fixed hidden layers’ outputs, the new target function is convex in connecting weight variables; with fixed connecting weight values, the new target function is convex in hidden layers’ outputs. Thus, when connecting weight values and hidden layers’ outputs are optimized alternately, the new target function is convex in them, doesn’t exist local minimum point, and the algorithm’s sensitiveness is reced for original weight values .
2.Because the punishment factor is increased graally, weight values ’ searching space gets much bigger, so big networks can be trained and the possibility of entering local minimum point can be reced to a certain extent in network training process.

Using these characteristics can overcome efficiently in the former feed forward neural networks’ training algorithms the big disadvantage that networks training enters local minimum point easily. This creats a new idea for feed forward neural networks’ learning algorithms by using convex optimization theory .In networks training, connecting weight variables and hidden layer outputs can be optimized alternately. The new algorithm is much better than traditional algorithms for feed forward neural networks. The numerical experiments show that the new algorithm is successful.

By comparing the new algorithm with the traditional ones, a primary conclusion of their relationship is reached. It is proved theoretically that when the punishment factor nears infinity, the new algorithm is BP algorithm yet. The meaning and function of the punishment factor are also explained by numerical experiments. For three-layer feed forward neural networks, when the punishment factor is smaller, hidden layer outputs’ variable range is bigger and this is in favor to updating of the connecting weights values, when the punishment factor is bigger, hidden layer outputs’ variable range is smaller and this is not in favor to updating of the connecting weights values but it can improve precision of networks. This explains the reason that the punishment factor should be increased graally in networks training process. It also explains feasibility of the new algorithm and BP algorithm’s disadvantage that connecting weigh values can not be updated sometimes.

Deposit forecasting is very important in deposit geology. The previous algorithms’ effect is not good in deposit forecasting because of much more input samples. The paper applies the new algorithm to deposit forecasting and expectant result is reached.
The paper points out the new algorithm’s strongpoint as well as to-be-improved places in the end.

Keywords: feed forward neural networks, convex optimization theory, training algorithm, deposit forecasting, application

BP算法及其改进

2.1 BP算法步骤

1°随机抽取初始权值ω0；

2°输入学习样本对（Xp,Yp），学习速率η，误差水平ε；

3°依次计算各层结点输出opi,opj,opk；

4°修正权值ωk+1=ωk+ηpk,其中pk=,ωk为第k次迭代权变量；

5°若误差E<ε停止，否则转3°。

2.2 最优步长ηk的确定

在上面的算法中，学习速率η实质上是一个沿负梯度方向的步长因子，在每一次迭代中如何确定一个最优步长ηk，使其误差值下降最快，则是典型的一维搜索问题，即E(ωk+ηkpk)=(ωk+ηpk)。令Φ(η)=E(ωk+ηpk)，则Φ′(η)=dE(ωk+ηpk)/dη=E(ωk+ηpk)Tpk。若ηk为(η)的极小值点，则Φ′(ηk)=0，即E(ωk+ηpk)Tpk=-pTk+1pk=0。确定ηk的算法步骤如下

1°给定η0=0,h=0.01,ε0=0.00001；

2°计算Φ′(η0),若Φ′(η0)=0,则令ηk=η0，停止计算；

3°令h=2h, η1=η0+h；

4°计算Φ′(η1)，若Φ′(η1)=0，则令ηk=η1，停止计算；

若Φ′(η1)>0，则令a=η0,b=η1；若Φ′(η1)<0，则令η0=η1，转3°；

5°计算Φ′(a)，若Φ′(a)=0，则ηk=a，停止计算；

6°计算Φ′(b)，若Φ′(b)=0，则ηk=b，停止计算；

7°计算Φ′(a+b/2),若Φ′(a+b/2)=0，则ηk=a+b/2，停止计算；

若Φ′(a+b/2)<0,则令a=a+b/2;若Φ′(a+b/2)>0，则令b=a+b/2

8°若｜a-b｜<ε0，则令，ηk=a+b/2,停止计算，否则转7°。

2.3 改进BP算法的特点分析

在上述改进的BP算法中，对学习速率η的选取不再由用户自己确定，而是在每次迭代过程中让计算机自动寻找最优步长ηk。而确定ηk的算法中，首先给定η0=0，由定义Φ(η)=E(ωk+ηpk)知，Φ′(η)=dE(ωk+ηpk)/dη=E(ωk+ηpk)Tpk，即Φ′(η0)=-pTkpk≤0。若Φ′(η0)=0，则表明此时下降方向pk为零向量，也即已达到局部极值点，否则必有Φ′(η0)<0，而对于一维函数Φ(η)的性质可知，Φ′(η0)<0则在η0=0的局部范围内函数为减函数。故在每一次迭代过程中给η0赋初值0是合理的。

改进后的BP算法与原BP算法相比有两处变化，即步骤2°中不需给定学习速率η的值；另外在每一次修正权值之前，即步骤4°前已计算出最优步长ηk。