演算法改進

⑴ Floyd演算法的改進

判斷連通可以在輸入時作一下預處理
Floyd已經是DP的思想了.
可以有些小優化.但求一個圖中任意兩點的最短路徑目前只有o(n^3)的演算法

⑵ 對演算法進行改進是因為不能實現還是因為實現的效果不好

1、你需要理解世界上沒有完美的演算法，永遠存在可以改進的空間。
2、改進的原因，一般來說不能實現很少。因為不能實現，這個演算法就根本沒完成，還談不上改進。
3、一般來說，實現效果不好倒是個多見的原因。更多原因是需求調整，性能優化，模型優化等等。
4、希望對你有幫助。

⑶ 鮑威爾方法的基本演算法與改進演算法的區別

鮑威爾基本演算法的問題在於，可能發生退化問題，具體而言就是可能在某一環迭代中出現基本方向組線性相關的情況，這種情況下按新方向替代第一個方向的方法進行替換，就會導致搜索在降維的空間中進行，無法得到原本n維空間的函數極小值，計算將失敗。

而改進的方法和原來方法本質區別在於替換方向的規則不同。改進的方法，能夠保證每輪迭代中搜索方向都線性無關，而且隨著迭代的延續，共軛的程度會逐漸增加。

具體展開比較復雜，簡單來說就是每次產生了新生方向，都要判斷一下這個方向好不好，如果不好就不換進來；如果覺得這個方向好，就看一下舊方向中哪個函數下降量最大，把這個下降量最大的方向替換掉。

⑷ 如何改進演算法，提高程序效率

從根本上了解演算法是怎麼執行的，這樣可以做到一通百通。

一般來說，降低時間復雜度是比較好的方法。 有時候，佔用更多的內存可以幫助程序更快的運行。還有就是選用效率高的語言，例如C。

⑸ 如何改進此演算法，使得演算法效率提高

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++;}//關鍵在這里
for(j=i;j<length-1;j++)
elem[j-n]=elem[j];
length=length-n;
}
}

解析：這里用了一個變數n，可以更好的解決連續出現x的情況，你可以想一下，假設數據是{1,2，x,x,x,3,3,3},按照原先的代碼，連續的3個x需要連續3次運行

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

而此處則僅需要一次，相對而言提高了效率，但是這也不是絕對的，比如：如果所有的x都不是連續出現的，那麼這兩個代碼沒什麼區別！

⑹ A*演算法如何改進

十萬火急：此改進的模糊C-此函數實現遺傳演算法，用於模糊C－均值聚類 %% A=farm(:,Ser(1)); B=farm(:,Ser(2)); P0=unidrnd(M-1); a=[

⑺ 如何改進SVM演算法，最好是自己的改進方法，別引用那些前人改進的演算法

樓主對於這種問題的答案完全可以上SCI了，知道答案的人都在寫論文中，所以我可以給幾個改進方向給你提示一下：
1 SVM是分類器對於它的准確性還有過擬合性都有很成熟的改進，所以採用數學方法來改進感覺很難了，但是它的應用很廣泛 SVMRank貌似就是netflix電影推薦系統的核心演算法，你可以了解下
2 與其他演算法的聯合，boosting是一種集成演算法，你可以考慮SVM作為一種弱學習器在其框架中提升學習的准確率
SVM的本身演算法真有好的改進完全可以在最高等級雜志上發論文，我上面說的兩個方面雖然很簡單但如果你有實驗數據證明，在國內發表核心期刊完全沒問題，本人也在論文糾結中。。

⑻ BP演算法及其改進

傳統的BP演算法及其改進演算法的一個很大缺點是：由於其誤差目標函數對於待學習的連接權值來說非凸的，存在局部最小點，對網路進行訓練時，這些演算法的權值一旦落入權值空間的局部最小點就很難跳出，因而無法達到全局最小點(即最優點)而使得網路訓練失敗。針對這些缺陷，根據凸函數及其共軛的性質，利用Fenchel不等式，使用約束優化理論中的罰函數方法構造出了帶有懲罰項的新誤差目標函數。

用新的目標函數對前饋神經網路進行優化訓練時，隱層輸出也作為被優化變數。這個目標函數的主要特點有：
1.固定隱層輸出，該目標函數對連接權值來說是凸的；固定連接權值，對隱層輸出來說是凸的。這樣在對連接權值和隱層輸出進行交替優化時，它們所面對的目標函數都是凸函數，不存在局部最小的問題，演算法對於初始權值的敏感性降低；
2.由於懲罰因子是逐漸增大的，使得權值的搜索空間變得比較大，從而對於大規模的網路也能夠訓練，在一定程度上降低了訓練過程陷入局部最小的可能性。

這些特性能夠在很大程度上有效地克服以往前饋網路的訓練演算法易於陷入局部最小而使網路訓練失敗的重大缺陷，也為利用凸優化理論研究前饋神經網路的學習演算法開創了一個新思路。在網路訓練時，可以對連接權值和隱層輸出進行交替優化。把這種新演算法應用到前饋神經網路訓練學習中，在學習速度、泛化能力、網路訓練成功率等多方面均優於傳統訓練演算法，如經典的BP演算法。數值試驗也表明了這一新演算法的有效性。

本文通過典型的BP演算法與新演算法的比較，得到了二者之間相互關系的初步結論。從理論上證明了當懲罰因子趨於正無窮大時新演算法就是BP演算法，並且用數值試驗說明了懲罰因子在網路訓練演算法中的作用和意義。對於三層前饋神經網路來說，懲罰因子較小時，隱層神經元局部梯度的可變范圍大，有利於連接權值的更新；懲罰因子較大時，隱層神經元局部梯度的可變范圍小，不利於連接權值的更新，但能提高網路訓練精度。這說明了在網路訓練過程中懲罰因子為何從小到大變化的原因,也說明了新演算法的可行性而BP演算法則時有無法更新連接權值的重大缺陷。

礦體預測在礦床地質中佔有重要地位，由於輸入樣本量大，用以往前饋網路演算法進行礦體預測效果不佳。本文把前饋網路新演算法應用到礦體預測中，取得了良好的預期效果。

本文最後指出了新演算法的優點，並指出了有待改進的地方。

關鍵詞：前饋神經網路，凸優化理論，訓練演算法，礦體預測，應用

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

傳統的BP演算法及其改進演算法的一個很大缺點是：由於其誤差目標函數對於待學習的連接權值來說非凸的，存在局部最小點，對網路進行訓練時，這些演算法的權值一旦落入權值空間的局部最小點就很難跳出，因而無法達到全局最小點(即最優點)而使得網路訓練失敗。針對這些缺陷，根據凸函數及其共軛的性質，利用Fenchel不等式，使用約束優化理論中的罰函數方法構造出了帶有懲罰項的新誤差目標函數。

用新的目標函數對前饋神經網路進行優化訓練時，隱層輸出也作為被優化變數。這個目標函數的主要特點有：
1.固定隱層輸出，該目標函數對連接權值來說是凸的；固定連接權值，對隱層輸出來說是凸的。這樣在對連接權值和隱層輸出進行交替優化時，它們所面對的目標函數都是凸函數，不存在局部最小的問題，演算法對於初始權值的敏感性降低；
2.由於懲罰因子是逐漸增大的，使得權值的搜索空間變得比較大，從而對於大規模的網路也能夠訓練，在一定程度上降低了訓練過程陷入局部最小的可能性。

這些特性能夠在很大程度上有效地克服以往前饋網路的訓練演算法易於陷入局部最小而使網路訓練失敗的重大缺陷，也為利用凸優化理論研究前饋神經網路的學習演算法開創了一個新思路。在網路訓練時，可以對連接權值和隱層輸出進行交替優化。把這種新演算法應用到前饋神經網路訓練學習中，在學習速度、泛化能力、網路訓練成功率等多方面均優於傳統訓練演算法，如經典的BP演算法。數值試驗也表明了這一新演算法的有效性。

本文通過典型的BP演算法與新演算法的比較，得到了二者之間相互關系的初步結論。從理論上證明了當懲罰因子趨於正無窮大時新演算法就是BP演算法，並且用數值試驗說明了懲罰因子在網路訓練演算法中的作用和意義。對於三層前饋神經網路來說，懲罰因子較小時，隱層神經元局部梯度的可變范圍大，有利於連接權值的更新；懲罰因子較大時，隱層神經元局部梯度的可變范圍小，不利於連接權值的更新，但能提高網路訓練精度。這說明了在網路訓練過程中懲罰因子為何從小到大變化的原因,也說明了新演算法的可行性而BP演算法則時有無法更新連接權值的重大缺陷。

礦體預測在礦床地質中佔有重要地位，由於輸入樣本量大，用以往前饋網路演算法進行礦體預測效果不佳。本文把前饋網路新演算法應用到礦體預測中，取得了良好的預期效果。

本文最後指出了新演算法的優點，並指出了有待改進的地方。

關鍵詞：前饋神經網路，凸優化理論，訓練演算法，礦體預測，應用

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演算法及其改進

2.1 BP演算法步驟

1°隨機抽取初始權值ω0；

2°輸入學習樣本對（Xp,Yp），學習速率η，誤差水平ε；

3°依次計算各層結點輸出opi,opj,opk；

4°修正權值ωk+1=ωk+ηpk,其中pk=,ωk為第k次迭代權變數；

5°若誤差E<ε停止，否則轉3°。

2.2 最優步長ηk的確定

在上面的演算法中，學習速率η實質上是一個沿負梯度方向的步長因子，在每一次迭代中如何確定一個最優步長ηk，使其誤差值下降最快，則是典型的一維搜索問題，即E(ωk+ηkpk)=(ωk+ηpk)。令Φ(η)=E(ωk+ηpk)，則Φ′(η)=dE(ωk+ηpk)/dη=E(ωk+ηpk)Tpk。若ηk為(η)的極小值點，則Φ′(ηk)=0，即E(ωk+ηpk)Tpk=-pTk+1pk=0。確定ηk的演算法步驟如下

1°給定η0=0,h=0.01,ε0=0.00001；

2°計算Φ′(η0),若Φ′(η0)=0,則令ηk=η0，停止計算；

3°令h=2h, η1=η0+h；

4°計算Φ′(η1)，若Φ′(η1)=0，則令ηk=η1，停止計算；

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

5°計算Φ′(a)，若Φ′(a)=0，則ηk=a，停止計算；

6°計算Φ′(b)，若Φ′(b)=0，則ηk=b，停止計算；

7°計算Φ′(a+b/2),若Φ′(a+b/2)=0，則ηk=a+b/2，停止計算；

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

8°若｜a-b｜<ε0，則令，ηk=a+b/2,停止計算，否則轉7°。

2.3 改進BP演算法的特點分析

在上述改進的BP演算法中，對學習速率η的選取不再由用戶自己確定，而是在每次迭代過程中讓計算機自動尋找最優步長ηk。而確定ηk的演算法中，首先給定η0=0，由定義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，則表明此時下降方向pk為零向量，也即已達到局部極值點，否則必有Φ′(η0)<0，而對於一維函數Φ(η)的性質可知，Φ′(η0)<0則在η0=0的局部范圍內函數為減函數。故在每一次迭代過程中給η0賦初值0是合理的。

改進後的BP演算法與原BP演算法相比有兩處變化，即步驟2°中不需給定學習速率η的值；另外在每一次修正權值之前，即步驟4°前已計算出最優步長ηk。