# A Novel UCP Model Based on Artificial Neural Networks and Orthogonal Arrays
## 3 New, Improved UCP--Our Approach
### The Methodology Used within the Improved UCP Model
#### Step 3:  
The sigmoid function, as the activation function of the hidden layer, is used (19):  
\[y_{i}=\frac{1}{1+e^{-X_{i}}},\ i=\overline{1,n} \tag{19}\]  
The construction of the activation function is based on a combination of input values and corresponding weight coefficients \(W_{i}\) for each of the listed ANN architectures. The hidden and output layer functions, for the ANN-L16 architecture, are as follows (20)-(22):  
\[Y_{1}=1/\Big{(}1+e^{-(X_{1}\cdot W_{1}+X_{2}\cdot W_{3}+X_{3}\cdot W_{5}+X_{4 }\cdot W_{7}+X_{5}\cdot W_{9}+X_{6}\cdot W_{11})}\Big{)} \tag{20}\]  
\[Y_{2}=1/\Big{(}1+e^{-(X_{1}\cdot W_{2}+X_{2}\cdot W_{4}+X_{3}\cdot W_{6}+X_{4 }\cdot W_{8}+X_{5}\cdot W_{10}+X_{6}\cdot W_{12})}\Big{)} \tag{21}\]  
\[EstEffANN-L16=1/\Big{(}1+e^{-(Y_{1}\cdot W_{12}+Y_{2}\cdot W_{14}+1\cdot W_{15} )}\Big{)} \tag{22}\]  
where \(Y_{1}\), \(Y_{2}\), and \(Y_{3}\) are the hidden layer functions and \(EstEffortANN\)-\(L16\) represents the output function. The hidden and output layer functions for the ANN-L36 prim architecture are as follows (23)-(26):  
\[Y_{1}=\frac{1}{1+e^{-(X_{1}\cdot W_{1}+X_{2}\cdot W_{4}+X_{3}\cdot W_{7}+X_{4 }\cdot W_{10})}} \tag{23}\]  
Figure 3: Robust design algorithm for performing the experiment (UCP). \[Y_{2}=\frac{1}{1+e^{-(X_{1}\cdot W_{2}+X_{2}\cdot W_{5}+X_{3}\cdot W_{8}+X_{4} \cdot W_{11})}} \tag{24}\]  
\[Y_{3}=\frac{1}{1+e^{-(X_{1}\cdot W_{3}+X_{2}\cdot W_{6}+X_{3}\cdot W_{9}+X_{4} \cdot W_{12})}} \tag{25}\]  
\[EstEffortANN-L36 prim=\frac{1}{1+e^{-(Y_{1}\cdot W_{13}+Y_{2}\cdot W_{14}+Y_{3} \cdot W_{15}+1\cdot W_{16})}} \tag{26}\]  
where \(Y_{1}\), \(Y_{2}\), and \(Y_{3}\) are the hidden layer functions and \(EstEffortANN\)-L36 prim represents the output function. In the first proposed ANN-L16 architecture, an orthogonal vector plan of two levels L1 and L2, and the initial values of the weighting factors \(W_{i}\) that take the values from the interval \([-1,1]\), are used. The second proposed architecture has an orthogonal vector plan of three levels, L1, L2, and L3, and the initial values of the weighting factors \(W_{i}\) that take the values from the interval \([-1,0,1]\). For each subsequent iteration, new weight factor values must be calculated as follows (e.g., for ANN-L16 architecture) [2; 3; 4] (27):  
\[ \begin{array}{l}W_{1}L1=\text{cost1}+\text{cost2}+\dots+\text{cost8}\\ W_{1}L2=\text{cost9}+\text{cost10}+\dots+\text{cost16}\\ \dots\\ W_{15}L1=\text{cost1}+\text{cost6}+\dots+\text{cost16}\\ W_{15}L2=\text{cost2}+\text{cost3}+\dots+\text{cost15}\\ \text{where cost}(i)=\Sigma\ MRE(ANN(i))\end{array}  \tag{27}\]  
For each subsequent iteration, the interval \([-1,1]\) is divided depending on the cost effect function as follows [7; 30] (28):  
\[ \begin{array}{l}W_{1}L1 new=W_{1}L1 old\\ W_{1}L2 new=W_{1}L2 old+(W_{1}L3 old-W_{1}L2 old)/2\\ W_{1}L3 new=W_{1}L3 old\end{array}  \tag{28}\]  
where \(W_{1}L1 old\), \(W_{1}L2 old\), and \(W_{1}L3 old\) are values form the previous iteration. The set of input values of each dataset converges depending on the value of the cost effect function. **Step 4:**  
The defuzzification method is used according to the following Formulas (29) and (30) [35]:  
\[Y_{i}=(X_{min}+\mu_{D}(X_{i}))\cdot(X_{max}-X_{min}) \tag{29}\]  
\[\text{OA(ANN}i)=Yi,\text{ where }i=16,i=36. \tag{30}\]  
where OA represents actual effort of the particular project, which is calculated based on ANN-L12 and ANN-L36 prim. **Step 5:**  
For each iteration in our experiment, the output values are obtained according to the following formulas/measures [2; 4; 30] (31)-(35):  
\[Deviation=|ActEffort-EstEffort| \tag{31}\]  
\[MAE_{i}=\frac{1}{n}\sum_{i=1}^{n}|ActEffort-EstEffort| \tag{32}\]  
\[MRE=Deviation/ActEffort \tag{33}\]  
\[MRE=\frac{1}{n}\cdot\sum_{i=1}^{n}MRE_{i} \tag{34}\]  
\[\text{MMRE}=mean\text{ (MRE)} \tag{35}\]  
on all training data for the two ANN architectures was examined. It can be concluded that the ANN-L36 prim architecture quickly converges to the minimum knowledge of MMRE compared to the ANN-L16 architecture (Figure 4).