esa-sceva/satcom-chunk-collection huggingface dataset:
## 3 Development and Results
### Training and Evaluation Phases
#### 3.1.2 Tests Performed Using the Complete Database  
After having confirmed in the previous tests that the increase of the database provided new information, we proceeded to carry out tests using the complete database using the architecture C2, which was the one that provided the best results in the previous test conducted with half of the database. The obtained results in the training and evaluation phases are shown in Table 5.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **Tests** & **Image** & **Steps** & \multicolumn{2}{c}{**Training**} & \multicolumn{2}{c}{**Evaluation**} \\ \cline{4-7}  & & & **Loss** & **Accuracy** & **Loss** & **Accuracy** \\ \hline \multirow{3}{*}{C3} & T1 & RGB & 17,000 & 0.28 & 0.81 & 0.28 & 0.87 \\  & T2 & Gray & 9000 & 0.29 & 0.79 & 0.33 & 0.85 \\  & T3 & Gray & 11,000 & 0.12 & 0.82 & 0.35 & 0.87 \\ \hline \multirow{3}{*}{C4} & T4 & RGB & 19,000 & 0.21 & 0.82 & 0.29 & 0.86 \\  & T2 & Gray & 15,000 & 0.13 & 0.85 & 0.32 & 0.86 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Results obtained with the networks based on ZF Net—Using half of the database.  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & **Configurations** \\ \hline C3 & C4 & C5 \\ \hline Conv \(7\times 7\) - 64 & Conv \(7\times 7\) - 92 & Conv \(7\times 7\) - 92 \\  & Max-Pooling \(3\times 3\) & \\ \hline Conv \(5\times 5\) - 128 & Conv \(5\times 5\) - 192 & Conv \(5\times 5\) - 192 \\  & Max-Pooling \(3\times 3\) & \\ \hline Conv \(3\times 3\) - 192 & Conv \(3\times 3\) - 256 & Conv \(3\times 3\) - 256 \\ Conv \(3\times 3\) - 192 & Conv \(3\times 3\) - 256 & Conv \(3\times 3\) - 256 \\ Conv \(3\times 3\) - 128 & Conv \(3\times 3\) - 192 & Conv \(3\times 3\) - 192 \\  & Max-Pooling \(3\times 3\) & \\ \hline FC - 2048 & FC - 4096 & FC - 4096 \\ FC - 2 & FC - 2 & FC - 2048 \\  & & SoftMax & \\ \hline \hline \end{tabular}
\end{table}
Table 3: Proposed networks based on ZF Net—Using half of the database.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & **Tests** & **Image** & **Steps** & \multicolumn{2}{c}{**Training**} & \multicolumn{2}{c}{**Evaluation**} \\ \cline{4-7}  & & & **Loss** & **Accuracy** & **Loss** & **Accuracy** \\ \hline \multirow{3}{*}{C3} & T1 & RGB & 17,000 & 0.28 & 0.81 & 0.28 & 0.87 \\  & T2 & Gray & 9000 & 0.29 & 0.79 & 0.33 & 0.85 \\  & T3 & Gray & 11,000 & 0.12 & 0.82 & 0.35 & 0.87 \\ \hline \multirow{3}{*}{C4} & T4 & RGB & 19,000 & 0.21 & 0.82 & 0.29 & 0.86 \\  & T5 & Gray & 15,000 & 0.13 & 0.85 & 0.32 & 0.86 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Results obtained with the configuration C2—Using the complete database.  
The best results were obtained in test T2 using grayscale images, resulting in an improvement in the evaluation phase in accuracy of 0.22% and in loss of 34.3% in comparison with the results obtained in test T1. Therefore, the model used in test T2 with grayscale images was used in the implementation of the system.
## 2 Materials and Methods
### ERI\({}_{TCP}\) Definition and Performance Evaluation  
According to the original definition, the early regression index was calculated as follows [23]:  
\[ERI_{TCP}=-ln\left(\left(1-\left(\frac{V_{ther}}{V_{pre}}\right)\right)^{V_{ pre}}\right)\]  
where \(V_{pre}\) is the GTV volume calculated on the MR image acquired during simulation and \(V_{ther}\) represents the volume measured on the MR images acquired during the MRgRT treatment.  
To identify the optimal time for pCR prediction, GTVs were delineated on MR images acquired at different fractions, and the \(ERI_{TCP}\) was calculated at different dose levels. The physical dose values were converted in biologically effective doses (\(BED\)) to make generalizable the results, using the following formula:  
\[BED=nd\left(1+\frac{d}{\frac{\alpha}{\beta}}\right)\]  
where \(d\) is the dose per fraction, \(n\) is the number of fractions and \(\alpha/\beta\) is the ratio representative of the tumor radio sensitivity, set equal to 10 Gy [27].  
ERI\({}_{TCP}\) was then calculated at the following BED values: 14, 28, 42, 54 and 62 Gy.  
The ERI\({}_{TCP}\) performance in identifying pCR patients was evaluated calculating the area under curve (AUC) under the receiver operating characteristic (ROC) curve for each dose level, estimating also the 95% exact binomial confidence interval according to the Clopper-Pearson method [28].  
Figure 1: Gross tumor volume (GTV) delineated on simulation imaging and at fraction 10 in axial (**A**) and (**B**) and sagittal plan (**C**) and (**D**).  
For each ERI index calculated, the Youden index (J) was also calculated at different threshold levels, and the one maximizing J was considered as best cut-off level.  
The performance of the different ERI\({}_{\text{TCP}}\) indices at the best cut-off level was then quantified considering specificity and sensitivity. The same analysis in terms of ROC curve was performed for the tumor volume calculated at simulation.  
The BED value where the ERI\({}_{\text{TCP}}\) reported the higher AUC value was identified as the optimal BED level to predict pCR. The ROC curves calculated at different BED values were then compared using the [PERSON]'s test for correlated ROC curves [29].  
Lastly, the robustness of ERI\({}_{\text{TCP}}\) against inter-observer variability in tumor delineation was tested, comparing the volume of the contours independently delineated by the two radiation oncologists using the Mann-Whitney test for paired samples and the intra-class correlation index (ICC) [30; 31]. The whole statistical analysis was performed using various software packages implemented in R environment [32; 33].
## 3 Proposed Methodology
### Performance Evaluation Metrics  
Model evaluation involves assessing the performance of a model on test data. In this study, the following evaluation metrics were used: _precision_ (_PRE_), _recall_ (_REC_), _F1_-_score_ (_F1_), _and accuracy_ (_ACC_). These metrics are computed based on the counts of _true positives_(_TPv_), _false positives_ (_FPv_), _true negatives_ (_TNv_), and _false negatives_ (_FNv_). The calculations for these metrics are given by Equations (5)-(8).  
\[Accuracy(ACC)=\frac{TPv+TNv}{TPv+TNv+FPv+FNv} \tag{5}\]  
\[Precision(PRE)=\frac{TPv}{TPv+FPv} \tag{6}\]  
\[Recall(REC)=\frac{TPv}{TPv+FNv} \tag{7}\]  
\[F1-score(F1)=2\times\left(\frac{Precision(PRE)\times Recall(REC)}{Precision(PRE)+ Recall(REC)}\right) \tag{8}\]  
In these equations:  
_True positives_ (_TPv_) are positive instances that were accurately predicted as positive. _False positives_ (_FPv_) are instances that were predicted as positive when the actual label is negative. Observations that were accurately classified as negative are known as _astrae negative_ (_TNv_) observations. Observations that were incorrectly classified as negative when they actually belonged to the positive class are known as _false negatives_ (_FNv_).
## 1 Introduction
Thus, it can be seen that the difficulties in the leakage location of thin plates such as those used spacecraft are the effects of dispersion on wave speed and the band adaptability of practical applications. In order to solve the above problems and to improve the accuracy of the beamforming algorithm for leak location, a frequency weighting matrix beamforming (FWMB) algorithm is proposed in this paper. In this method, narrowband filtering is used to match the dispersion curve to achieve the matrix superposition of wave speeds at different frequencies. An energy evaluation on the frequency band of the signal is performed to determine the selected frequency band and its weighting coefficient matrix, and the weighting method is used to compensate for the frequency band response that is caused by different leaks to achieve a frequency band adaptation. The FWMB algorithm was validated by laboratory tests that used an L-shaped acoustic emission array, and its performance was evaluated. The method in this paper has the potential to be used in spacecraft in orbit due to its light weight and easy integration. The remainder of this paper is organized as follows. In Section 2, the FWMB process is proposed. In Section 3, the experiment platform in the laboratory is introduced. In Section 4, the conducted experiments are described in order to demonstrate the performance of the FWMB algorithm. The conclusions are presented in Section 5.
# Minimum-Energy Scheduling of Flexible Job-Shop Through Optimization and Comprehensive Heuristic
## 2 The Considered Class of Flexible Job Shops and Their Representation
### Absolute Time Bounds  
In this subsection, lower bounds for the earliest start times and upper bounds for the latest start times of the operations of each job for a given machine assignment \(j\) are introduced:  
* \(est_{\bar{i}\bar{j}}\) is the earliest start time of operation \(O_{ik}\) with machine assignment \(A_{\bar{i}\bar{j}}\) when the release time is respected.
* \(lst_{\bar{i}\bar{j}\bar{i}}\) is the latest start time of operation \(O_{ik}\) with machine assignment \(A_{\bar{i}\bar{j}}\) when the due time is respected. We have the following for job \(i\) with machine assignment \(A_{\bar{i}\bar{j}}\): \[est_{\bar{i}\bar{j}}=rt_{i}\ \text{and}\ est_{\bar{i}\bar{j}}=est_{\bar{i}\bar{ k}-1\bar{j}}\ +\max_{h\in\Gamma_{ik}^{-1}}\Big{\{}est_{\bar{i}\bar{j}}+d_{\bar{i}\bar{j}}+T_{ \bar{i}\bar{i}\bar{k}\bar{j}}\Big{\}},k=2\ \text{to}\ S_{i}\] (3) \[lst_{\bar{i}\bar{j}\bar{i}}=dt_{i}-d_{\bar{i}\bar{S}_{i}}\ \text{and}\ lst_{\bar{i}\bar{j}}=\min_{h\in\Gamma_{ik}}\Big{\{} lst_{\bar{i}\bar{j}\bar{i}\bar{j}}-T_{\bar{i}\bar{i}\bar{k}\bar{j}}\Big{\}}-d_{ \bar{i}\bar{k}\bar{j}},k=S_{i}-1\ \text{to}\ 1\] (4) where \(rt_{i}\) and \(dt_{i}\) are, respectively, the release time and the due time of job \(i\).  
It can be observed that these earliest and latest start times do not consider the possible concurrent use of the machines by different jobs and the resulting additional delays, so they are, respectively, a lower bound for the earliest start time and an upper bound of the latest start times. Consistency conditions for the time data are  
\[est_{ikj}\leq lst_{ikj},\quad i=1\text{ to }n,\;k=1\text{ to }S_{i},\;j=1\text{ to }|A_{i}| \tag{5}\]  
\[lst_{i1j}-d_{i1j}\geq rt_{i}\quad\text{and}\quad est_{iS_{i1j}}+d_{iS_{i}j} \leq dt_{i}\qquad i=1\text{ to }n,\;j=1\text{ to }|A_{i}| \tag{6}\]  
If a machine assignment \(j\) for job \(i\) does not satisfy fully relations (5) and (6), it must be eliminated from \(A_{i}\).  
It is also possible to compute the absolute earliest start time for each operation of each job:  
\[Est_{ik}=\min_{j\in A_{i}}\Bigl{\{}est_{ikj}\Bigr{\}}\;\;\;i=1\text{ to }n,\;k=1\text{ to }S_{i} \tag{7}\]  
It can be observed here that the release time and the due times are not, in general, of the same nature: the release times are independent of the considered process and result from upstream logistics; the due times result from downstream logistics. Then, here, release times are hard constraints, while due times can be a production objective that may not be completely achieved. Thus, the latest starting times and due times constraints can be violated, and the resulting delays characterize a deficit in the production capacity of the job shop to process a given production plan.
## 3 Path Model Design
### Obstacle--Reluctant Path  
In a realtime environment, obstacles may be found in the experimental area that may prevent radio contact between the mobile anchor node and other sensor nodes. In [12], the mobile anchor node turns around the obstacle and propagates the messages sent to the unknown nodes with a detour flag. The unknown sensor nodes calculate their positions using the information in the messages that contain a detour flag to compute the virtual mobile anchor node positions paused at to turn around the obstacle. When the mobile node walks away from the obstacle, it returns back to the main path and resumes propagating the mobile node normal messages.  
In [34], the mobile node can find out any anonymous obstacle once it existed in the communication range. The R-Curve and Arrow-Curve are static and deterministic paths, the path pattern and the mobile node pausing points are fixed so the mobile node knows the position of the obstacles and can resume its path after it moves away from the obstacle. The R-Curve and Arrow-Curve obstacle-reluctant path is introduced to resolve the obstacle problem in the real environment to improve R-Curve and Arrow-Curve path pattern at the presence of an obstacle.  
We define an obstacle mode as illustrated in Figure 9, where the mobile node firstly moves on the path trajectory. Then, when and if it detects an obstacle in its trajectory, it first broadcasts the arriving point S, then the mobile node switches on the obstacle mode. It starts to broadcast messages containing its position s\({}_{0}\), s\({}_{1}\) with a detour flag for each detour to inform the sensor nodes that it is turning around an obstacle. When the anchor node crosses the obstacle, it switches back to the normal mode and returns to the original path. Once it reaches the departure position s\({}^{\prime}\), it starts to broadcast messages containing s\({}^{\prime}\). R-Curve and Arrow-Curve obstacle-reluctant paths are illustrated in Figure 11; Figure 12. The green blocks illustrate the obstacles and the orange lines illustrate the path around the obstacle.  
Figure 9: (a) R-Curve obstacle existence; (b) Arrow-Curve obstacle existence.
# TKEO-Enhanced Machine Learning for Classification of Bearing Faults in Predictive Maintenance
## 5 Discussion  
### Ease of Implementation  
In this study, the data preprocessing steps included data normalization (centering and standardization) and splitting the data into training and testing sets. The CWRU bearing signals were relatively clean; so, they could be processed without additional noise filtering. However, to further test the model's robustness, we introduced white noise and applied singular spectrum analysis (SSA) [27], which effectively extracted significant components from the time series, revealing the underlying structure and patterns in the signal.  
For hyperparameter tuning, we used GridSearchCV1.3.0, which exhaustively searched through all possible combinations of parameters to find the optimal model configuration. To speed up this process, RandomizedSearchCV was employed; parameter combinations were randomly sampled to find an approximate optimal range, thus reducing computation time.  
All experiments were conducted using the scikit-learn library, which provided comprehensive and mature support for the machine learning algorithms, making the implementation of the experiments more straightforward.  
SVCs require strict normalization of the data, and the selection of hyperparameters is relatively complex. In contrast, RFCs do not have strict requirements regarding data distribution and they also possess built-in processing capabilities, making them easier to implement. Additionally, RFCs have fewer hyperparameters, which makes them suitable for quick implementation.
## 4 Validation and Comparison of Analytical Methods
### Comparison of Calculation Time  
In order to compare the computational time of each method, the computational time of each step is listed in Table 3. The calculation process of each method is completed on a Windows 7 system, 64-bit, Intel (R) Xeon (R) 2x2.4 GHz, 32 GB memory workstation. Because the emphasis is on computing time, the modeling time is not included. The calculation process of each method can be roughly divided into the following five steps:  
* Numerical solution of external flow field: including the compressible and incompressible steady-state and transient numerical calculation, obtaining the fluctuating pressure data of the side mirror (CGNS or CASE format). Because the discrete N-S equation needs to be solved and the mesh size is required, this process has the longest calculation period.
* Read the FSP data file and its Fourier transform.
* Extract the convective component.
* Extract the acoustic component.
* Calculate the radiated SPL.  
In Table 3, for the simulation of incompressible flow field, the BEM method is often used to extract the acoustic component, so the time of extracting the acoustic component is the same. For the simulation of compressible flow field, the FSP contains the acoustic component, so it is not necessary to extract the acoustic component.  
In Table 3, it can be seen that the simulation time of the compressible flow field is 16 days, which is three times longer than that of the incompressible calculation. The object of this paper is the idealized side mirror model, which is simple. If the more complex surface of the automobile body is considered, the calculation time will be much longer. Although the method of obtaining the random modal force by the WFS method in the compressible numerical simulation is closer to the experimental result, its calculation time is much longer. However, the method of incompressible random modal force coupling BEM method is more balanced in calculation time and accuracy. Therefore, the method of incompressible random modal force coupling BEM method can be used to calculate the interior radiated noise SPL at high speed. At different stages of automobile development, an appropriate method can be selected for different purposes.
## 3 Methodology
### Post-Processing
#### 3.4.5 Maximum Height Value Extraction  
Following outlier removal, we extracted the maximum height values within each 50-m grid by focusing on PS points exhibiting the highest elevations. This selective aggregation allowed us to accurately determine building heights and effectively manage the varied distribution of PS points, ensuring our height estimations reflect actual vertical growth within each grid.
## 3 Numerical Analysis
### Tilt Angle Monitoring
extent, the gravity stiffness of the inverted pendulum exceeds the elastic stiffness of the pivot, and the small angle approximation condition after gravity acceleration coupling is no longer satisfied. The amplification angle and the total stiffness will increase rapidly according to an exponential law. Because \(mgL_{cm}\sin(\theta+\varphi)\approx k\theta\) is a transcendental equation, it is difficult to solve analytically. Numerical simulation analysis can be used to obtain suitable design parameters. For this purpose, Simscape Multibody can also be used for simulation to model the structure, dimensions, and weight of the inverted pendulum on a 1:1 scale. Here, assuming a reference tilt of 1 mrad for the inverted pendulum, different masses of counterweights are used, and the stabilized angle is observed. The data are then fitted using a binomial exponential function, as shown in Figure 8. By considering the maximum deflection angle that the bearing can withstand, an appropriate mass of counterweight (e.g., 180-190 g) can be found to achieve an amplification factor of around 10.
## 4 Discussion
### Validation of Diffuse Reflectance PLSR Model  
The accuracy of the diffuse reflectance spectral model was validated using an independent validation set, with the results detailed in Table 11. This validation set included 40 samples with SSC values ranging from 4.85 to 16.50 \({}^{\circ}\)Brix, an average SSC of 8.24 \({}^{\circ}\)Brix, and a standard deviation of 4.57 \({}^{\circ}\)Brix.  
The validation results demonstrated that the model exhibited good adaptability across a broad SSC range. Initially, the PLSR model constructed from the diffuse reflectance spectral data achieved coefficients of determination of \(R_{C}^{2}\) = 0.96 for the calibration set and \(R_{p}^{2}\) = 0.97 for the prediction set. The RMSEC and RMSEP were 0.54 and 0.74 \({}^{\circ}\)Brix, respectively. These results indicated that the model demonstrated high accuracy and low error even at the initial stage.  
To further enhance model performance, the CARS method was employed for feature wavelength selection. As detailed in Table 12, the optimized model exhibited significant improvements. The coefficients of determination increased to \(R_{C}^{2}\) = 0.98 for the calibration set and \(R_{p}^{2}\) = 0.98 for the prediction set. Additionally, the RMSE values were notably reduced, with RMSEC decreasing to 0.40 \({}^{\circ}\)Brix and RMSEP to 0.66 \({}^{\circ}\)Brix.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Processing** & **LVs** & \(R_{C}^{2}\) & \(R_{p}^{2}\) & \
\begin{tabular}{c} **RMSEC** \\ (\({}^{\circ}\)Brix) \\ \end{tabular} &
\begin{tabular}{c} **RMSEP** \\ (\({}^{\circ}\)Brix) \\ \end{tabular} \\ \hline MSC & 10 & 0.99 & 0.94 & 0.98 & 1.00 \\ MSC + CARS & 9 & 0.98 & 0.95 & 0.61 & 0.93 \\ \hline \hline \end{tabular}
\end{table}
Table 10: Diffuse transmittance independent validation set PLSR model construction.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Sample Sets** & \begin{tabular}{c} **No. of** \\ **Samples** \\ \end{tabular} & \begin{tabular}{c} **Min.** \\ **(\({}^{\circ}\)Brix)** \\ \end{tabular} & \begin{tabular}{c} **Max.** \\ **(\({}^{\circ}\)Brix)** \\ \end{tabular} & \
\begin{tabular}{c} **Mean** \\ **(\({}^{\circ}\)Brix)** \\ \end{tabular} &
\begin{tabular}{c} **STD.** \\ **(\({}^{\circ}\)Brix)** \\ \end{tabular} \\ \hline Whole sample & 141 & 5.00 & 16.50 & 8.15 & 2.89 \\ Validation set & 40 & 4.85 & 16.50 & 8.24 & 4.57 \\ \hline \hline \end{tabular}
\end{table}
Table 11: Diffuse reflectance prediction set and independent validation set SSC distribution.  
The application of CARS not only effectively reduced the computational load but also markedly improved both efficiency and accuracy. The enhanced performance of the optimized PLSR model in both the calibration and prediction sets emphasized its reliability and precision in practical applications. These results indicated that the model with CARS feature wavelength selection demonstrated exceptional performance and wide applicability in real-world scenarios.
# Secrecy Rate of Resource-Constrained Mobile Relay Model under Two-Way Wiretap Channel
## 2 Materials and Methods
### Local Optimal Solution to P1
#### 2.3.3 Local Optimal Solution of \(\mathbf{s}\)  
With \(\widehat{R}^{Ssc}\), \(\{\widehat{Z}_{mj,j}\}\), \(\{\widehat{t}_{m},\widehat{p}_{m},\widehat{q}_{m},\widehat{P}_{m},\widehat{Q}_ {m}\}\), which were derived in a previous section, the secrecy rate, the left-hand sides of Equations (13) and (14) with \(\mathbf{s}=\widehat{\mathbf{s}}\), can be written as  
\[\Phi(\widehat{\mathbf{s}}) =\widehat{R}^{Ssc}\] \[\Xi(\widehat{\mathbf{s}}) =\zeta(a)(\sum_{m=1}^{M}\sum_{j=1}^{M}\widehat{Z}_{mj,j}D_{mj})+ \sum_{m=1}^{M}\widehat{P}_{m} \tag{26}\] \[\Psi(\widehat{\mathbf{s}}) =\sum_{m=1}^{M}\widehat{Q}_{m}\]  
Therefore, problem P1 is re-written as  
\[\text{P3}: \max_{\mathbf{s}}\quad\Phi(\mathbf{s})\] \[\text{s.t.}\quad\Xi(\mathbf{s})\leq E \tag{27a}\] \[\Psi(\mathbf{s})\leq Q\] (27b) \[s_{1}=1,\quad s_{m}\in\{0,1\},\quad\forall m\geq 2 \tag{27c}\]  
To solve P3, an effective way is to apply the neighborhood search method (NSM) [19; 20; 21], which greatly reduces the amount of computation compared to an exhaustive search. The critical point of NSM is the idea of the neighborhood \(\mathcal{N}(\cdot)\). Taking \(\mathbf{s}^{(0)}=[1,0,\cdots,0]^{T}\), for example, the neighborhood \(\mathcal{N}(\mathbf{s}^{(0)})\) is  
\[\mathcal{N}(\mathbf{s}^{(0)})=\{\mathbf{s}\in\{0,1\}^{M}:||\mathbf{s}-\mathbf{ s}^{(0)}||_{0}\leq L,s_{1}=1  
of Algorithm 2 is dominated by \(O(X\cdot[(M-1)^{2}\cdot 2^{M-1}+(3M+1)^{3.5}])\), where \(X\) is the number of iterations.  
```
1:Repeat
2: Select a candidate \(\mathbf{s}^{\prime}\) from \(\mathcal{N}(\mathbf{s}^{(n)})\), where \(\mathcal{N}(\mathbf{s}^{(n)})\) is obtained through Algorithm 1.
3: Set \(\mathbf{s}=\mathbf{s}^{\prime}\), and solve P2 to obtain \(\Phi(\mathbf{s}^{\prime})\) (namely \(R^{\text{Scr}}\)).
4: If \(\Phi(\mathbf{s}^{\prime})\geq\Phi(\mathbf{s}^{(n)})\), update \(\mathbf{s}^{(n+1)}\leftarrow\mathbf{s}^{\prime}\) and \(n\gets n+1\).
5: Else go to step 2.
6:Until Convergence.
```  
**Algorithm 2** Proposed local optimal solution to P1