esa-sceva/satcom-chunk-collection huggingface dataset:
# A Novel Fast Parallel Batch Scheduling Algorithm for Solving the Independent Job Problem
## 6 Computational Experiments
### Comparison of 2-Approximation Algorithm (LIM) and CPLEX  
For the problem \(P[s_{j},p=p,p-batch_{l},K_{i}]\big{|}C_{\text{max}}\), minimizing the makespan with equal running times, arbitrary job sizes (which may exceed the processing power of certain batches), and different machine capacities should be the solution. The running time of jobs was set to a default value of 8. Then, the \(LB\) and \(UB\) are denoted as  
\[LB=8\]  
\[UB=n*8.\]  
Table 6 show the experimental results given by the CPLEX and the LIM algorithm for all the test suites. Column SQL-AVG (the average value of SQL) reports the average makespan obtained using the LIM algorithm. Compared with the CPLEX makespan, the LIM algorithm can obtain the efficient solution in only little running time (Column Run Times). Figure 3: Results of J1M1S1P1K1. (**a**) Comparison makespan of CPLEX and the 4.5-approximation algorithm with one-job-overfull batches and the 4.5-approximation algorithm with a feasible schedule. (**b**) Comparison makespan of the 4.5-approximation algorithm with one-job-overfull batches and \(9T/4\). (**c**) Comparison makespan of the 4.5-approximation algorithm with a feasible schedule and \(4.5T\). (**d**) Comparison running time of CPLEX and the 4.5-approximation algorithm with one-job-overfull batches and the 4.5-approximation algorithm with a feasible schedule. \begin{table}
\begin{tabular}{l c c c c c c c c c c c} \hline \hline \multicolumn{1}{c}{**Test Suite**} & \multicolumn{3}{c}{**CPLEX**} & \multicolumn{3}{c}{**SOL 1**} & \multicolumn{3}{c}{**SOL**} \\ \cline{2-13} \cline{5-13} \multicolumn{1}{c}{**Makespan**} & **GAP (\%)** & **Run Time (s)** & **Best** & **AVG** & **Worst** & **Run Time (s)** & **Best** & **AVG** & **Worst** & **Run Time (s)** \\ \hline JIMIS1 PIK1 & 24 & 0 & 0.25 & 16 & 18.82 & 24 & 0 & 24 & 31.84 & 48 & 0 \\ JIMIS21 PIK1 & 24 & 66.67 & 0.20 & 8 & 9.10 & 16 & 0 & 16 & 17.10 & 34 & 0 \\ JIMIS1 PIK1 & 40 & 13.93 & 3.11 & 24 & 38.27 & 56 & 0 & 44 & 66.20 & 88 & 0 \\ JIMIS21 PIK1 & 24 & 33.33 & 2.13 & 16 & 23.22 & 40 & 0 & 32 & 42.04 & 72 & 0 \\ JIMIS1 PIK1 & 80 & 87.06 & 1800 & 64 & 89.41 & 120 & 0 & 112 & 195.93 & 224 & 0 \\ JIMIS21 PIK1 & 64 & 87.5 & 38.34 & 40 & 61.96 & 96 & 0 & 72 & 109.96 & 160 & 0 \\ JIMIS1 PIK1 & 200 & 96 & 306.73 & 136 & 186.67 & 232 & 0 & 240 & 337.73 & 452 & 0 \\ JIMIS21 PIK1 & 144 & 95.83 & 1800 & 80 & 121.25 & 192 & 0 & 136 & 219.61 & 344 & 0 \\ JIMIS1 PIK1 & 412 & 98.59 & 1800 & 264 & 374.12 & 456 & 0 & 480 & 679.06 & 848 & 0 \\ JIMIS21 PIK1 & - & - & 1800 & 160 & 245.49 & 336 & 0 & 296 & 453.02 & 656 & 0 \\ JIMIS1 PIK1 & - & - & 1800 & 424 & 569.10 & 744 & 0 & 744 & 1031.37 & 1360 & 0 \\ JIMIS21 PIK1 & - & - & 1800 & 232 & 343.22 & 512 & 0 & 416 & 633.57 & 944 & 0 \\ \hline \hline \end{tabular}  
* Note: When run time is labeled as 0, it was less than \(10^{-2}\).  
\end{table} 
Table 6: Simulation results of CPLEX and the 2-approximation algorithm with one-job-overfull batches and a feasible schedule.
## 2 Numerical Model for Grout Permeability in Backfilling Layers
### Construction of the Numerical Model
The third step applies Boolean operations to remove particles while preserving the pores between them, resulting in a geometric model of the pores in the backfilling layer. The fourth step is to convert the obtained pore geometric model into a mesh, which will be used for the subsequent simulation in COMSOL. The generated mesh consists entirely of triangular elements, with a maximum mesh size of 0.02 m and a minimum mesh size of 5.6 \(\times\) 10\({}^{-5}\) m.  
In this study, two fluid materials, air and grout, were used. The relevant material parameters are shown in Table 1. The material parameters for air were set based on the physical properties under standard atmospheric pressure and a temperature of 20 \({}^{\circ}\)C, while  
Figure 3: Simulation of pea gravel consolidation. the material parameters for cement mortar were based on the experimental data of [PERSON] et al. (2015). All the pores are initially filled with air. A small portion of initial fluid elements is created near the entrance as the grout pipe, which is initially filled with grout. Since the model is annular, the azimuth angle can conveniently represent positional information. Therefore, in the following sections of this study, the position descriptions are expressed using the angle \(\alpha\). The values of \(\alpha\) corresponding to the grouting port are 30\({}^{\circ}\), 90\({}^{\circ}\), and 150\({}^{\circ}\), as shown in Figure 5a. Figure 5b shows the setup of the fluid boundary conditions. The boundary condition at the fluid outlet is set as a pressure boundary condition with the pressure value set to zero. Two boundary condition schemes are considered at the inlet:  
1. Pressure Boundary Condition: A fixed pressure is applied at the inlet. 2. Flow Velocity Boundary Condition: A constant flow velocity is applied at the inlet. Subsequently, the transient solver with default parameters was used to perform the simulation. The fluid exists only within the pores, with the particle boundaries set as impermeable and no-slip boundary conditions applied at the particle contours. As shown in Figure 5c, the generated porous medium model contains areas that are not connected to other regions, and these areas do not contribute to fluid exchange. Therefore, they are excluded from the model. \begin{table}
\begin{tabular}{c c c c} \hline
**Density of Air** & **Viscosity of Air** & **Density of Grout** & **Viscosity of Grout** \\ \hline
1.204 kg/m\({}^{3}\) & 1.81 \(\times\) 10\({}^{-5}\) Pa\(\cdot\)s & 1500 kg/m\({}^{3}\) & 0.01 Pa\(\cdot\)s \\ \hline \end{tabular}
\end{table} 
Table 1: Calculation parameters. Figure 4: Generation process of the porous media model.
## 4 Intraday MPC Rolling Optimization
### Rolling Optimization  
The core principle of MPC resides in implementing a rolling optimization strategy. This strategy involves solving an optimization problem over the prediction horizon at each time step to determine an optimal sequence of control actions. However, only the first control action from this sequence is applied to the system. Subsequently, the optimization is repeated in the next time step, incorporating real-time feedback on the system's state to update the control plan. The specific mathematical model for this rolling optimization process is formulated as follows:  
(1) Upper-Layer Model  
The upper-layer model involves four types of energy: heating, cooling, gas, and hydrogen. The state variable \(x_{\text{up}}\) and control variable \(u_{\text{up}}\) are represented as follows:  
\[x_{\text{up}}=\begin{bmatrix}H_{\text{chp}},H_{\text{hfc}},H_{\text{ac}},C_{ \text{ecc}},C_{\text{ac}},H_{\text{hs,dis}},H_{\text{hs,chr}},S_{\text{h}},G_{ \text{grid}},\\ G_{\text{mr}},G_{\text{chp}},T_{\text{chp}},T_{\text{el}},T_{\text{mr}},T_{ \text{hfc}},T_{\text{ts,dis}},T_{\text{ts,chr}},S_{\text{t}}\end{bmatrix}^{ \text{T}} \tag{35}\]  
\[u_{\text{up}}=\begin{bmatrix}\Delta H_{\text{chp}},\Delta H_{\text{hfc}}, \Delta H_{\text{ac}},\Delta C_{\text{ec}},\Delta C_{\text{ac}},\Delta H_{ \text{hs,dis}},\\ \Delta H_{\text{hs,chr}},\Delta S_{\text{h}},\Delta G_{\text{grid}},\Delta G_{ \text{mr}},\Delta G_{\text{chp}},\Delta T_{\text{chp}},\\ \Delta T_{\text{el}},\Delta T_{\text{mr}},\Delta T_{\text{hfc}},\Delta T_{ \text{ts,chr}},\Delta S_{\text{t}}\end{bmatrix}^{\text{T}} \tag{36}\]  
They also satisfy the state-space Equation (34) in the prediction model. Thus, the standard form of the objective function for the upper-layer MPC optimization model can be established as follows:  
\[\min\sum_{i=1}^{M}\Bigl{(}\|x_{\text{up}}(t+i|t)-x_{\text{ref}}(t+i)\|_{Q_{ \text{up}}}^{2}+\|u_{\text{up}}(t+i|t)\|_{R_{\text{up}}}^{2}\Bigr{)} \tag{37}\]  
where \(M\) is the prediction horizon length, \(x_{\text{up}}(t+i|t)\) is the predicted value of the upper-layer state variable at time \(t+i\) given information at time \(t\), and \(u_{\text{up}}(t+i|t)\) is the control variable relative to the time \(t+i\) given information at time \(t_{\text{up}}\). The tracking term, denoted by \(\|x-x_{\text{ref}}\|_{Q}^{2}\), minimizes the deviation of state variables from the day-ahead reference schedule, ensuring operational continuity across time steps. The regulation term, expressed as \(\|u\|_{R}^{2}\), penalizes the magnitude of control adjustments to prevent aggressive fluctuations and safeguard the operational stability of energy conversion devices.  
The constraints mainly include range constraints on state variables, internal coupling constraints, energy storage constraints, and balance constraints. These are expressed as follows:  
\[s.t.\begin{cases}x_{\text{up,min}}\leq x_{\text{up}}(t)\leq x_{\text{up,max}} \\ u_{\text{up,min}}\leq u_{\text{up}}(t)\leq u_{\text{up,max}}\\ \text{Equations \eqref{eq:
## 3 The Dynamic Harmonic Compensation Sliding Mode Control Method
### Parameter Design of the Proportional Resonant Filter
By substituting the motor parameters \(L_{q}=2.45\) mH and \(R_{s}=1.6\)\(\Omega\) into Equation (20) and selecting a gain value \(k_{s}=400\), the Bode plot of the system is obtained, as shown in Figure 5.  
Figure 4: Bode plot of the quasi-proportional-resonant controller with \(k_{p}=0.1\), \(k_{r}=80\), and \(w_{c}=2\,\mathrm{rad/s}\). Figure 3: Bode plot of the quasi-proportional-resonant controller with different parameter values. As shown in Figure 5, the system exhibits high gain at the resonant frequency while displaying significant gain attenuation at non-resonant frequencies. This result demonstrates the effectiveness of the proposed method in suppressing harmonic disturbances at the resonant frequency. The system maintains a narrow gain bandwidth at the resonant frequency point, allowing for more precise selection of response frequencies, enhancing robustness to frequency variations, and thereby improving overall system stability. Additionally, the appropriate proportional coefficient increases the gain across the entire frequency range, accelerating the dynamic response speed of the system. Therefore, the selection of these parameters effectively balances the filtering performance and dynamic performance of the system.
## 3 Models
### Equally Spaced Obstacles Model
#### 3.2.2 Lattice-Based Surrogate Model  
Figure 4 illustrates the construction of the 2D lattice-based surrogate model for the equally spaced obstacles case (Figure 2(a)). A periodic extension of the RVE is shown, with a primary transition from the center subdomain illustrated. Due to extensive symmetries in this case, all internal transitions across boundary walls between subdomains are equivalent. The probability of diagonal transitions is zero due to the presence of obstacles at the subdomain corners. Hence, the lattice model has only two distinct transition probabilities, that the particle (1) stays in its current subdomain (\(p_{1}^{\text{E}}\)) or (2) moves to a neighboring subdomain in a cardinal direction (\(p_{2}^{\text{E}}\)). The corresponding state transitions are illustrated for subdomain 5 in Figure 3(b). Since transition probabilities within a subdomain must sum to 1, only one surrogate model probability needs to be calculated from the results of continuous model simulations.  
Figure 3: Sample domains (RVEs) for continuous model simulations (\(R_{\text{part}}=1.0\)), with numbered subdomains: (**a**) equally spaced obstacles model (with \(R_{\text{obs}}=2.0\)); (**b**) multisize obstacles model (with \(R_{\text{obs}_{1}}=1.0\) and \(R_{\text{obs}_{2}}=2.0\)). Obstacles are shown as black circles and the particle undergoing random walks is shown as a red circle.  
Results of the continuous model simulations (Figure 4a) are tracked via the time course \(\eta(t_{k})\ (t_{k}=k\Delta t,\ k=0,\ldots,N)\), where \(N\) is the total number of time steps. \(\eta(t_{k})\) records the state of a particle as the index of the \(i\)th subdomain \((i=1,\ldots,9)\) at time \(t_{k}\) if its center is located in that subdomain at time \(t_{k}\). A \(9\times 9\) matrix \(S^{(k)}\) is used to track all transitions (including remaining in the same subdomain) up to the current time step (\(S^{(0)}\) is the zero matrix). \(S^{(k)}\) is updated according to the formula  
\[S^{(k)}(\eta(t_{k-1}),\eta(t_{k}))=S^{(k-1)}(\eta(t_{k-1}),\eta(t_{k}))+1,\ \ k=1, \ldots N. \tag{12}\]  
\(S^{(k)}\) is then used to build a vector \(\vec{p}^{E}\) of transition probabilities. Within each time step, a vector \(\vec{T}^{E}_{i}\ (i=1,\ldots,9)\) is created to count transitions that occurred for each subdomain. In particular, the rows of \(S^{(k)}\) are used to create vector \(\vec{T}^{E}_{i}\) by grouping transition sums by transition type; since the equally spaced obstacles model has two transition types, \(\vec{T}^{E}_{i}\) has dimensions of \(1\times 2\). At the current time \(t_{k}\), we construct \(\vec{T}^{E}_{i}\) from \(S^{(k)}\) as follows,  
\[\vec{T}^{E}_{i}=\left[S^{(k)}(i,i),\ \ \sum_{\{j\
eq i\}}S^{(k)}(i,j)\right],\ \ i=1, \ldots,9. \tag{13}\]  
Due to the symmetries in the equally spaced obstacles case, we create the transition probability vector \(\vec{p}^{E}\) via the average:  
\[\vec{p}^{E}=\frac{1}{N}\sum_{i=1}^{N}\vec{T}^{E}_{i}. \tag{14}\]
## 3 Incremental Launching Construction and Monitoring Technology
### Alignment Control  
Alignment control is an important part of the bridge incremental launching construction process. In this project, the alignment of the ramp guide girder and the arrangement of the incremental launching piers are consistent with the alignment of the steel box girder. Considering that the alignment of the steel box girder in this project is on a curve with a radius of 230 m, the actual alignment deviation is too large. It will cause secondary stress when the bearing is disengaged, which will cause irreversible collapse and overturning throughout the incremental launching construction, cause uneven stress between the pier and the steel box girder, and reduce the service life of the bridge. Therefore, in splicing within construction, it is necessary to control the actual alignment to ensure that it is basically consistent with the theoretical alignment. Considering the influence of welding, summer temperature, construction environment, and other aspects in practical engineering, deviation in alignment cannot be avoided. A Nikon XS total station (manufactured by Nikon Corporation in Tokyo, Japan) is used to collect alignment data in the process of incremental launching in real time and then adjust the actual alignment according to that data.  
Figure 4: Central isolation belt emergency temporary pier.  
Figure 3: Assembly support and Nikon XS total station.  
Alignment control includes horizontal alignment control and vertical alignment control. Horizontal alignment control is adjusted by rectification measures during incremental launching, and vertical alignment is adjusted by the coordination of the total station and the incremental launching rectification device. By arranging the prism elevation control points on the top of the steel box girder, the actual alignment of the steel box girder is obtained according to the measured elevation data.  
In order to carry out total station observation, four displacement reference points are set up at the front end and the back end of the steel box girder. The incremental launching trajectory of the steel box girder is plotted with AutoCAD. According to the four displacement measuring points on the upper part of the steel box girder, horizontal alignment control of incremental launching is carried out to advance along the incremental launching trajectory. The incremental launching trajectory of the whole section of the steel box girder is illustrated in Figure 5.  
The incremental launching displacement control steps are as follows:  
(1) When carrying out incremental launching on each one-meter section, the lateral movement of the control point is tracked in real time;  
(2) Comparing the calculated displacement with the monitored displacement;  
(3) Using the correction function of the incremental launching equipment to correct the deviation.
# Fast-RRT: A RRT-Based Optimal Path Finding Method
## 2 Background
### Problem Definition  
Two issues of motion planning, including the feasible solution and the optimal problems, is be discussed and defined in a similar way to [26].  
Let \(X\in\mathbb{R}^{n}\) be the state space of the planning problem, where \(n\in\mathbb{N}\) is the dimension of the motion planning problem. \(X_{obs}\in X\) is the obstacle space, which cannot be reached due to the collision with obstacles. \(X_{free}=X/X_{obs}\) represents the free state space. \(x_{init}\in X_{free}\) and \(x_{goal}\in X_{free}\) are the initial state and the goal state, respectively, and \(X_{goal}=\left\{x\in X\big{|}\|x-x_{goal}\|<r\right\}\) is the goal region. A feasible path is defined as a path \(\sigma:[0:T]\to X_{free}\) such that \(\sigma(0)=x_{init}\) and \(\sigma(T)\in X_{goal}\).  
The feasible problem of motion planning is to find a feasible path if one exists; otherwise, it should report failure. Problem 1 defines the feasibility problem of path planning.  
**Problem 1 (Feasible Path Planning)** Given a state space of planning problem \(X\in\mathbb{R}^{n}\), a free space \(X_{free}\), an initial state \(x_{init}\) and a goal region \(X_{goal}\in X_{free}\), find a path \(\sigma:[0:T]\to X_{free}\) such that \(\sigma(0)=x_{init}\) and \(\sigma(T)\in X_{goal}\), if one exists. If no feasible path exists, then report failure.  
Path cost is an important concept in motion planning. By defining the cost function, a feasible path is assigned a non-negative cost. The optimal problem of motion planning is to find a path with minimal cost. Problem 2 formalizes the optimal problem of motion planning.  
**Problem 2 (Optimal Path Planning)** Given a state space \(X\in\mathbb{R}^{n}\), a free state space \(X_{free}\), an initial state \(x_{init}\) and a goal region \(X_{goal}\in X_{free}\), if a solution to problem1 exists, find a path \(\sigma:[0:T]\to X_{free}\) such that \(\sigma(0)=x_{init}\), and \(\sigma(T)\in X_{goal}\) and \(c(\sigma^{*})=min_{\sigma\in\sum_{f/n}c(\sigma)}\).  
The path-find algorithm based on sampling is a time-consuming process refereed to find an optimal path. Therefore, a near-optimal path is usually obtained through a certain number of iterations. The near-optimal problem refers to finding a path where the difference of cost and the optimal path is less than the threshold. Problem 3 formalizes the near-optimal problem of motion planning.  
**Problem 3 (Near-Optimal Path Planning)** Given a state space \(X\in\mathbb{R}^{n}\), a free state space \(X_{free}\), an initial state \(x_{init}\) and a goal region \(X_{goal}\in X_{free}\), if a solution to problem 1 exists, and \(\sigma^{*}\) is the solution to Problem 2, find a path \(\sigma:[0:T]\to X_{free}\) such that \(\sigma(0)=x_{init}\), and \(\sigma(T)\in X_{goal}\) and \(c(\sigma)<c(\sigma^{*})*(1+threshold)\).
# Power Control and Channel Allocation Algorithm for Energy Harvesting D2D Communications
## 1 Introduction
In [12], energy harvesting enabled D2D users to act as relays operating in a half-duplex mode to enhance the data transmissions of other D2D users, and D2D relays were unable to harvest energy and transmit data simultaneously; the energy harvesting time and transmission power of relays are optimized to maximize the D2D users' throughput. In [13], D2D users harvest energy from a power station and transmit information signals simultaneously, and the sum throughput is maximized via joint time scheduling and power control. Literature [11; 12; 13] assumes that the energy harvesting time of different D2D user is same, but in fact the energy harvesting time of multiple D2D transmitters is different because the distance between D2D transmitter and BS, the distance between D2D user pair are different. In this paper, we consider that D2D transmitter can harvest energy by wireless power transfer, while the energy harvesting time of the different D2D users is different, multiple D2D users can reuse the same channel. The contributions of this paper are summarized as follows:  
1. The optimization problem of joint power control and channel allocation is constructed by considering the constraints of harvesting energy on transmission power, QoS (Quality of Service) of cellular users and channel multiplexing, so as to maximize the total capacity of D2D users. The original mixed integer nonlinear problem is transformed into a convex optimization problem by variable substitution and fractional programming. 2. The optimal joint power control and channel allocation algorithm is proposed. The optimal transmission power and energy harvesting time of D2D users are determined by the joint iterative method. The KM algorithm is used to complete the optimal matching between D2D users and cellular users' channel. 3. The simulation results of the proposed algorithm are provided to verify the effectiveness of the proposed resource allocation algorithm. The system performance of the proposed algorithm in terms of D2D users' total capacity is compared with the algorithm in [13] and equal time allocation (ETA) methods. The simulation results show that the proposed algorithm can effectively improve the system performance. The rest of this paper is organized as follows. We describe the system model of D2D communication based on energy harvesting in Section 2. Then, in Section 3, the proposed optimal joint power control and channel allocation algorithm is investigated. Simulation results are provided and analyzed in Section 4 to show the performance of the proposed algorithm. Finally, conclusions are drawn in Section 5.