Fast Solution Method Research Articles

Multi-objective two-level medical facility location problem and tabu search algorithm

The medical facility location problem has attracted increasing attention in recent years because the rational layout of medical facilities plays an important role in implementing the hierarchical diagnosis and treatment system in many countries. To promote the implementation of a hierarchical diagnosis and treatment system, a two-level medical facility location problem with multiple patient flows between demand points and medical facilities is studied in this paper. We use a direct interpretation of the two-level medical facility location problem as a multi-objective problem to effectively balance different conflicting objectives. Based on the multi-objective tabu search algorithm and the fast construction method of the Pareto non-dominated solution, we also propose a solution approach to yield a set of solutions that can represent the trade-offs among conflicting objectives. The applicability and validation of the presented model and performance of the proposed optimization approach are evaluated using a real case. The experimental results not only indicate that the proposed solution approach can effectively solve the two-level medical facility location problem, but also suggest that the presented model can provide significant results in determining locations for medical facilities.

Guest Editorial: Situational awareness of integrated energy systems

Guest Editorial: Situational awareness of integrated energy systems

Fast solution method and simulation for the 2D time-space fractional Black-Scholes equation governing European two-asset option pricing

Fast solution method and simulation for the 2D time-space fractional Black-Scholes equation governing European two-asset option pricing

Wind-Photovoltaic-Energy Storage System Collaborative Planning Strategy Considering the Morphological Evolution of the Transmission and Distribution Network

The collaborative planning of a wind-photovoltaic (PV)-energy storage system (ESS) is an effective means to reduce the carbon emission of system operation and improve the efficiency of resource collaborative utilization. In this paper, a wind-PV-ESS collaborative planning strategy considering the morphological evolution of the transmission and distribution network is proposed. Firstly, aiming at the optimal economy of transmission and distribution network and considering the constraints of safe and stable operation of the system, the planning model of the transmission network based on DC power flow and the planning model of the distribution network based on AC power flow are constructed. Further, considering the coupling interaction between the transmission and distribution networks, a collaborative planning model of transmission and distribution networks based on second-order cone relaxation (SOCR) is constructed. Secondly, in order to reduce the computational complexity of the model and ensure the global optimality of the model solution, a fast model solution method based on heterogeneous decomposition architecture is proposed. Thirdly, the multiple driving factors of the morphological evolution of transmission and distribution network are analyzed, the morphological evolution path and typical characteristics of transmission and distribution network are determined, and a wind-PV-ESS collaborative planning strategy considering the morphological evolution of a transmission and distribution network is proposed. Finally, the results show that, compared with the sprouting period, the overall economy of the development period and maturity period is improved by 3342 k$ and 5751 k$ respectively, and the effectiveness and necessity of the collaborative planning strategy proposed in this paper is verified.

Varying Condition SCOPF Optimization Based on Deep Learning and Knowledge Graph

Security-constrained optimal power flow (SCOPF) is a vital task for independent system operators (ISO) in daily scheduling. However, the large number of inequality constraints bring us big challenges to solve large-scale SCOPF in real time. This paper proposes a fast solution method for SCOPF by predicting active constraints based on machine learning approaches. Namely, deep neural networks (DNNs) are employed to predict active security constraints based on historical data, thus accelerating the SCOPF calculation. Active margin functions are proposed to quantify how likely these security constraints will be active, thus improving our prediction accuracy. Knowledge graph is adopted to record system working conditions, pertinent learning results and their relationship, thus improving the transferability of the learning model under varying operation conditions. Simulations have been done on IEEE 30-bus, 118-bus and 300-bus systems to demonstrate the effectiveness of the proposed DNN approach. The influence of artificial parameters and the effectiveness of the knowledge graph are also illustrated.

Fast Solution Method for the Kinematics of Wrist Offset Robot Oriented to Wheel Hub Grinding and Polishing

Fast Solution Method for the Kinematics of Wrist Offset Robot Oriented to Wheel Hub Grinding and Polishing

Fast Power Series Solution of Large 3-D Electrodynamic Integral Equation for PEC Scatterers

This paper presents a new fast power series solution method to solve the Hierarchal Method of Moment (MoM) matrix for a large complex, perfectly electric conducting (PEC) 3D structures. The proposed power series solution converges in just two (2) iterations which is faster than the conventional fast solver–based iterative solution. The method is purely algebraic in nature and, as such applicable to existing conventional methods. The method uses regular fast solver Hierarchal Matrix (H-Matrix) and can also be applied to Multilevel Fast Multipole Method Algorithm (MLFMA). In the proposed method, we use the scaling of the symmetric near-field matrix to develop a diagonally dominant overall matrix to enable a power series solution. Left and right block scaling coefficients are required for scaling near-field blocks to diagonal blocks using Schur’s complement method. However, only the right-hand scaling coefficients are computed for symmetric near-field matrix leading to saving of computation time and memory. Due to symmetric property, the left side-block scaling coefficients are just the transpose of the right-scaling blocks. Next, the near-field blocks are replaced by scaled near-field diagonal blocks. Now the scaled near-field blocks in combination with far-field and scaling coefficients are subjected to power series solution terminating after only two terms. As all the operations are performed on the near-field blocks, the complexity of scaling coefficient computation is retained as O(N)O⁢(N). The power series solution only involves the matrix-vector product of the far-field, scaling coefficients blocks, and inverse of scaled near-field blocks. Hence, the solution cost remains O(NlogN)O⁢(N⁢l⁢o⁢g⁢N). Several numerical results are presented to validate the efficiency and robustness of the proposed numerical method.

Efficient Method Based on SMW Formula for Analyzing PEC Targets with Partial and Thin Coatings

The analysis of the electromagnetic scattering from the perfect electric conductor (PEC) partially coated with thin material is a significant task in stealth design. Previous research has shown the scattering can be calculated by only discretizing the current on PEC in the case of thin coating layers. However, it has a downside that it will recalculate a complete solution when the geometry or electromagnetic properties of the coating changes. In this paper, a Sherman-Morrison-Woodbury (SMW) formula-based method is proposed to address this problem. According to the SMW formulation, it can reuse the inverse impedance matrix of the PEC part to efficiently obtain the solutions when local coating changes, so it can avoid the subsequent complete inverse of the new impedance matrix. Furthermore, it employs the fast direct solution method based on the SMW formulation to accelerate the calculation of inverse matrix of the PEC part. Numerical results demonstrate the performance of the proposed method.

A hybrid triangulation method for banded linear systems

We propose a fast solution method for banded linear systems that transforms the original system into an equivalent one with an almost block triangular coefficient matrix, and then constructs a preconditioner based on this formulation. We analyze the algorithmic complexity of the new method and the eigenvalue distribution of the resulting preconditioned matrix. Numerical examples involving block tridiagonal, block Hessenberg and block pentadiagonal systems are illustrated to demonstrate the computational performance and the efficiency of the new matrix solver.

Highly precise and efficient solution strategy for linear heat conduction and structural dynamics

AbstractTime‐dependent parabolic and hyperbolic equations are widely encountered in practical engineering. Accurate and fast solution methods for such equations have always attracted attention. To reach this aim, this article proposes a strategy to construct highly precise and efficient time integration methods (TIMs) for linear heat conduction and structural dynamic systems. In the proposed strategy, an integrated amplification matrix of a TIM is created to precisely transfer the free responses of the previous step, and the Gauss–Legendre quadrature is employed to precisely compute the forced responses of the current step. To reduce computational cost and rounding error, a 2m algorithm and a method of storing incremental matrix are applied in the construction of the integrated matrix. Moreover, the L‐stable backward difference formula for heat conduction and the generalized trapezoidal rule for structural dynamics, which is A‐stable and has controllable dissipation, are utilized to conduct this strategy. Numerical experiments validate that compared with some existing TIMs, the TIMs generated by the proposed strategy enjoy advantages both in precision and efficiency.

Production Analysis for Fractured Vertical Well in Coal Seam Reservoirs with Stimulated Reservoir Volume

The development and utilization of coalbed methane is of great significance to reduce carbon dioxide emission. Through the research, this paper presents a fast analytical solution method for the productivity of coalbed methane reservoir with finite-conductivity fractured well and stimulated reservoir volume region. Based on the dual-porosity flowing mechanism, combined with the Langmuir adsorb equation, Fick diffusion law, and Darcy law, a mathematical model considering diffusion in matrix and transport in natural fracture system is established, using spherical matrix to describe the transient steady-state sorption, and using cubic matrix to describe the pseudosteady-state sorption. Then, combined with the inner system and outer system, the analytical solution was obtained. Furthermore, the accuracy of the solution was validated against a numerical simulation. According to the Duhamel principle, the effect of wellbore storage and skin factor was got. Due to the SRV region, the linear flow and radial flow will appear before the pressure wave reach the outer region. And then, based on the pressure analysis result, we will have made the sensitivity analysis with different influence parameter. The result reveals that storage coefficient and conductivity factor mainly influence the early time; the permeability ratio and dimensionless SRV region radius mainly influence the property of SRV region. Finally, the analytical solution of the new model was applied to field history match. This model takes into account the adsorption and desorption characteristics of coalbed methane, as well as the SRV zones generated during fracturing. The calculation speed of the new model is increased while the calculation accuracy is retained, and the intensity of software application is reached. The model achieves the purpose of rapid evaluation and accurate prediction of gas well productivity and obtains a set of productivity evaluation method suitable for coalbed methane reservoir with fractured vertical well, which provides a basis for the development and productivity evaluation of coalbed methane reservoir in domestic and international cooperation.

A Generic GPU-Accelerated Framework for the Dial-A-Ride Problem

Accelerating the performance of optimization algorithms is crucial for many day-to-day applications. Mobility-on-demand is one such application that is transforming urban mobility by offering reliable and convenient on-demand door-to-door transportation at any time. Dial-a-ride problem (DARP) is an underlying optimization problem in the operational planning of mobility-on-demand systems. The primary objective of DARP is to design routes and schedules to serve passenger transportation requests with high-level user comfort. DARP often arises in dynamic real-world scenarios, where rapid route planning is essential. The traditional CPU-based algorithms are generally too slow to be useful in practice. Since customers expect quick response for their mobility requests, there has been a growing interest in fast solution methods. Therefore, in this paper, we introduce a GPU-based solution methodology for the dial-a-ride problem to produce good solutions in a short time. Specifically, we develop a GPU framework to accelerate time-critical neighborhood exploration of local search operations under the guidance of metaheuristics such as tabu search and variable neighborhood search. Besides, we propose device-oriented optimization strategies to enhance the utilization of a current-generation GPU architecture (Tesla P100). We report speedup achieved by our GPU approach when compared to its classical CPU counterpart, and the effect of each device optimization strategy on computational speedup. Results are based on standard test instances from the literature. Ultimately, the proposed GPU methodology generates better solutions in a short time when compared to the existing sequential approaches.

A High-precision and Fast Solution Method of Gamma Raindrop Size Distribution based on 0-Moment and 3-Moment in South China

AbstractAccording to the high accuracy linear shape-slope (μ-Λ) relationship observed by several 2-Dimensional-Video-Distrometers (2DVD) in South China, a high-precision and fast solution method of gamma (Γ) raindrop size distribution (RSD) function based on the zeroth order moment (M0) and the third order moment (M3) of RSD has been proposed. The 0-moment (M0) and 3-moment (M3) of RSD can be easily calculated from rain mass mixing ratio (Qr) and total number concentration (Ntr) simulated by the two-moment (2M) microphysical scheme, respectively. Three typical heavy rainfall processes and all RSD samples observed during 2019 in South China were selected to verify the accuracy of the method. Compared to the current widely used exponential RSD with a fixed shape parameter of zero in 2M microphysical scheme, the Γ RSD function using the linear constrained gamma (C-G) method agreed better with the Γ fit RSD from 2DVD observations. The characteristic precipitation parameters (e.g., rain rate, M2, M6 and M9) obtained by the proposed method are generally consistent with the parameters calculated by Γ fit RSD from 2DVD observations. The proposed method has effectively solved the problem that the shape parameter in the 2M microphysical scheme set to a constant, so that the Γ RSD functions are closer to the observations and have obviously smaller errors. This method has a good potential to be applied to the 2M microphysical schemes to improve the simulation of heavy precipitation in South China, but also paves the way for in-depth applications of radar data in numerical weather prediction models.

Accuracy and performance analysis for Bloch and Bloch-McConnell simulation methods

PurposeTo introduce new solution methods for the Bloch and Bloch-McConnell equations and compare them quantitatively to different known approaches. Theory and MethodsA new exact solution per time step is derived by means of eigenvalues and generalized eigenvectors. Fast numerical solution methods based on asymmetric and symmetric operator splitting, which are already known for the Bloch equations, are extended to the Bloch-McConnell equations. Those methods are compared to other numerical methods including spin domain, one-step and multi-step methods, and matrix exponential. Error metrics are introduced based on the exact solution method, which allows to assess the accuracy of each solution method quantitatively for arbitrary example data. ResultsAccuracy and performance properties for nine different solution methods are analyzed and compared in extensive numerical experiments including various examples for non-selective and slice-selective MR imaging applications. The accuracy of the methods heavily varies, in particular for short relaxation times and long pulse durations. ConclusionIn absence of relaxation effects, the numerical results confirm the rotation matrices approach as accurate and computationally efficient Bloch solution method. Otherwise, as well as for the Bloch-McConnell equations, symmetric operator splitting methods are recommended due to their excellent numerical accuracy paired with efficient run time.

A Fast Solution Method to Economic Dispatch Type Problem

Economic dispatch (ED) aims to minimize the generation cost subject to power balance constraints. It is extensively used in power system operation and planning. ED problem as well as other problems with the same formulation are named as ED-type problems in this letter and a fast solution method is provided. The proposed method is achieved by solving a series of relaxed problems. With a closed-form solution for the relaxed ED-type problems, it is demonstrated that the proposed method consumes far less computing time and memory space than the off-the-shelf solvers and other quadratic programming (QP) methods. Finally, the effectiveness and computational efficiency of the proposed method are verified by the case studies, which shows the great potential in power system planning and operation.

Fast solution method to prepare hexagonal tellurium nanosheets for optoelectronic and ultrafast photonic applications

High-quality hexagonal Te nanosheets were prepared by a unique solution method and exhibited good optoelectronic and ultrafast photonic properties.

Enhancing the stabilization of nanostructured rocksalt-like high entropy oxide by Gd addition

In this work, nanostructured single phase high entropy oxide was easily synthesized by a fast polymeric solution method. Despite the higher ionic radius, coordination and oxidation state, gadolinium was homogeneously distributed in crystallites. Their effect on the lattice was studied by Raman spectroscopy, transmission electron microscopy and X-ray diffraction. The configurational entropy increased with the addition of Gd3+, but the expansion in the lattice is mostly associated to the diffusion of copper to the crystal. However, gadolinium enhances the asymmetry on longitudinal-optic (A1g) Raman mode and also prevents the excessive growth of crystallites.

Research on the Fast Solution Method of Pilots’ Head Attitude

Aiming at the problem of poor accuracy and poor real-time performance in the process of head pose calculation in pilot cabin simulation, a high accuracy and fast algorithm for head pose calculation is proposed. On the basis of traditional EPNP algorithm was improved, and combining with POSIT algorithm’s speed advantage, select face five key feature points as virtual control points, according to the mapping relationship between space and virtual control point coordinates, establish a system of linear equations, then the internal camera parameters is calculated using Zhengyou Zhang camera calibration method, finally using POSIT algorithm of calculating to get the head rotation matrix and translation vector, by conversion from the head of Euler angle in real time. The experimental results show that compared with DLT, EPNP, POSIT and other traditional methods, the proposed method has higher accuracy, better real-time performance and better robustness in solving pilots’ head attitude in continuous video.

An Overview of Methods and a New Three-Dimensional FEA and Analytical Hybrid Technique for Calculating AC Winding Losses in PM Machines

This article proposes a new hybrid analytical and numerical finite element (FE) based method for calculating ac eddy current losses in wire windings and demonstrates its applicability for axial flux permanent magnet electric machines. The method takes into account three-dimensional (3-D) field effects in order to achieve accurate results and yet greatly reduce computational efforts. The new 3-D FE-based method is advantageous as it employs minimum simplifications and considers the end turns in the eddy current path, the magnetic flux density variation along the effective length of coils, and the field fringing and leakage, which ultimately increases the accuracy of simulations. This study is one of the first ones to compare meticulous 3-D finite element analysis (FEA) models with more approximate, but faster solution methods, which can be employed in the optimization process. The accuracy of the 3-D FEA calculations has been confirmed through tests on a prototype axial flux permanent magnet machine. The proposed method is applicable for cases with majority of ac copper losses induced due to external magnetic flux sources, such as permanent magnets. Examples of such machines designs are coreless or open slot PM machines with conductors sizes smaller than skin depth.

Tensor product method for fast solution of optimal control problems with fractional multidimensional Laplacian in constraints

We introduce the tensor numerical method for solution of the d-dimensional optimal control problems (d=2,3) with spectral fractional Laplacian type operators in constraints discretized on large n⊗d tensor-product Cartesian grids. The approach is based on the rank-structured approximation of the matrix valued functions of the corresponding fractional finite difference Laplacian. We solve the equation for the control function, where the system matrix includes the sum of the spectral fractional d-dimensional Laplacian and its inverse. The matrix valued functions of discrete Laplace operator on a tensor grid are diagonalized by using the fast Fourier transform (FFT). Then the low rank approximation of the d-dimensional tensors obtained by folding of the corresponding large diagonal matrices of eigenvalues are computed, which allows to solve the governing equation for the control function in a tensor-structured format. The existence of low rank canonical approximation to the class of matrix valued functions involved is justified by using the sinc quadrature approximation method applied to the Laplace transform of the generating function. The linear system of equations for the control function is solved by the PCG iterative method with the rank truncation at each iteration step, where the low Kronecker rank preconditioner is pre-computed. The right-hand side, the solution vector, and the governing system matrix are maintained in the rank-structured tensor format which beneficially reduces the numerical cost to O(nlog⁡n), outperforming the standard FFT based methods of complexity O(n3log⁡n) for 3D case. Numerical tests for the 2D and 3D control problems confirm the linear complexity scaling of the method in the univariate grid size n.