An efficient implementation of parallel simulated annealing algorithm in GPUs

Summary The Simulated Annealing (SA) algorithm has been widely used in geophysical data processing. However, the seri al SA algorithm is limited by low computing efficiency. In this paper, the annealing schedule has been improved in the SA algorithm, and a constrained inversion of magnetotelluric (MT) data using the parallel SA algorithm has been applied. The test of synthetic data shows that the improved Very Fast Simulated Annealing (VFSA) method is significantly better than the traditional method. Additionally, the computing efficiency has been improved using the parallel SA inversion algorithm. This method has also been applied in MT data processing for geothermal exploration and good geological results have been achieved.

A combined strategy of an improved simulated annealing (SA) algorithm and genetic algorithm is presented, with the goal of reducing the computational expenses. The improvements made on the SA algorithm include two parts, i.e., the adaptive regulating for the step vector, and the dynamic testing for the equilibrium of the Metropolis process. The proposed strategy has both the advantage of SA algorithm, the ability to avoid being trapped in a local optimum, and that of genetic algorithm, the ability to use the information about the searched states for the next iteration. A practical application on geometry optimization of pole shoes in large salient pole synchronous generators is effectively implemented using the strategy. The numerical results show that the number of iterations used by executing the combined strategy are only about 75% of those by executing basic SA algorithm.

Based on the principle of QR loop iterations, this paper implements a parallel algorithm based on the hardware of GPU (Graphic Process Unit) by using routines from CUDA (Computer Unified Device Architecture) to find the eigenvalues of general matrices. CPU and GPU computing card form a client-server computing framework. Here, CPU can be regarded as a client and GPU card is considered as a computing server. For the experiment environment, this paper chooses a GPU card with the model of NVIDIA GeForce GTX460 as a server side and a CPU with the model of Intel Core i5-760 quad-core as a client side. Win7 64-bit is selected as the operating system. The parallel implementation consists of two parts:PA H and PA QR. PA H is a procedure that transforms a matrix A into the Hessenberg matrix B. PA QR is the actual parallel algorithm of the QR iterations that is imposed on the Hessenberg matrix B for finding eigenvalues of the general matrix A. The speedup ratio of the proposed algorithm is jarless when the number of iterations becomes greater. The experimental results show that the parallel implementation with CUDA on GPU only makes use of less running time than traditional sequential algorithms. The speedup ratio of PA H is between 1.79 and 7.81. The speedup ratio of PA QR is between 3.24 and 118.9. Especially, when the order of general matrix equals 8192, the amount of iterations becomes 10000. The speedup ratio of the PA-H and the PA QR can run up to 7.81 and 118.9 respectively.

This paper addressed the modeling and optimization of loading path in T‐shape hydroforming of tubes using Simulated Annealing (SA) algorithm. Analysis of variance shows that some of pre‐selected parameters in loading paths have not significant effect on the deformed tube. Hence, some of optimized parameters found initially, are replaced with their own fixed optimum values in order to seek for the other parameters in more detail by the Simulated Annealing (SA) algorithm. According to the intensity of effectiveness on the deformation, six more important parameters are chosen and their minimum and maximum limitation values are determined. In this case, sixty four different tests for different loading paths are designed by Design of Experiment (DOE) and full factorial method. By using mathematical modeling all required loading parameters are obtained. Proposed models of formability embedded into Simulated Annealing algorithm and optimum value for loading parameters and optimal load paths are found. The obtained results show that more accurate loading path may be found for T‐shape of tube hydroforming.

A hybrid imperialist competitive-simulated annealing algorithm for a multisource multi-product location-routing-inventory problem

Implementation of Image Enhancement Algorithms and Recursive Ray Tracing using CUDA

In this paper, simulated annealing (SA) algorithm is employed to solve the flowshop scheduling problem with the objective of minimising the completion time variance (CTV) of jobs. Four variants of the two-phase SA algorithm (SA-I to SA-IV) are proposed to solve flowshop scheduling problem with the objective of minimising the CTV of jobs without considering the right shifting of completion time of jobs on the last machine. The proposed SA algorithms have been tested on 90 benchmark flowshop scheduling problems. The solutions yielded by the proposed SA variants are compared with the best CTV of jobs reported in the literature, and the proposed SA-III is found to perform well in minimising the chosen performance measure (CTV) particularly in medium and large size problems.

A modification of the simulated annealing (SA) algorithm for solving discrete stochastic optimization problems where the objective function is stochastic and can be evaluated only through Monte Carlo simulation is proposed. In this modification, the Metropolis criterion depends on whether the objective function values indicate a statistically significant difference at each iteration. The differences between objective function values are considered to be statistically significant based on confidence intervals associated with these values. Unlike the original SA, the proposed method uses a constant temperature. It is shown that the configuration that has been visited most often in the first k iterations converges almost surely to a global optimizer. Computational results and comparisons with other SA algorithms are presented to demonstrate the performance of the proposed SA algorithm.

Graphic processing units (GPUs) emerged recently as an exciting new hardware environment for a truly parallel implementation and execution of Nature and Bio-inspired Algorithms with excellent price-to-power ratio. In contrast to common multicore CPUs that contain up to tens of independent cores, the GPUs represent a massively parallel single-instruction multiple-data devices that can nowadays reach peak performance of hundreds and thousands of giga floating-point operations per second. Nature and Bio-inspired Algorithms implement parallel optimization strategies in which a single candidate solution, a group of candidate solutions (population), or multiple populations seek for optimal solution or set of solutions of given problem. Genetic algorithms (GA) constitute a family of traditional and very well-known nature-inspired populational meta-heuristic algorithms that have proved its usefulness on a plethora of tasks through the years. Differential evolution (DE) is another efficient populational meta-heuristic algorithm for real-parameter optimization. Particle swarm optimization (PSO) can be seen as nature-inspired multiagent method in which the interaction of simple independent agents yields intelligent collective behavior. Simulated annealing (SA) is global optimization algorithm which combines statistical mechanics and combinatorial optimization with inspiration in metallurgy. This survey provides a brief overview of the latest state-of-the-art research on the design, implementation, and applications of parallel GA, DE, PSO, and SA-based methods on the GPUs.

Summary form only given. Numerical analysis of electromagnetic scattering has been widely studied in the past. The method of moments (MoM) is suitable to simulate scattering from an object in an open region. In order to solve problems with complicated geometries and materials, the finite element method (FEM) is preferred. However, when solving unbounded problems with FEM, the use of absorbing boundary conditions or perfectly matched layers will result in truncation errors. To combine the advantages of both MoM and FEM, the finite element-boundary integral (FE-BI) method was developed and widely used (J. M. Jin, The Finite Element Method in Electromagnetics, Second Edition. New York: Wiley, 2002). This algorithm is not only able to deal with highly complicated geometry and material, but also able to eliminate the truncation error. However, since the MoM has O(N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2)</sup> computational and storage complexities, the computational cost of the BI-related algorithm is still prohibitively high when solving large-scale scattering problems. To alleviate this problem, the multilevel fast multipole algorithm (MLFMA) has been incorporated into the FE-BI method (J. Liu and J. M. Jin, IEEE Trans. Antennas Propag., vol. 51, pp.1157-1167, Jun. 2003). Another important technique to accelerate the computation is to resort to parallel computers. Recently, the graphics processing unit (GPU), as one of many-core computing systems, has received intensive attention from the scientific computing community due to its low price, a massive number of processors, and the resulting high computational efficiency. In this work, we discuss the GPU implementation of the FE-BI algorithm for solving electromagnetic scattering problems. First, the assembly of the BI-related matrix is parallelized on GPU by NVIDIA's compute unified device architecture (CUDA). A massive number of threads are assigned to carry out the assembly, and each thread computes one element in the BI-related matrix. Second, both the direct and iterative solvers are implemented on GPU. For the direct solver, the Intel's math kernel library (MKL) is used for LU decomposition, and the CUSPARSE (a set of basic linear algebra subroutines used for handling sparse matrices) is employed to speedup forward and backward substitutions. For the iterative solver, the high performance CUDA Basic Linear Algebra Subprograms (BLAS) is utilized for the matrix-vector multiplication and the vector-vector multiplication. Extensive numerical experiments are conducted to validate the implementation and demonstrate the achievable computational speedup.

With the rapid development of information technology, hospital informatization has become the general trend. In this context, disease monitoring based on medical big data has been proposed and has aroused widespread concern. In order to overcome the shortcomings of the BP neural network, such as slow convergence speed and easy to fall into local extremum, simulated annealing algorithm is used to optimize the BP neural network and high-order simulated annealing neural network algorithm is constructed. After screening the potential target indicators using the random forest algorithm, based on medical big data, the experiment uses high-order simulated annealing neural network algorithm to establish the obesity monitoring model to realize obesity monitoring and prevention. The results show that the training times of the SA-BP neural network are 1480 times lower than those of the BP neural network, and the mean square error of the SA-BP neural network is 3.43 times lower than that of the BP neural network. The MAE of the SA-BP neural network is 1.81 times lower than that of the BP neural network, and the average output error of the obesity monitoring model is about 2.35 at each temperature. After training, the average accuracy of the obesity monitoring model was 98.7%. The above results show that the obesity monitoring model based on medical big data can effectively complete the monitoring of obesity and has a certain contribution to the diagnosis, treatment, and early warning of obesity.

In practical application scenarios such as logistics distribution and UAV cruise, the spherical multi-point path optimization problem has significant research value and practical significance. This research focuses on solving the spherical multi-point path optimization problem. The study first establishes a spherical distance calculation model, deriving the distance formula between any two points using spherical geometric principles. Taking eight specific points as research objects, the problem is transformed into a graph theory problem, and a single-objective linear programming model is constructed. The study employs Simulated Annealing Algorithm and Ant Colony Algorithm for comparative analysis. Through parameter optimization, the Simulated Annealing Algorithm achieved a shortest path length of 7.0381 kilometers. In comparison, the Ant Colony Algorithm obtained an optimal path (44-61-158-83-147-100-31-115) with a length of 4.0635 kilometers and a total time of 390.2 minutes, showing a 2.2% improvement in efficiency compared to the Simulated Annealing Algorithm. The results demonstrate that the Ant Colony Algorithm exhibits better performance and stability in this spherical multi-point path optimization problem.

<strong class="journal-contentHeaderColor">Abstract.</strong> With semiconductor technology gradually approaching its physical and thermal limits, Graphics processing unit (GPU) is becoming an attractive solution in many scientific applications due to their high performance. This paper presents an application of GPU accelerators in air quality model. We endeavor to demonstrate an approach that runs a PPM solver of horizontal advection (HADVPPM) for air quality model CAMx on GPU clusters. Specifically, we first convert the HADVPPM to a new Compute Unified Device Architecture C (CUDA C) code to make it computable on the GPU (GPU-HADVPPM). Then, a series of optimization measures are taken, including reducing the CPU-GPU communication frequency, increasing the size of data computation on GPU, optimizing the GPU memory access, and using thread and block indices in order to improve the overall computing performance of CAMx model coupled with GPU-HADVPPM (named as CAMx-CUDA model). Finally, a heterogeneous, hybrid programming paradigm is presented and utilized with the GPU-HADVPPM on GPU clusters with Massage Passing Interface (MPI) and CUDA. Offline experiment results show that running GPU-HADVPPM on one NVIDIA Tesla K40m and NVIDIA Tesla V100 GPU can achieve up to 845.4x and 1113.6x acceleration. By implementing a series of optimization schemes, the CAMx-CUDA model resulted in a 29.0x and 128.4x improvement in computational efficiency using a GPU accelerator card on a K40m and V100 cluster, respectively. In terms of the single-module computational efficiency of GPU-HADVPPM, it can achieve 1.3x and 19.4x speedup on NVIDIA Tesla K40m GPU and NVIDA Tesla V100 GPU respectively. The multi-GPU acceleration algorithm enables 4.5x speedup with 8 CPU cores and 8 GPU accelerators on V100 cluster.

<strong class="journal-contentHeaderColor">Abstract.</strong> With semiconductor technology gradually approaching its physical and thermal limits, Graphics processing unit (GPU) is becoming an attractive solution in many scientific applications due to their high performance. This paper presents an application of GPU accelerators in air quality model. We endeavor to demonstrate an approach that runs a PPM solver of horizontal advection (HADVPPM) for air quality model CAMx on GPU clusters. Specifically, we first convert the HADVPPM to a new Compute Unified Device Architecture C (CUDA C) code to make it computable on the GPU (GPU-HADVPPM). Then, a series of optimization measures are taken, including reducing the CPU-GPU communication frequency, increasing the size of data computation on GPU, optimizing the GPU memory access, and using thread and block indices in order to improve the overall computing performance of CAMx model coupled with GPU-HADVPPM (named as CAMx-CUDA model). Finally, a heterogeneous, hybrid programming paradigm is presented and utilized with the GPU-HADVPPM on GPU clusters with Massage Passing Interface (MPI) and CUDA. Offline experiment results show that running GPU-HADVPPM on one NVIDIA Tesla K40m and NVIDIA Tesla V100 GPU can achieve up to 845.4x and 1113.6x acceleration. By implementing a series of optimization schemes, the CAMx-CUDA model resulted in a 29.0x and 128.4x improvement in computational efficiency using a GPU accelerator card on a K40m and V100 cluster, respectively. In terms of the single-module computational efficiency of GPU-HADVPPM, it can achieve 1.3x and 19.4x speedup on NVIDIA Tesla K40m GPU and NVIDA Tesla V100 GPU respectively. The multi-GPU acceleration algorithm enables 4.5x speedup with 8 CPU cores and 8 GPU accelerators on V100 cluster.

Novel computing paradigms for parameter estimation in Hammerstein controlled auto regressive auto regressive moving average systems