A Distributed Sailfish Optimizer Based on Multi-Agent Systems for Solving Non-Convex and Scalable Optimization Problems Implemented on GPU

Arctic puffin optimization: A bio-inspired metaheuristic algorithm for solving engineering design optimization

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.

In this paper, we propose a hybrid parallel programming approach for a numerical solution of a two-dimensional acoustic wave equation using an implicit difference scheme for a single computer. The calculations are carried out in an implicit finite difference scheme. First, we transform the differential equation into an implicit finite-difference equation and then using the alternating direction implicit (ADI) method, we split the equation into two sub-equations. Using the cyclic reduction algorithm, we calculate an approximate solution. Finally, we change this algorithm to parallelize on graphics processing unit (GPU), GPU + Open Multi-Processing (OpenMP), and Hybrid (GPU + OpenMP + message passing interface (MPI)) computing platforms. The special focus is on improving the performance of the parallel algorithms to calculate the acceleration based on the execution time. We show that the code that runs on the hybrid approach gives the expected results by comparing our results to those obtained by running the same simulation on a classical processor core, Compute Unified Device Architecture (CUDA), and CUDA + OpenMP implementations.

MSA Probs is a parallel algorithm developed to align multiple sequence alignment using a central processing unit (CPU). Whereas the CPU has some limitations, such as the inability to parallelize tasks in the processor (latency-oriented). To overcome these limitations, this paper proposes an improved version of MSA Probs that is compatible with a graphical Processing Unit (GPU). This idea helps in enhancing the performance of our algorithm (MSAprobs). To parallelize the sequential algorithm, Compute Unified Device Architecture (CUDA) or OpenCL is commonly used on GPUs. The NIVIDIA API is used to investigate the GPU's computing power. The results of using CPU only in MSAprobs versus the CPU and GPU are compared using two data sets from the Bali Base and OX Bench. The evaluation of the CPU and GPU is done using Threads 1,2 and 4. The results showed that by combining CPU and GPU, performance is improved and execution time is reduced.

A solution algorithm for non-convex mixed integer optimization problems with only few continuous variables

With the rapid development of multimedia technologies and network communication, the parallel architecture such as the Graphic Processing Unit (GPU) is introduced in high-performance computing. But, how to program this GPU and how to obtain the best execution time remains usually an art. In this paper, a search study is performed on the Thread and the Block number that leads to a Prediction Unit of 64×64 (PU64) computation in the High Efficiency Video Coding (HEVC). It is proposed through the Compute Unified Device Architecture (CUDA). This method is described to optimize the GPU execution time. Experimental results show that the best Grid topology chosen to run the GPU kernel is obtained for 128 Block and 32 Thread. This proposed repartition gives the minimum GPU execution time compared to the CPU one, where the speed-up obtained here is around 50%.

A neurodynamic optimization technique based on overestimator and underestimator functions for solving a class of non-convex optimization problems

Watershed analysis, as a fundamental component of digital terrain analysis, is based on the Digital Elevation Model (DEM), which is a grid (raster) model of the Earth surface and topography. Watershed analysis consists of computationally and data intensive computing algorithms that need to be implemented by leveraging parallel and high-performance computing methods and techniques. In this paper, the Multiple Flow Direction (MFD) algorithm for watershed analysis is implemented and evaluated on multi-core Central Processing Units (CPU) and many-core Graphics Processing Units (GPU), which provides significant improvements in performance and energy usage. The implementation is based on NVIDIA CUDA (Compute Unified Device Architecture) implementation for GPU, as well as on OpenACC (Open ACCelerators), a parallel programming model, and a standard for parallel computing. Both phases of the MFD algorithm (i) iterative DEM preprocessing and (ii) iterative MFD algorithm, are parallelized and run over multi-core CPU and GPU. The evaluation of the proposed solutions is performed with respect to the execution time, energy consumption, and programming effort for algorithm parallelization for different sizes of input data. An experimental evaluation has shown not only the advantage of using OpenACC programming over CUDA programming in implementing the watershed analysis on a GPU in terms of performance, energy consumption, and programming effort, but also significant benefits in implementing it on the multi-core CPU.

In this paper, the classical exact absolute value penalty function method is used for solving a new class of nonconvex nonsmooth optimization problems. Nonconvex nondifferentiable optimization problems with both inequality and equality constraints are considered here, in which not all functions constituting them have the fundamental property of convex functions and most classes of generalized convex functions—namely, a stationary point of such a function is its global minimum. It is proved for such nonconvex optimization problems that there exists a finite threshold of penalty parameters equal to the largest absolute value of a Lagrange multiplier such that, for every penalty parameter exceeding this lower bound, there is the equivalence between an optimal solution in the original constrained minimization problem with ‐invex functions and a minimizer in its associated penalized optimization problem with the exact l1 penalty function. Further, under nondifferentiable ‐invexity assumptions, a characterization of a saddle point of the Lagrange function, defined for the considered constrained optimization problem in terms of minimizers of its associated exact penalized optimization problem with the exact l1 penalty function, is presented.

Turbo Similarity Searching (TSS) is a two phases searching procedure that has been proven by previous works as one of the best searching method on chemical databases. TSS however consumes lots of computation time due to the number of searches and fusion carried out in the second phase of its procedure. Hence, TSS would not be able to cater the increase in the chemical database size due to this limitation. With the emergence of the parallel technology, this research looks into accelerating TSS on the widely-used many-cores i.e. the Graphics Processing Unit (GPU) and multi-cores platform. This would not only solve the computational time issue but also the cost as GPUs can be obtained at a lower cost. Hence, the implementation of TSS will help the medicinal chemist to execute the virtual screening in an accurate and fast manner. This study investigates the best possible method to parallelize TSS via experimentation of three parallel designs; two designs were implemented on GPU platform using the Compute Unified Device Architecture (CUDA) API namely CUDA 1 and CUDA 2 whilst one design was implemented on multi-core platform using OpenMP API. The CUDA 1 design had shown tremendous speedup and low GPU-memory utilization as compared to CUDA 2 design. In general observation, the parallel CUDA 1 was 131 times faster than sequential and 51 times faster than parallel OpenMP. This leads to the conclusion that CUDA 1 design as the best parallel design for TSS.

Network coding has recently been widely applied in various networks for system throughput improvement and/or resilience to network dynamics. However, the computational overhead introduced by the network coding operations is not negligible and has become the cornerstone for real deployment of network coding. In this paper, we exploit the computing power of contemporary Graphic Processing Units (GPUs) to accelerate the network coding operations. We proposed three parallel algorithms that maximize the parallelism of the encoding and decoding processes, i.e., the power of GPUs is fully utilized. This paper also shares our optimization design choices and our workarounds to the challenges encountered in working with GPUs. With our implementation of the algorithms, we are able to achieve up to 12 times of speedup over the highly optimized CPU counterpart, using the NVIDIA GPU and the Computer Unified Device Architecture (CUDA) programming model.

The Sailfish Optimizer: A novel nature-inspired metaheuristic algorithm for solving constrained engineering optimization problems

Many-core framework, represented by Graphic Processing Unit (GPU), has been becoming more popular in scientific computing and data analysis, and Compute Unified Device Architecture (CUDA) allows developers to carry out computation on GPUs more conveniently. Matrix operation is one of the most important application scenarios of GPU computation and CUDA, widely appearing in domains like graph applications and artificial intelligence. This paper focuses on accelerating matrix power operation (MPO) process, which appears in many engineering problems and may be time-consuming when the scale of matrixes is large, with GPUs and CUDA. In this paper, three techniques are used to speed up the MPO process: matrix parallel reduction, matrix parallel multiplication and CUDA dynamic parallelism. The experiments were carried out on NVIDIA RTX 2080 Super and Intel(R) Core(TM) i7-10750H. The code is compiled and executed in Visual Studio 2019 community, the GPU driver version is 461.40, the CUDA version is 11.1, and the NVCC version is 11.1.74. With all three techniques, the MPO process can get hundreds of times speedup compared with the sequential multiplication process executed by Eigen library, even though the code of algorithm is hardly optimized. Moreover, with the number of power increasing, the efficiency of algorithm can be even higher because of the relatively fixed time consumed in data transmission and GPU memory allocation.

The small slop approximation (SSA) is an accurate method to calculate the electromagnetic (EM) scattering properties of rough surfaces. However, its computational complexity restricts its application to smaller domains and there is always the need for speedup in very large cases using pure central processing units (CPUs) hardware. With the development of graphics processing units (GPUs), more processors are dedicated to perform independent calculations. In addition, NVIDIA introduced a parallel computing platform, compute unified device architecture (CUDA), which provides researchers an easy way to use processors on GPU. To calculate EM scattering properties on GPU, we reformulate the SSA method with CUDA to take advantage of GPU threads. Because each thread executes synchronously and deals with a corresponding point data of rough surface, the CUDA-based SSA method calculates faster than the pure-CPU equivalent. To overcome memory limitations, the data of large rough surface are stored on hard disk. Moreover, a subsidiary thread is used to deal with the process of data transmission between the memory and the hard disk and reduce transmitting time further. The factors, block size, data transfers, and register, are also discussed in the optimization of the CUDA application. Test cases running on a NVIDIA GTX 460 GPU indicate that two orders of magnitude speedup, including file input and output, is obtained with our new formulation.

We develop new fast and efficient algorithms for designing single or multiple unimodular waveforms with good auto- and cross-correlation or weighted correlation properties, which are highly desired in radar and communication systems. The waveform design is based on the minimization of the integrated sidelobe level (ISL) and weighted ISL (WISL) of waveforms. As the corresponding problems can quickly grow to a large scale with increasing the code length and the number of waveforms, the main issue turns to be the development of fast large-scale optimization techniques. The difficulty is also that the corresponding optimization problems are nonconvex, but the required accuracy is high. Therefore, we formulate the ISL and WISL minimization problems as nonconvex quartic optimization problems in frequency domain, and then simplify them into quadratic problems via majorization-minimization technique, which is one of the basic techniques for addressing large-scale and/or nonconvex optimization problems. While designing our fast algorithms, we explore and use the inherent algebraic structures in objective functions to rewrite them into quartic forms, and in the case of WISL minimization, to derive additionally an alternative quartic form that allows us to apply the quartic-quadratic transformation. Our algorithms are applicable to large-scale unimodular waveform design problems as they are proved to have lower or comparable computational burden (analyzed theoretically) and faster convergence speed (confirmed by comprehensive simulations) than the state-of-the-art algorithms. In addition, the waveforms designed by our algorithms demonstrate better correlation properties compared to their counterparts.