Accelerating Large-Scale Sorting through Parallel Algorithms

This study explores the application of parallel algorithms to enhance large-scale sorting, focusing on the QuickSort method. Implemented in both sequential and parallel forms, the paper provides a detailed comparison of their performance. This study investigates the efficacy of both techniques through the lens of array generation and pivot selection to manage datasets of varying sizes. This study meticulously documents the performance metrics, recording 16,499.2 milliseconds for the serial implementation and 16,339 milliseconds for the parallel implementation when sorting an array by using C++ chrono library. These results suggest that while the performance gains of the parallel approach over its serial counterpart are not immediately pronounced for smaller datasets, the benefits are expected to be more substantial as the dataset size increases.

A Class of Parallel Algorithms of Real-TimeNumerical Simulation for Stiff Dynamic System

In this paper a class of real-time parallel modified Rosenbrock methods of numerical simulation is constructed for stiff dynamic systems on a multiprocessor system, and convergence and numerical stability of these methods are discussed. A-stable real-time parallel formula of two-stage third-order and A(α)-stable real-time parallel formula with o ≈ 89.96° of three-stage fourth-order are particularly given. The numerical simulation experiments in parallel environment show that the class of algorithms is efficient and applicable, with greater speedup.

PARALLEL ALGORITHMS OF ONE-LEG METHOD AND ITERATED DEFECT CORRECTION METHODS

The parallel algorithms of iterated defect correction methods (PIDeCM’s) are constructed, which are of efficiency and high order B-convergence for general nonlinear stiff systems in ODE’S. As the basis of constructing and discussing PIDeCM’s. a class of parallel one-leg methods is also investigated, which are of particular efficiency for linear systems.

Some Massively Parallel Algorithms from Nature

We introduced the work on parallel problem solvers from physics and biology being developed by the research team at the State Key Laboratory of Software Engineering, Wuhan University. Results on parallel solvers include the following areas: Evolutionary algorithms based on imitating the evolution processes of nature for parallel problem solving, especially for parallel optimization and model-building; Asynchronous parallel algorithms based on domain decomposition which are inspired by physical analogies such as elastic relaxation process and annealing process, for scientific computations, especially for solving nonlinear mathematical physics problems. All these algorithms have the following common characteristics: inherent parallelism, self-adaptation and self-organization, because the basic ideas of these solvers are from imitating the natural evolutionary processes.

Design of efficient parallel algorithms on shared memory multiprocessors

The design of parallel algorithms is studied in this paper. These algorithms are applicable to shared memory MIMD machines In this paper, the emphasis is put on the methods for design of the efficient parallel algorithms. The design of efficient parallel algorithms should be based on the following considerationst algorithm parallelism and the hardware-parallelism; granularity of the parallel algorithm, algorithm optimization according to the underling parallel machine. In this paper , these principles are applied to solve a model problem of the PDE. The speedup of the new method is high. The results were tested and evaluated on a shared memory MIMD machine. The practical results were agree with the predicted performance.

CONVERGENCE ANALYSIS OF SOME FINITE ELEMENT PARALLEL ALGORITHMS FOR THE STATIONARY INCOMPRESSIBLE MHD EQUATIONS

By combination of iteration methods with the partition of unity method(PUM),some finite element parallel algorithms for the stationary incompressible magnetohydrodynamics(MHD)with different physical parameters are presented and analyzed.These algorithms are highly efficient.At first,a global solution is obtained on a coarse grid for all approaches by one of the iteration methods.By parallelized residual schemes,local corrected solutions are calculated on finer meshes with overlapping sub-domains.The subdomains can be achieved flexibly by a class of PUM.The proposed algorithm is proved to be uniformly stable and convergent.Finally,one numerical example is presented to confirm the theoretical findings.

Application of a Parallel Adaptive Cuckoo Search Algorithm in the Rectangle Layout Problem

The meta-heuristic algorithm is a global probabilistic search algorithm for the iterative solution.It has good performance in global optimization fields such as maximization.In this paper,a new adaptive parameter strategy and a parallel communication strategy are proposed to further improve the Cuckoo Search(CS)algorithm.This strategy greatly improves the convergence speed and accuracy of the algorithm and strengthens the algorithm’s ability to jump out of the local optimal.This paper compares the optimization performance of Parallel Adaptive Cuckoo Search(PACS)with CS,Parallel Cuckoo Search(PCS),Particle Swarm Optimization(PSO),Sine Cosine Algorithm(SCA),Grey Wolf Optimizer(GWO),Whale Optimization Algorithm(WOA),Differential Evolution(DE)and Artificial Bee Colony(ABC)algorithms by using the CEC-2013 test function.The results show that PACS algorithmoutperforms other algorithms in 20 of 28 test functions.Due to the superior performance of PACS algorithm,this paper uses it to solve the problem of the rectangular layout.Experimental results show that this scheme has a significant effect,and the material utilization rate is improved from89.5%to 97.8%after optimization.

Parallel Optimization of Program Instructions Using Genetic Algorithms

This paper describes an efficient solution to parallelize softwareprogram instructions, regardless of the programming language in which theyare written. We solve the problem of the optimal distribution of a set ofinstructions on available processors. We propose a genetic algorithm to parallelize computations, using evolution to search the solution space. The stagesof our proposed genetic algorithm are: The choice of the initial populationand its representation in chromosomes, the crossover, and the mutation operations customized to the problem being dealt with. In this paper, geneticalgorithms are applied to the entire search space of the parallelization ofthe program instructions problem. This problem is NP-complete, so thereare no polynomial algorithms that can scan the solution space and solve theproblem. The genetic algorithm-based method is general and it is simple andefficient to implement because it can be scaled to a larger or smaller number ofinstructions that must be parallelized. The parallelization technique proposedin this paper was developed in the C# programming language, and our resultsconfirm the effectiveness of our parallelization method. Experimental resultsobtained and presented for different working scenarios confirm the theoreticalresults, and they provide insight on how to improve the exploration of a searchspace that is too large to be searched exhaustively.

Local and parallel finite element algorithms for time-dependent convection-diffusion equations

Local and parallel finite element algorithms based on two-grid discretization for the time-dependent convection-diffusion equations are presented. These algorithms are motivated by the observation that, for a solution to the convection-diffusion problem, low frequency components can be approximated well by a relatively coarse grid and high frequency components can be computed on a fine grid by some local and parallel proce- dures. Hence, these local and parallel algorithms only involve one small original problem on the coarse mesh and some correction problems on the local fine grid. One technical tool for the analysis is the local a priori estimates that are also obtained. Some numerical examples are given to support our theoretical analvsis.

Research on Grid Planning of Dual Power Distribution Network Based on Parallel Ant Colony Optimization Algorithm

A distribution network plays an extremely important role in the safe and efficient operation of a power grid.As the core part of a power grid’s operation,a distribution network will have a significant impact on the safety and reliability of residential electricity consumption.it is necessary to actively plan and modify the distribution network’s structure in the power grid,improve the quality of the distribution network,and optimize the planning of the distribution network,so that the network can be fully utilized to meet the needs of electricity consumption.In this paper,a distribution network grid planning algorithm based on the reliability of electricity consumption was completed using ant colony algorithm.For the distribution network structure planning of dual power sources,the parallel ant colony algorithm was used to prove that the premise of parallelism is the interactive process of ant colonies,and the dual power distribution network structure model is established based on the principle of the lowest cost.The artificial ants in the algorithm were compared with real ants in nature,and the basic steps and working principle of the ant colony optimization algorithm was studied with the help of the travelling salesman problem(TSP).Then,the limitations of the ant colony algorithm were analyzed,and an improvement strategy was proposed by using python for digital simulation.The results demonstrated the reliability of model-building and algorithm improvement.

Concise review of relaxations and approximation algorithms for nonidentical parallel-machine scheduling to minimize total weighted completion times

A class of nonidentical parallel machine scheduling problems are considered in which the goal is to minimize the total weighted completion time. Models and relaxations are collected. Most of these problems are NP-hard, in the strong sense, or open problems, therefore approximation algorithms are studied. The review reveals that there exist some potential areas worthy of further research.

Multi-objective Collaborative Optimization for Scheduling Aircraft Landing on Closely Spaced Parallel Runways Based on Genetic Algorithms

A scheduling model of closely spaced parallel runways for arrival aircraft was proposed,with multi-objections of the minimum flight delay cost,the maximum airport capacity,the minimum workload of air traffic controller and the maximum fairness of airlines′scheduling.The time interval between two runways and changes of aircraft landing order were taken as the constraints.Genetic algorithm was used to solve the model,and the model constrained unit delay cost of the aircraft with multiple flight tasks to reduce its delay influence range.Each objective function value or the fitness of particle unsatisfied the constrain condition would be punished.Finally,one domestic airport hub was introduced to verify the algorithm and the model.The results showed that the genetic algorithm presented strong convergence and timeliness for solving constraint multi-objective aircraft landing problem on closely spaced parallel runways,and the optimization results were better than that of actual scheduling.

Forward and backward models for fault diagnosis based on parallel genetic algorithms

In this paper, a mathematical model consisting of forward and backward models is built on parallel genetic algorithms (PGAs) for fault diagnosis in a transmission power system. A new method to reduce the scale of fault sections is developed in the forward model and the message passing interface (MPI) approach is chosen to parallel the genetic algorithms by global sin-gle-population master-slave method (GPGAs). The proposed approach is applied to a sample system consisting of 28 sections, 84 protective relays and 40 circuit breakers. Simulation results show that the new model based on GPGAs can achieve very fast computation in online applications of large-scale power systems.

Niche pseudo-parallel genetic algorithms for path optimization of autonomous mobile robot

A new genetic algorithm named niche pseudo-parallel genetic algorithm （NPPGA） is presented for path evolution and genetic optimization of autonomous mobile robot. The NPPGA is an effective improvement to maintain the population diversity as well for the sake of avoiding premature and strengthen parallelism of the population to accelerate the search process combined with niche genetic algorithms and pseudo-parallel genetic algorithms. The proposed approach is evaluated by robotic path optimization, which is a specific application of traveler salesman problem （TSP）. Experimental results indicated that a shortest path could be obtained in the practical traveling salesman problem named ＂Robot tour around Pekin＂, and the performance conducted by NPPGA is better than simple genetic algorithm （SGA） and distributed paralell genetic algorithms （DPGA）.

PARALLEL SCHWARZ ALGORITHMS FOR PARABOLIC EQUATIONS AND ERROR ESTIMATES

In this paper we introduce two kinds of parallel Schwarz domain decomposition me thods for general, selfadjoint, second order parabolic equations and study the dependence of their convergence rates on parameters of time-step and space-mesh. We prove that the, approximate solution has convergence independent of iteration times at each time-level. And the L^2 error estimates are given.

Bisection technique for designing synchronous parallel algorithms

A basic technique for designing synchronous parallel algorithms, the so-called bisection technique, is proposed. The basic pattern of designing parallel algorithms is described. The relationship between the designing idea and I Ching (principles of change) is discussed.

Efficient Parallel Algorithms for Some Graph Theory Problems

In this paper,a sequential algorithm computing the all vertex pair distance matrix D and the path matrix Pis given.On a PRAM EREW model with p,1≤p≤n^2,processors,a parallel version of the sequential algorithm is shown.This method can also be used to get a parallel algorithm to compute transitive closure arrayof an undirected graph.The time complexify of the parallel algorithm is O(n^3/p).If D,P andare known,it is shown that the problems to find all connected components, to compute the diameter of an undirected graph,to determine the center of a directed graph and to search for a directed cycle with the minimum(maximum)length in a directed graph can all be solved in O(n^2/p^+ logp)time.

Research on the Optimal Parallel Algorithms of Broadcast-Class Problems

Speedup is considered as the criterion of determining whether a parallel algorithm is optimal. But broadcast-class problems, existing only on parallel computer system, have no sequential algorithms at all. Speedup standard becomes invalid here. Through this research on broadcast algorithms under several typical parallel computation models,a model-independent evaluation standard min C2 is developed, which can be not only used to determine an optimal broadcasting algorithm, but also normalized to apply to any parallel algorithm. As a new idea, min C2 will lead to a new way in this field.

A HYBRID GRANULARITY PARALLEL ALGORITHM FOR PRECISE INTEGRATION OF STRUCTURAL DYNAMIC RESPONSES

Precise integration methods to solve structural dynamic responses and the corresponding time integration formula are composed of two parts： the multiplication of an exponential matrix with a vector and the integration term. The second term can be solved by the series solution. Two hybrid granularity parallel algorithms are designed, that is, the exponential matrix and the first term are computed by the fine-grained parallel algorithra and the second term is computed by the coarse-grained parallel algorithm. Numerical examples show that these two hybrid granularity parallel algorithms obtain higher speedup and parallel efficiency than two existing parallel algorithms.

Parallel Algorithms for Large-scale Linearly Constrained Minimization Problem

In this paper, two PVD-type algorithms are proposed for solving inseparable linear constraint optimization. Instead of computing the residual gradient function, the new algorithm uses the reduced gradients to construct the PVD directions in parallel computation, which can greatly reduce the computation amount each iteration and is closer to practical applications for solve large-scale nonlinear programming. Moreover, based on an active set computed by the coordinate rotation at each iteration, a feasible descent direction can be easily obtained by the extended reduced gradient method. The direction is then used as the PVD direction and a new PVD algorithm is proposed for the general linearly constrained optimization. And the global convergence is also proved.