Parallel two-stage algorithms for solving the PageRank problem

In this work we present parallel algorithms based on the use of two-stage methods for solving the PageRank problem as a linear system. Different parallel versions of these methods are explored and their convergence properties are analyzed. The parallel implementation has been developed using a mixed MPI/OpenMP model to exploit parallelism beyond a single level. In order to investigate and analyze the proposed parallel algorithms, we have used several realistic large datasets. The numerical results show that the proposed algorithms can speed up the time to converge with respect to the parallel Power algorithm and behave better than other well-known techniques.This research was supported by the Spanish Ministry of Economy and Competitiveness (MINECO) and the European Commission (FEDER funds) under Grant Number TIN2015-66972-C5-4-R

Non-Stationary Acceleration Strategies for PageRank Computing

In this work, a non-stationary technique based on the Power method for accelerating the parallel computation of the PageRank vector is proposed and its theoretical convergence analyzed. This iterative non-stationary model, which uses the eigenvector formulation of the PageRank problem, reduces the needed computations for obtaining the PageRank vector by eliminating synchronization points among processes, in such a way that, at each iteration of the Power method, the block of iterate vector assigned to each process can be locally updated more than once, before performing a global synchronization. The parallel implementation of several strategies combining this novel non-stationary approach and the extrapolation methods has been developed using hybrid MPI/OpenMP programming. The experiments have been carried out on a cluster made up of 12 nodes, each one equipped with two Intel Xeon hexacore processors. The behaviour of the proposed parallel algorithms has been studied with realistic datasets, highlighting their performance compared with other parallel techniques for solving the PageRank problem. Concretely, the experimental results show a time reduction of up to 58.4% in relation to the parallel Power method, when a small number of local updates is performed before each global synchronization, outperforming both the two-stage algorithms and the extrapolation algorithms, more sharply as the number of processes increases.This research was supported by the Spanish Ministry of Science, Innovation and Universities Grant RTI2018-098156-B-C54, co-financed by the European Commission (FEDER funds)

Parallel alternating iterative algorithms with and without overlapping on multicore architectures

We consider the problem of solving large sparse linear systems where the coefficient matrix is possibly singular but the equations are consistent. Block two-stage methods in which the inner iterations are performed using alternating methods are studied. These methods are ideal for parallel processing and provide a very general setting to study parallel block methods including overlapping. Convergence properties of these methods are established when the matrix in question is either M-matrix or symmetric matrix. Different parallel versions of these methods and implementation strategies, with and without overlapping blocks, are explored. The reported experiments show the behavior and effectiveness of the designed parallel algorithms by exploiting the benefits of shared memory inside the nodes of current SMP supercomputers.This research was partially supported by the Spanish Ministry of Science and Innovation under grant number TIN2011-26254, and by the European Union FEDER (CAPAP-H5 network TIN2014-53522- REDT)

A heuristic relaxed extrapolated algorithm for accelerating PageRank

The PageRank algorithm for determining the importance of Web pages has become a central technique in Web search. This algorithm uses the Power method to compute successive iterates that converge to the principal eigenvector of the Markov chain representing the Web link graph. In this work we present an effective heuristic Relaxed and Extrapolated algorithm based on the Power method that accelerates its convergence. A hybrid parallel implementation of this algorithm has been designed by combining various OpenMP threads for each MPI process and several strategies of data distribution among nodes have been analyzed. The results show that the proposed algorithm can significantly speed up the convergence time with respect to the parallel Power algorithm.This research was partially supported by the Spanish Ministry of Science and Innovation under Grant Number TIN2011-26254 and Grant Number TIN2015-66972-C5-4-R, and by the European Union FEDER (CAPAP-H5 network TIN2014-53522-REDT)

A Parallel Meta-Heuristic Approach to Reduce Vehicle Travel Time in Smart Cities

The development of the smart city concept and inhabitants’ need to reduce travel time, in addition to society’s awareness of the importance of reducing fuel consumption and respecting the environment, have led to a new approach to the classic travelling salesman problem (TSP) applied to urban environments. This problem can be formulated as “Given a list of geographic points and the distances between each pair of points, what is the shortest possible route that visits each point and returns to the departure point?”. At present, with the development of Internet of Things (IoT) devices and increased capabilities of sensors, a large amount of data and measurements are available, allowing researchers to model accurately the routes to choose. In this work, the aim is to provide a solution to the TSP in smart city environments using a modified version of the metaheuristic optimization algorithm Teacher Learner Based Optimization (TLBO). In addition, to improve performance, the solution is implemented by means of a parallel graphics processing unit (GPU) architecture, specifically a Compute Unified Device Architecture (CUDA) implementation.This research was supported by the Spanish Ministry of Science, Innovation and Universities and the Research State Agency under Grant RTI2018-098156-B-C54 co-financed by FEDER funds, and by the Spanish Ministry of Economy and Competitiveness under Grant TIN2017-89266-R, co-financed by FEDER funds

Settings-Free Hybrid Metaheuristic General Optimization Methods

Several population-based metaheuristic optimization algorithms have been proposed in the last decades, none of which are able either to outperform all existing algorithms or to solve all optimization problems according to the No Free Lunch (NFL) theorem. Many of these algorithms behave effectively, under a correct setting of the control parameter(s), when solving different engineering problems. The optimization behavior of these algorithms is boosted by applying various strategies, which include the hybridization technique and the use of chaotic maps instead of the pseudo-random number generators (PRNGs). The hybrid algorithms are suitable for a large number of engineering applications in which they behave more effectively than the thoroughbred optimization algorithms. However, they increase the difficulty of correctly setting control parameters, and sometimes they are designed to solve particular problems. This paper presents three hybridizations dubbed HYBPOP, HYBSUBPOP, and HYBIND of up to seven algorithms free of control parameters. Each hybrid proposal uses a different strategy to switch the algorithm charged with generating each new individual. These algorithms are Jaya, sine cosine algorithm (SCA), Rao’s algorithms, teaching-learning-based optimization (TLBO), and chaotic Jaya. The experimental results show that the proposed algorithms perform better than the original algorithms, which implies the optimal use of these algorithms according to the problem to be solved. One more advantage of the hybrid algorithms is that no prior process of control parameter tuning is needed.This research and APC was funded by the Spanish Ministry of Science, Innovation and Universities and the Research State Agency under Grant RTI2018-098156-B-C54 co-financed by FEDER funds, and by the Spanish Ministry of Economy and Competitiveness under Grant TIN2017-89266-R, co-financed by FEDER funds

Parallel relaxed and extrapolated algorithms for computing PageRank

In this paper, parallel Relaxed and Extrapolated algorithms based on the Power method for accelerating the PageRank computation are presented. Different parallel implementations of the Power method and the proposed variants are analyzed using different data distribution strategies. The reported experiments show the behavior and effectiveness of the designed algorithms for realistic test data using either OpenMP, MPI or an hybrid OpenMP/MPI approach to exploit the benefits of shared memory inside the nodes of current SMP supercomputers.This research was partially supported by the Spanish Ministry of Science and Innovation under Grant Number TIN2011-26254

Multipopulation-based multi-level parallel enhanced Jaya algorithms

To solve optimization problems, in the field of engineering optimization, an optimal value of a specific function must be found, in a limited time, within a constrained or unconstrained domain. Metaheuristic methods are useful for a wide range of scientific and engineering applications, which accelerate being able to achieve optimal or near-optimal solutions. The metaheuristic method called Jaya has generated growing interest because of its simplicity and efficiency. We present Jaya-based parallel algorithms to efficiently exploit cluster computing platforms (heterogeneous memory platforms). We propose a multi-level parallel algorithm, in which, to exploit distributed-memory architectures (or multiprocessors), the outermost layer of the Jaya algorithm is parallelized. Moreover, in internal layers, we exploit shared-memory architectures (or multicores) by adding two more levels of parallelization. This two-level internal parallel algorithm is based on both a multipopulation structure and an improved heuristic search path relative to the search path of the sequential algorithm. The multi-level parallel algorithm obtains average efficiency values of 84% using up to 120 and 135 processes, and slightly accelerates the convergence with respect to the sequential Jaya algorithm.This research was supported by the Spanish Ministry of Economy and Competitiveness under Grant TIN2015-66972-C5-4-R and Grant TIN2017-89266-R, co-financed by FEDER funds (MINECO/FEDER/UE)

Jaya optimization algorithm with GPU acceleration

Optimization methods allow looking for an optimal value given a specific function within a constrained or unconstrained domain. These methods are useful for a wide range of scientific and engineering applications. Recently, a new optimization method called Jaya has generated growing interest because of its simplicity and efficiency. In this paper, we present the Jaya GPU-based parallel algorithms we developed and analyze both parallel performance and optimization performance using a well-known benchmark of unconstrained functions. Results indicate that parallel Jaya implementation achieves significant speed-up for all benchmark functions, obtaining speed-ups of up to 190×, without affecting optimization performance.This research was supported by the Spanish Ministry of Economy and Competitiveness under Grant TIN2015-66972-C5-4-R, co-financed by FEDER funds (MINECO/FEDER/UE)

Parallel Improvements of the Jaya Optimization Algorithm

A wide range of applications use optimization algorithms to find an optimal value, often a minimum one, for a given function. Depending on the application, both the optimization algorithm’s behavior, and its computational time, can prove to be critical issues. In this paper, we present our efficient parallel proposals of the Jaya algorithm, a recent optimization algorithm that enables one to solve constrained and unconstrained optimization problems. We tested parallel Jaya algorithms for shared, distributed, and heterogeneous memory platforms, obtaining good parallel performance while leaving Jaya algorithm behavior unchanged. Parallel performance was analyzed using 30 unconstrained functions reaching a speed-up of up to 57.6x using 60 processors. For all tested functions, the parallel distributed memory algorithm obtained parallel efficiencies that were nearly ideal, and combining it with the shared memory algorithm allowed us to obtain good parallel performance. The experimental results show a good parallel performance regardless of the nature of the function to be optimized.This research was supported by the Spanish Ministry of Economy and Competitiveness under Grants TIN2015-66972-C5-4-R and TIN2017-89266-R, co-financed by FEDER funds (MINECO/FEDER/UE)