A WOA-based optimization approach for task scheduling in cloud Computing systems

Task scheduling in cloud computing can directly affect the resource usage and operational cost of a system. To improve the efficiency of task executions in a cloud, various metaheuristic algorithms, as well as their variations, have been proposed to optimize the scheduling. In this work, for the first time, we apply the latest metaheuristics WOA (the whale optimization algorithm) for cloud task scheduling with a multiobjective optimization model, aiming at improving the performance of a cloud system with given computing resources. On that basis, we propose an advanced approach called IWC (Improved WOA for Cloud task scheduling) to further improve the optimal solution search capability of the WOA-based method. We present the detailed implementation of IWC and our simulation-based experiments show that the proposed IWC has better convergence speed and accuracy in searching for the optimal task scheduling plans, compared to the current metaheuristic algorithms. Moreover, it can also achieve better performance on system resource utilization, in the presence of both small and large-scale tasks

Krylov implicit integration factor discontinuous Galerkin methods on sparse grids for high dimensional reaction-diffusion equations

Computational costs of numerically solving multidimensional partial differential equations (PDEs) increase significantly when the spatial dimensions of the PDEs are high, due to large number of spatial grid points. For multidimensional reaction-diffusion equations, stiffness of the system provides additional challenges for achieving efficient numerical simulations. In this paper, we propose a class of Krylov implicit integration factor (IIF) discontinuous Galerkin (DG) methods on sparse grids to solve reaction-diffusion equations on high spatial dimensions. The key ingredient of spatial DG discretization is the multiwavelet bases on nested sparse grids, which can significantly reduce the numbers of degrees of freedom. To deal with the stiffness of the DG spatial operator in discretizing reaction-diffusion equations, we apply the efficient IIF time discretization methods, which are a class of exponential integrators. Krylov subspace approximations are used to evaluate the large size matrix exponentials resulting from IIF schemes for solving PDEs on high spatial dimensions. Stability and error analysis for the semi-discrete scheme are performed. Numerical examples of both scalar equations and systems in two and three spatial dimensions are provided to demonstrate the accuracy and efficiency of the methods. The stiffness of the reaction-diffusion equations is resolved well and large time step size computations are obtained