A Task Scheduling Algorithm with Improved Makespan Based on Prediction of Tasks Computation Time algorithm for Cloud Computing

Cloud computing is extensively used in a variety of applications and domains, however task and resource scheduling remains an area that requires improvement. Put simply, in a heterogeneous computing system, task scheduling algorithms, which allow the transfer of incoming tasks to machines, are needed to satisfy high performance data mapping requirements. The appropriate mapping between resources and tasks reduces makespan and maximises resource utilisation. In this contribution, we present a novel scheduling algorithm using Directed Acyclic Graph (DAG) based on the Prediction of Tasks Computation Time algorithm (PTCT) to estimate the preeminent scheduling algorithm for prominent cloud data. In addition, the proposed algorithm provides a significant improvement with respect to the makespan and reduces the computation and complexity via employing Principle Components Analysis (PCA) and reducing the Expected Time to Compute (ETC) matrix. Simulation results confirm the superior performance of the algorithm for heterogeneous systems in terms of efficiency, speedup and schedule length ratio, when compared to the state-of-the-art Min-Min, Max-Min, QoS-Guide and MiM-MaM scheduling algorithms

AUGMENTED LAGRANGIAN BASED ALGORITHMS FOR NONCONVEX OPTIMIZATION WITH APPLICATIONS IN SUBSPACE CLUSTERING

This thesis considers the design, analysis, and implementation of algorithms for nonconvex optimization that utilize the augmented Lagrangian function. In the first part of the thesis, we address general nonconvex optimization problems that have smooth objective and constraint functions. Observing a potential drawback of a traditional augmented Lagrangian (AL) method, we propose adaptive trust-region and linesearch AL algorithms that use the same novel feature, namely, an adaptive update for the penalty parameter. As with a traditional AL algorithm, the adaptive methods are matrix-free (i.e., they do not need to form or factorize problem matrices) and thus represent a viable option for solving large-scale problems. We prove global convergence for our adaptive AL algorithms and illustrate through extensive numerical experiments that our methods outperform traditional AL methods in terms of efficiency and reliability. In the latter part of the thesis, we focus on a structured nonconvex nonsmooth problem arising from a machine learning application called subspace clustering. We show that the alternating direction method of multipliers (ADMM), which may roughly be described as an application of block-wise coordinate minimization of the AL function, is well suited for this machine learning task. Moreover, we establish a global convergence result for the algorithm since it was previously unknown. Numerical results are presented to show that the chosen optimization modeling formulation together with ADMM can achieve subspace clustering accuracy that is on par with other state-of-the-art methods

Resource Management in Cloud-based Radio Access Networks: a Distributed Optimization Perspective

University of Minnesota Ph.D. dissertation. 2015. Major: Electrical Engineering. Advisor: Zhi-Quan Luo. 1 computer file (PDF); ix, 136 pages.In this dissertation, we consider the base station (BS) and the resource management problems for the cloud-based radio access network (C-RAN). The main difference of the envisioned future 5G network architecture is the adoption of multi-tier BSs to extend the coverage of the existing cellular BSs. Each of the BS is connected to the multi-hop backhaul network with limited bandwidth. For provisioning the network, the cloud centers have been proposed to serve as the control centers. These differences give rise to many practical challenges. The main focus of this dissertation is the distributed strategy across the cloud centers. First, we show that by jointly optimizing the transceivers and determining the active set of BSs, high system resource utilization can be achieved with only a small number of BSs. In particular, we provide efficient distributed algorithms for such joint optimization problem, under the following two common design criteria: i) minimization of the total power consumption at the BSs, and ii) maximization of the system spectrum efficiency. In both cases, we introduce a nonsmooth regularizer to facilitate the activation of the most appropriate BSs, and the algorithms are, respectively, developed with Alternating Direction Method of Multipliers (ADMM) and weighted minimum mean square error (WMMSE) algorithm. In the second part, we further explicitly consider the backhaul limitation issues. We propose an efficient algorithm for joint resource allocation across the wireless links and the flow control over the entire network. The algorithm, which maximizes the utility function of the rates among all the transmitted commodities, is based on a decomposition approach leverages both the ADMM and the WMMSE algorithms. This algorithm is shown to be easily parallelizable within cloud centers and converges globally to a stationary solution. Lastly, since ADMM has been popular for solving large-scale distributed convex optimization, we further consider the issues of the network synchronization across the cloud centers. We propose an ADMM-type implementation that can handle a specific form of asynchronism based on the so-called BSUM-M algorithm, a new variant of ADMM. We show that the proposed algorithm converges to the global optimal solution