Scaling Optimal Allocation of Cloud Resources Using Lagrange Relaxation

The rapid growth of Cloud Computing (CC) has increased the variety of computing resources, storage, and communication services that pose significant new challenges for the efficient use of cloud resources. The cost-efficient allocation of cloud resources has become a decisive premise for the adoption of CC services. The cost-efficient selection and scheduling of these resources to meet the demands of a scientific workflow is a challenging problem that is exacerbated by the inclusion of multiple CC providers. In this paper, we present a new strategy for the cost-efficient selection of CC resources using Lagrange relaxation. Our approach is based on preselection of resources and demand decomposition to create a series of smaller sub-problems, which allow the estimation of the best cost-structures and selection of CC service providers for a subset of the time period of the planning horizon. Decomposition of the demand is achieved through the boundary analysis of a continuous relaxation of the problem. Using the metrics defined in terms of the cost and time of completion, we demonstrate excellent performance with respect to optimal solutions. Our method reduced the computational time from hours to seconds for a representative 36-month problem and provided high-quality solutions (<0.05% relative error). Given the importance of selecting resources and scheduling complex scientific workflows, we believe that this novel strategy will be beneficial for many researchers and users of cloud computing resources.