Fast divide-and-conquer algorithms for preemptive scheduling problems with controllable processing times – A polymatroid optimization approach

We consider a variety of preemptive scheduling problems with controllable processing times on a single machine and on identical/uniform parallel machines, where the objective is to minimize the total compression cost. In this paper, we propose fast divide-and-conquer algorithms for these scheduling problems. Our approach is based on the observation that each scheduling problem we discuss can be formulated as a polymatroid optimization problem. We develop a novel divide-and-conquer technique for the polymatroid optimization problem and then apply it to each scheduling problem. We show that each scheduling problem can be solved in O(Tfeas(n) log n) time by using our divide-and-conquer technique, where n is the number of jobs and Tfeas(n) denotes the time complexity of the corresponding feasible scheduling problem with n jobs. This approach yields faster algorithms for most of the scheduling problems discussed in this paper

Approximation Algorithms for Energy Minimization in Cloud Service Allocation under Reliability Constraints

We consider allocation problems that arise in the context of service allocation in Clouds. More specifically, we assume on the one part that each computing resource is associated to a capacity constraint, that can be chosen using Dynamic Voltage and Frequency Scaling (DVFS) method, and to a probability of failure. On the other hand, we assume that the service runs as a set of independent instances of identical Virtual Machines. Moreover, there exists a Service Level Agreement (SLA) between the Cloud provider and the client that can be expressed as follows: the client comes with a minimal number of service instances which must be alive at the end of the day, and the Cloud provider offers a list of pairs (price,compensation), this compensation being paid by the Cloud provider if it fails to keep alive the required number of services. On the Cloud provider side, each pair corresponds actually to a guaranteed success probability of fulfilling the constraint on the minimal number of instances. In this context, given a minimal number of instances and a probability of success, the question for the Cloud provider is to find the number of necessary resources, their clock frequency and an allocation of the instances (possibly using replication) onto machines. This solution should satisfy all types of constraints during a given time period while minimizing the energy consumption of used resources. We consider two energy consumption models based on DVFS techniques, where the clock frequency of physical resources can be changed. For each allocation problem and each energy model, we prove deterministic approximation ratios on the consumed energy for algorithms that provide guaranteed probability failures, as well as an efficient heuristic, whose energy ratio is not guaranteed

Scheduling reentrant jobs on parallel machines with a remote server

This paper explores a specific combinatorial problem relating to re-entrant jobs on parallel primary machines, with a remote server machine. A middle operation is required by each job on the server before it returns to its primary processing machine. The problem is inspired by the logistics of a semi-automated micro-biology laboratory. The testing programme in the laboratory corresponds roughly to a hybrid flowshop, whose bottleneck stage is the subject of study. We demonstrate the NP-hard nature of the problem, and provide various structural features. A heuristic is developed and tested on randomly generated benchmark data. Results indicate solutions reliably within 1.5% of optimum. We also provide a greedy 2-approximation algorithm. Test on real-life data from the microbiology laboratory indicate a 20% saving relative to current practice, which is more than can be achieved currently with 3 instead of 2 people staffing the primary machines

Solving Lotsizing Problems on Parallel Identical Machines Using Symmetry Breaking Constraints

Production planning on multiple parallel machines is an interesting problem, both from a theoretical and practical point of view. The parallel machine lotsizing problem consists of finding the optimal timing and level of production and the best allocation of products to machines. In this paper we look at how to incorporate parallel machines in a Mixed Integer Programming model when using commercial optimization software. More specifically, we look at the issue of symmetry. When multiple identical machines are available, many alternative optimal solutions can be created by renumbering the machines. These alternative solutions lead to difficulties in the branch-and-bound algorithm. We propose new constraints to break this symmetry. We tested our approach on the parallel machine lotsizing problem with setup costs and times, using a network reformulation for this problem. Computational tests indicate that several of the proposed symmetry breaking constraints substantially improve the solution time, except when used for solving the very easy problems. The results highlight the importance of creative modeling in solving Mixed Integer Programming problems.Mixed Integer Programming;Formulations;Symmetry;Lotsizing

A Genetic Algorithm for Power-Aware Virtual Machine Allocation in Private Cloud

Energy efficiency has become an important measurement of scheduling algorithm for private cloud. The challenge is trade-off between minimizing of energy consumption and satisfying Quality of Service (QoS) (e.g. performance or resource availability on time for reservation request). We consider resource needs in context of a private cloud system to provide resources for applications in teaching and researching. In which users request computing resources for laboratory classes at start times and non-interrupted duration in some hours in prior. Many previous works are based on migrating techniques to move online virtual machines (VMs) from low utilization hosts and turn these hosts off to reduce energy consumption. However, the techniques for migration of VMs could not use in our case. In this paper, a genetic algorithm for power-aware in scheduling of resource allocation (GAPA) has been proposed to solve the static virtual machine allocation problem (SVMAP). Due to limited resources (i.e. memory) for executing simulation, we created a workload that contains a sample of one-day timetable of lab hours in our university. We evaluate the GAPA and a baseline scheduling algorithm (BFD), which sorts list of virtual machines in start time (i.e. earliest start time first) and using best-fit decreasing (i.e. least increased power consumption) algorithm, for solving the same SVMAP. As a result, the GAPA algorithm obtains total energy consumption is lower than the baseline algorithm on simulated experimentation.Comment: 10 page