1,044 research outputs found
Generalized Totalizer Encoding for Pseudo-Boolean Constraints
Pseudo-Boolean constraints, also known as 0-1 Integer Linear Constraints, are
used to model many real-world problems. A common approach to solve these
constraints is to encode them into a SAT formula. The runtime of the SAT solver
on such formula is sensitive to the manner in which the given pseudo-Boolean
constraints are encoded. In this paper, we propose generalized Totalizer
encoding (GTE), which is an arc-consistency preserving extension of the
Totalizer encoding to pseudo-Boolean constraints. Unlike some other encodings,
the number of auxiliary variables required for GTE does not depend on the
magnitudes of the coefficients. Instead, it depends on the number of distinct
combinations of these coefficients. We show the superiority of GTE with respect
to other encodings when large pseudo-Boolean constraints have low number of
distinct coefficients. Our experimental results also show that GTE remains
competitive even when the pseudo-Boolean constraints do not have this
characteristic.Comment: 10 pages, 2 figures, 2 tables. To be published in 21st International
Conference on Principles and Practice of Constraint Programming 201
Optimising for energy or robustness? Trade-offs for VM consolidation in virtualized datacenters under uncertainty
The final publication is available at Springer via http://dx.doi.org/10.1007/s11590-016-1065-xReducing the energy consumption of virtualized datacenters and the Cloud is very important in order to lower CO2 footprint and operational cost of a Cloud operator. However, there is a trade-off between energy consumption and perceived application performance. In order to save energy, Cloud operators want to consolidate as many Virtual Machines (VM) on the fewest possible physical servers, possibly involving overbooking of resources. However, that may involve SLA violations when many VMs run on peak load. Such consolidation is typically done using VM migration techniques, which stress the network. As a consequence, it is important to find the right balance between the energy consumption and the number of migrations to perform. Unfortunately, the resources that a VM requires are not precisely known in advance, which makes it very difficult to optimise the VM migration schedule. In this paper, we therefore propose a novel approach based on the theory of robust optimisation. We model the VM consolidation problem as a robust Mixed Integer Linear Program and allow to specify bounds for e.g. resource requirements of the VMs. We show that, by using our model, Cloud operators can effectively trade-off uncertainty of resource requirements with total energy consumption. Also, our model allows us to quantify the price of the robustness in terms of energy saving against resource requirement violations.Peer ReviewedPostprint (author's final draft
Cloud engineering is search based software engineering too
Many of the problems posed by the migration of computation to cloud platforms can be formulated and solved using techniques associated with Search Based Software Engineering (SBSE). Much of cloud software engineering involves problems of optimisation: performance, allocation, assignment and the dynamic balancing of resources to achieve pragmatic trade-offs between many competing technical and business objectives. SBSE is concerned with the application of computational search and optimisation to solve precisely these kinds of software engineering challenges. Interest in both cloud computing and SBSE has grown rapidly in the past five years, yet there has been little work on SBSE as a means of addressing cloud computing challenges. Like many computationally demanding activities, SBSE has the potential to benefit from the cloud; âSBSE in the cloudâ. However, this paper focuses, instead, of the ways in which SBSE can benefit cloud computing. It thus develops the theme of âSBSE for the cloudâ, formulating cloud computing challenges in ways that can be addressed using SBSE
Local to Global: A Distributed Quantum Approximate Optimization Algorithm for Pseudo-Boolean Optimization Problems
With the rapid advancement of quantum computing, Quantum Approximate
Optimization Algorithm (QAOA) is considered as a promising candidate to
demonstrate quantum supremacy, which exponentially solves a class of Quadratic
Unconstrained Binary Optimization (QUBO) problems. However, limited qubit
availability and restricted coherence time challenge QAOA to solve large-scale
pseudo-Boolean problems on currently available Near-term Intermediate Scale
Quantum (NISQ) devices. In this paper, we propose a distributed QAOA which can
solve a general pseudo-Boolean problem by converting it to a simplified Ising
model. Different from existing distributed QAOAs' assuming that local solutions
are part of a global one, which is not often the case, we introduce community
detection using Louvian algorithm to partition the graph where subgraphs are
further compressed by community representation and merged into a higher level
subgraph. Recursively and backwards, local solutions of lower level subgraphs
are updated by heuristics from solutions of higher level subgraphs. Compared
with existing methods, our algorithm incorporates global heuristics into local
solutions such that our algorithm is proven to achieve a higher approximation
ratio and outperforms across different graph configurations. Also, ablation
studies validate the effectiveness of each component in our method.Comment: 12 pages, 6 figure
Allocation of Virtual Machines in Cloud Data Centers - A Survey of Problem Models and Optimization Algorithms
Data centers in public, private, and hybrid cloud settings make it possible to provision virtual machines
(VMs) with unprecedented flexibility. However, purchasing, operating, and maintaining the underlying physical
resources incurs significant monetary costs and also environmental impact. Therefore, cloud providers must
optimize the usage of physical resources by a careful allocation of VMs to hosts, continuously balancing between
the conflicting requirements on performance and operational costs. In recent years, several algorithms have been
proposed for this important optimization problem. Unfortunately, the proposed approaches are hardly comparable
because of subtle differences in the used problem models. This paper surveys the used problem formulations and
optimization algorithms, highlighting their strengths and limitations, also pointing out the areas that need further
research in the future
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