Influence of Variables Encoding and Symmetry Breaking on the Performance of Optimization Modulo Theories Tools Applied to Cloud Resource Selection

14 pages•Published: November 18, 2018

Madalina Erascu, Flavia Micota and Daniela Zaharie

Abstract

The problem of Cloud resource provisioning for component-based applications is very important. It consists in the allocation of virtual machines (VMs) from various Cloud Providers (CPs), to a set of applications such that the constraints induced by the inter- actions between components and by the components hardware/software requirements are satisfied and the performance objectives are optimized (e.g. costs are minimized). It can be formulated as a constrained optimization problem and tackled by state-of-the-art optimization modulo theories (OMT) tools. The performance of the OMT tools is highly dependent on the way the problem is formalized as this determines the size of the search space. In the case when the number of VMs offers is large, a naive encoding which does not exploit the symmetries of the underlying problem leads to a huge search space making the optimization problem intractable. We overcame this issue by reducing the search space by using: (1) a heuristic which exploits the particularities of the application by detect- ing cliques in the conflict graph of the application components fixing all components of the clique with the largest number of component instances, and (2) a lex-leader method for breaking variable symmetry where the canonical solution fulfills an order based on either the number of components deployed on VMs, or on the VMs price. As the result, the running time of the optimization problem improves considerably and the optimization problem scales up to hundreds of VM offers. We also observed that by combining the heuristic with the lex-leader method we obtained better computational results than by using them separately, suggesting the fact that symmetry breaking constraints have the advantage of interacting well with the search heuristic being used.

In: Gilles Barthe, Konstantin Korovin, Stephan Schulz, Martin Suda, Geoff Sutcliffe and Margus Veanes (editors). LPAR-22 Workshop and Short Paper Proceedings, vol 9, pages 1-14.

Links:	https://easychair.org/publications/paper/3PPV
	https://doi.org/10.29007/zwdh

BibTeX entry

@inproceedings{LPAR-IWIL2018:Influence_Variables_Encoding_Symmetry,
  author    = {Madalina Erascu and Flavia Micota and Daniela Zaharie},
  title     = {Influence of Variables Encoding and Symmetry Breaking on the Performance of Optimization Modulo Theories Tools Applied to Cloud Resource Selection},
  booktitle = {LPAR-22 Workshop and Short Paper Proceedings},
  editor    = {Gilles Barthe and Konstantin Korovin and Stephan Schulz and Martin Suda and Geoff Sutcliffe and Margus Veanes},
  series    = {Kalpa Publications in Computing},
  volume    = {9},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2515-1762},
  url       = {/publications/paper/3PPV},
  doi       = {10.29007/zwdh},
  pages     = {1-14},
  year      = {2018}}

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