Automated deployment of component-based applications in the Cloud consists in the allocation of virtual machines (VMs) offers from various Cloud Providers such that the constraints induced by the interactions 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 constraint optimization problem, hence, in principle, the optimization can be carried out automatically. In the case the set of VM offers is large (several hundreds), the computational requirement is huge, making the automatic optimization practically impossible with the current general optimization modulo theory (OMT) and mathematical programming (MP) tools. We overcame the difficulty by methodologically analyzing the particularities of the problem with the aim of identifying search space reduction methods. These are methods exploiting: (i) the symmetries of the general Cloud deployment problem, (ii) the graph representation associated to the structural constraints specific to each particular application, and (iii) their combination. An extensive experimental analysis has been conducted on four classes of real-world problems, using six symmetry breaking strategies and two types of optimization solvers.

As a result, the combination of a variable reduction strategy with a column-wise symmetry breaker leads to a scalable deployment solution, when OMT is used to solve the resulting optimization problem.

自动部署基于组件的应用程序云中的功能在于分配来自各种云提供商的虚拟机（VM）产品，从而满足由组件之间的交互以及组件的硬件/软件要求引起的约束，并优化了性能目标（例如，成本最小化） 。它可以表述为约束优化问题，因此，原则上可以自动进行优化。在VM提供的集合很大（数百个）的情况下，计算需求很大，这使得使用当前的一般优化模理论（OMT）和数学编程（MP）工具实际上无法进行自动优化。我们通过方法上分析问题的特殊性来克服困难，目的是确定搜索空间的减少方法。（i）一般云部署问题的对称性，（ii）与特定于每个特定应用程序的结构约束相关联的图形表示，以及（iii）它们的组合。使用六种对称破坏策略和两种类型的优化求解器，对四类现实问题进行了广泛的实验分析。

结果，当使用OMT解决最终的优化问题时，将变量减少策略与列式对称断路器结合使用，即可提供可扩展的部署解决方案。