基于Lagrange分解的云虚拟机最优映射的分枝定界算法
A Lagrange decomposition based Branch and Bound algorithm for the Optimal Mapping of Cloud Virtual Machines
摘要：
云计算的挑战之一是最佳和有效地将虚拟机分配给物理机。电信运营商的目标是在尊重关于位置、分配和容量的约束的同时使映射成本最小化。在本文中，我们首先提出了一个精确的配方导致0-1双线性约束问题。然后利用问题的结构引入了多种线性割，并提出了一种基于Lagrange分解的B&B算法，有效地获得了问题的最优解。数值上，我们表明，我们的有效的不等式关闭超过80%的最优性差距所产生的著名的麦考密克松弛，并证明了所提出的B&B算法与广泛的数值实验的计算优势。
英文摘要：
One of the challenges of cloud computing is to optimally and efficiently assign virtual ma- chines to physical machines. The aim of telecommunication operators is to minimize the map- ping cost while respecting constraints regarding location, assignment and capacity. In this paper we first propose an exact formulation leading to a 0-1 bilinear constrained problem. Then we introduce a variety of linear cuts by exploiting the problem structure and present a Lagrange decomposition based B&B algorithm to obtain optimal solutions efficiently. Numerically, we show that our valid inequalities close over 80% of the optimality gap incurred by the well-known McCormick relaxation, and demonstrate the computational advantage of the proposed B&B algorithm with extensive numerical experiments.
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