A Lagrange decomposition based Branch and Bound algorithm for the Optimal Mapping of Cloud Virtual Machines

TL;DR

This paper presents a novel Lagrange decomposition based Branch and Bound algorithm for optimally mapping cloud virtual machines to physical hosts, significantly improving solution efficiency and accuracy.

Contribution

It introduces an exact bilinear formulation, develops linear cuts exploiting problem structure, and demonstrates the algorithm's computational advantages over existing methods.

Findings

Valid inequalities close over 80% of the optimality gap.

The proposed B&B algorithm outperforms existing methods in computational experiments.

Numerical results show efficient and accurate optimal mappings.

Abstract

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.