At a high level, data centres are large IT facilities hosting physical machines (servers) that often run a large number of virtual machines (VMs)but at a lower level, data centres are an intricate collection of interconnected and virtualised computers, connected services, complex service-level agreements. While data centre managers know that reassigning VMs to the servers that would best serve them and also minimise some cost for the company can potentially save a lot of money-the search space is large and constrained, and the decision complicated as they involve different dimensions. This paper consists of a comparative study of heuristics and exact algorithms for the Multi-objective Machine Reassignment problem. Given the common intuition that the problem is too complicated for exact resolutions, all previous works have focused on various (meta)heuristics such as First-Fit, GRASP, NSGA-II or PLS. In this paper, we show that the state-of-art solution to the single objective formulation of the problem (CBLNS) and the classical multi-objective solutions fail to bridge the gap between the number, quality and variety of