  Machine Reassignment is a challenging problem for constraint programming (CP)
and mixed-integer linear programming (MILP) approaches, especially given the
size of data centres. The multi-objective version of the Machine Reassignment
Problem is even more challenging and it seems unlikely for CP or MILP to obtain
good results in this context. As a result, the first approaches to address this
problem have been based on other optimisation methods, including
metaheuristics. In this paper we study under which conditions a mixed-integer
optimisation solver, such as IBM ILOG CPLEX, can be used for the
Multi-objective Machine Reassignment Problem. We show that it is useful only
for small or medium-scale data centres and with some relaxations, such as an
optimality tolerance gap and a limited number of directions explored in the
search space. Building on this study, we also investigate a hybrid approach,
feeding a metaheuristic with the results of CPLEX, and we show that the gains
are important in terms of quality of the set of Pareto solutions (+126.9%
against the metaheuristic alone and +17.8% against CPLEX alone) and number of
solutions (8.9 times more than CPLEX), while the processing time increases only
by 6% in comparison to CPLEX for execution times larger than 100 seconds.
