MILP for the Multi-objective VM Reassignment Problem

TL;DR

This paper evaluates the effectiveness of MILP solvers for the multi-objective VM reassignment problem, demonstrating their limited scalability and proposing a hybrid approach that significantly improves solution quality and quantity.

Contribution

It analyzes conditions under which MILP solvers are effective for this problem and introduces a hybrid method combining MILP with metaheuristics for better results.

Findings

MILP is effective only for small to medium data centers with relaxations.

Hybrid approach yields 126.9% better Pareto solutions than metaheuristics alone.

Hybrid method produces 8.9 times more solutions than MILP alone with minimal time increase.

Abstract

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.