多目标VM重分配问题的MILP
MILP for the Multi-objective VM Reassignment Problem
摘要：
机器再分配是约束规划（CP）和混合整数线性规划（MILP）方法的一个具有挑战性的问题，特别是在数据中心规模较大的情况下。机器重分配问题的多目标版本更具挑战性，CP或MILP似乎不太可能在这种情况下获得好的结果。因此，解决这个问题的第一种方法是基于其他优化方法，包括元分析。在本文中，我们研究在何种条件下的混合整数优化求解器，如IBM的CPLEX，可以用于多目标机器重分配问题。我们表明，它是有用的，只有小型或中型的数据中心和一些放宽，如最优性公差差距和有限数量的方向探索的搜索空间。在这项研究的基础上，我们还研究了一种混合方法，用CPLEX的结果喂养一个元启发式，我们表明，收益在帕累托解决方案集的质量方面是重要的（单独使用元启发式算法时为+126.9%，单独使用CPLEX时为+17.8%）和解决方案数量（比CPLEX多8.9倍），而对于大于100秒的执行时间，与CPLEX相比，处理时间仅增加6%。
英文摘要：
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.
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