Multi-objective virtual machine (VM) placement is a powerful tool, which can achieve different goals in data centers. It is an NP-hard problem, and various works have been proposed to solve it. However, almost all of them ignore the selection of weights. The selection of weights is difficult, but it is essential for multi-objective optimization. The inappropriate weights will cause the obtained solution set deviating from the Pareto optimal set. Fortunately, we find that this problem can be easily solved by using the Chebyshev scalarization function in multi-objective reinforcement learning (RL). In this paper, we propose a VM placement algorithm based on multi-objective RL (VMPMORL). VMPMORL is designed based on the Chebyshev scalarization function. We aim to find a Pareto approximate set to minimize energy consumption and resource wastage simultaneously. Compared with other multi-objective RL algorithms in the field of VM placement, VMPMORL not only uses the concept of the Pareto set but also solves the weight selection problem. Finally, VMPMORL is compared with some state-of-the-art algorithms in recent years. The results show that VMPMORL can achieve better performance than the approaches above.

多目标虚拟机（VM）放置是一个功能强大的工具，可以在数据中心中实现不同的目标。这是一个NP难题，已经提出了各种解决方案。但是，几乎所有人都忽略了权重的选择。权重的选择很困难，但是对于多目标优化来说是必不可少的。不合适的权重将导致获得的解集偏离Pareto最优集。幸运的是，我们发现在多目标强化学习（RL）中使用Chebyshev标量函数可以轻松解决此问题。在本文中，我们提出了一种基于多目标RL（VMPMORL）的VM放置算法。VMPMORL是基于Chebyshev标量函数设计的。我们旨在找到一个帕累托近似集，以最大程度地减少能源消耗和资源浪费。与VM放置领域中的其他多目标RL算法相比，VMPMORL不仅使用了帕累托集的概念，而且还解决了权重选择问题。最后，将VMPMORL与近年来的一些最新算法进行了比较。结果表明，VMPMORL可以实现比上述方法更好的性能。