A cardinality constrained iterated local search for the virtual machine placement problem

The virtual machine placement (VMP) problem is a critical task in the field of cloud computing. The assignment of virtual machines to physical machines affects the quality of cloud services and running cost. Given a set of physical machines with certain capacities and a set of virtual machines with requirements, VMP aims to allocate each virtual machine to a capacity constrained physical machine in such a way that the total number of the physical machines used is minimized while their usage does not exceed the capacity. In this study, a cardinality constrained iterated local search algorithm is proposed to solve the VMP problem by transforming VMP into a sequence of cardinality-constrained problems, where each problem involves a fixed number $k$ of physical machines. The algorithm uses the tabu search procedure for solution improvement, which exploits two new neighborhoods based on dedicated evaluation functions for neighboring solution selection. In addition, it uses a simple perturbation strategy to prevent the algorithm from search stagnation. Numerical results show that the proposed algorithm is highly competitive in both solution quality and computational efficiency, compared to several state-of-the-art algorithms on 18 subsets of 1800 widely used benchmark instances. Specifically, the algorithm reports the best results in terms of the average objective values on 17 out of 18 instance subsets with a short run time of 5 s. Importantly, using the lower bounds, it proves for the first time the optimality of solutions for 1390 instances. We study the impact of the key components of the algorithm on its performance.