A Kernel search algorithm for virtual machine consolidation problem in cloud computing

Virtual machine consolidation refers to the process of reallocating virtual machines across a set of target servers. It can be formulated as a mixed integer linear programming problem, which is known to be NP-hard. In this paper, we propose a kernel search (KS) heuristic algorithm based on hard variable fixing to quickly obtain high-quality solutions for large-scale virtual machine consolidation problems (VMCPs). Since existing variable fixing strategies in KS algorithms may result in some VMCP instances being infeasible, our proposed KS algorithm employs a more efficient strategy to choose a set of fixed variables based on their corresponding reduced costs. Our numerical results on VMCP instances demonstrate that our proposed KS algorithm significantly outperforms mixed integer linear programming solvers in terms of CPU time. Moreover, our proposed strategy of variable fixing improves the efficiency of the KS algorithm significantly, with negligible degradation in solution quality.