A Two-Stage Algorithm for the Dynamic Bin Packing Problemwith Placement Groups

A new dynamic bin packing problem relevant to cloud computing is considered. The creation time, deletion time, and required resources are known for each item (virtual machine). The containers (servers) have a NUMA architecture and specific rules for placing the machines. The servers are grouped into racks, and some machines form groups. Each group is divided into partitions. Machines from different partitions cannot be placed on the same rack to ensure system fault tolerance. The objective is to pack all the machines into the minimum number of racks over a given planning horizon. A two-stage algorithm is developed to solve the problem: an initial solution is constructed, where some constraints may be violated, followed by iterative improvement using local search aimed at eliminating the violations. Using the proposed approach, an average deviation of 3.8% from the lower bound was achieved on open test cases.