A Grouping Genetic Algorithm for the Temporal Vector Bin Packing Problem

We consider the temporal vector bin packing problem, which has its origins in the field of cloud computing (Ratushnyi, Kochetov, 2021). Consider a finite collection of items, each associated with arrival and processing times, as well as two distinct weights or dimensions. A specific subset of items is designated as large items. Each bin possesses two capacities or dimensions, and it is partitioned into two identical sections. Large items are required to be split into two equal parts and allocated to both sections of a bin. Other items have the option to be placed in a single section of a bin, provided there is sufficient capacity in both dimensions. The objective is to efficiently fit all items into the least possible number of bins with matching dimensions. To address this challenge, we introduce a grouping genetic algorithm, compare its performance to the Column Generation heuristic, and outline the outcomes of a computational experiment. The evaluation of these algorithms was conducted using a publicly available dataset.