On the convergence of computational methods for the online bin stretching problem

Online bin stretching is an online packing problem where some of the best known lower and upper bounds were found through computational searches. The limiting factor in obtaining better bounds with such methods is the computational time allowed. However, there is still no theoretical guarantee that such methods do converge towards the optimal online performance. This paper shows that such methods do, in fact, converge; moreover, bounds on the gap to the optimal are also given. These results frame a theoretical foundation for the convergence of computational approaches for online problems.