I am investigating heuristics for optimising the packing a fixed number of knapsacks with a set of items of defined weights, however the knapsacks do not have a defined capacity limit. The objective of the optimisation is instead to find a configuration which minimises the difference in weights between the loaded knapsacks.
This differs from the traditional bin packing problem as it does not have an unlimited number of bins.
This seems to be a variant of the task scheduling problem, without a requirement for ordering.
Is there an existing name for this variant of the knapsack problem? Is it just the multiprocessor scheduling problem?