I have a multi-objective optimisation problem. I proposed the use of the 2D bin packing, which is known to be NP-hard. But instead of having multiple bins at a time, only one bin is available, and the model should pack the maximum of items in that bin.
I have three questions: 1/ is the problem still NP-hard even though the use of only one bin?
2/ By adding the second objective in parallel with 2D bin packing, could we conclude that the multi-objective optimization is NP-hard?
3/ Is the proposition of handling the two objectives separately is scientifically correct? Like proposing a model to find the optimal solution for the first objective, then the heuristic for the 2D bin packing to find the second objective optimal solution. And then propose an heuristic handling both objectives.
EDIT: The second objective consists in placing some objects in same position over the bins. So, in summary: given a set of disjoint bins, and several objects that should be packed on each bin, the objective is to place the similar objects between the bins in same position, and in parrallel perform the 2D bin packing for each bin.
Thank you,