Heuristics for vector bin packing
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Authors: Rina Panigrahy, Kunal Talwar, Lincoln Uyeda, Udi Wieder (MSR)
The resource allocation problem is actually a vector bin packing problem.
Generally, two types of methods can be used to solve this problem. One is based on First Fit Decreasing (FFD) heuristics, and the other is formulated as Integer Linear Program (ILP) (the disadvantage is that it cannot scale).
Item-centric
Sort items in decreasing order of "size".
Place items sequentially in the first bin with sufficient capacity.
Bin-centric
Open one bin at any time.
Place the "largest" item that fits the current bin.
Open a fresh bin if there is no feasible item.
FFDProd:
FFDSum:
FFDAvgSum:
FFDExpSum:
I
and the bin's remaining capacity r(t)
Dot Product: maximize
Norm-based Greedy (): minimize
Grasp and Bubblesearch: choose the -th "largest" item, where is chosen with probability proportional to . Random multiple times and pick the best allocation.