I wrote a branch and bound algorithm for the bin packing problem and now I would like to know when exactly it stops giving solutions in a polynomial time.
I have N items (each item i has a volume Vi) and each bin has a volume V.
I tested the output of the algorithm and the execution time while varying the number of items N , the total volume of items Vtotal and the bin's volume V too.
What I noticed is that the termination criterion of the B&B algorithm does not depend only on N , it also depends on Vtotal and V .
For instance, if I have:
N = 18
Vtotal = 18
V = 8
The algorithm works fine and I get the output I want in a polynomial time (few milliseconds)
But , If I have :
N = 18
Vtotal = 18
V = 14
I don't get an output.
same for this test instance:
N = 18
Vtotal = 21
V = 14
(If Vtotal = 25 I get a solution in few milliseconds)
What I need to know is : Is there a way (for example, assemble the three parameters in one formula) to know when exactly I don't get a solution in a polynomial time?
Thank you
