I have two questions on branch-bound-and-price.
Why does it sometimes fail? For instance, the paper by Dabia et al shows results where the proposed algorithm fails for some cases. The paper does not explain why it fails. Is it because of the time limit? Or is there any other reason the branch-bound-and-price fail for some problems?
An odd behavior of the branch-bound-and-price algorithm:
I am implementing a branch-bound-and-price algorithm with column generation for an electric vehicle routing problem to minimize a certain cost. I am modifying two software - vrpy and cspy for implementation.
My column generation currently works fine using the labeling algorithm. I know this because when I calculate the duality gap, it converges to 0 in the last iteration when there is no route found with a negative reduced cost.
I have a problem during the branch and bound though. I find that sometimes the parent node in the branch-and-bound search tree has a lower bound on the objective function value that is WORSE than the child node. This means that an additional constraint on the master problem (more bounding) has IMPROVED the objective function value for the child node.
I have double and triple-checked the master problem formulation with bounding but I don't see where it went wrong. It seems to happen when I have a larger network. It also seems to happen more when I have some negative edge costs in the network.
Does anyone know why this would be?