As expected, COBRA obtained a very

As expected, COBRA obtained a very high gap contrary to the other implementations. GA+AGH has tighter gap except for the instance (100,30). In fact, all algorithms have difficulties for this very specific instance. Not surprisingly, GA+H1H2 has better results than GA+H2 but worse than GA+H1. The difference between the results proposed by COBRA and the bounds computed directly through the UL-gap shows how a bad approximation can have strong implications on the upper-level objective function. One should not forget that the algorithm maximizes the profits. If the profits are too optimistic, the solver will continue to misinterpret results and will increase the deviations. This justifies and validates our first proposition to train heuristics for unseen lower-level instances with the aim of making them less sensitive and more general (robust) to solve different lower-level instances.