Challenging instances for discrete optimization problems
Résumé
Difficulty in complexity theory reflects worst case performances. However the practice of benchmarking for NP-hard problem is usually based on libraries of sample instances or random generators. We can question the relevance of such instances, in particular, whether they illustrate the actual difficulty of the problem. In our study, we look into some of these sample instances, analyze their hardness and suggest more challenging instances. This leads us to define several criteria to approach the informal concept of instance difficulty.