Towards a Characterization of Difficult Instances of the Bin Packing Problem

We address the multidimensional characterization of difficult instances of the Bin Packing Problem, well known in the combinatorial optimization realm. In search for efficient procedures to solve hard combinatorial optimization problems previous investigations have attempted to identify the instances´ characteristics with the greatest impact in their difficulty. In the same vein and focusing on the Bin Packing Problem, we used clustering techniques to determine not only one but a set of characteristics that altogether could be considered as the main source of the instances difficulty. To this aim we selected 1,615 available instances of the Bin Packing Problem, and then we solved each instance with six well-known heuristic algorithms. From our experiment we identified relevant characteristics that correspond to 22 instances whose optimal solution was not obtained by any of the six heuristics. Finally, to validate our findings an adhoc heuristic based on these characteristics was developed. Our heuristic found two optimal solutions not previously reported, showing thus that this characterization can help to find improved solution algorithms.