A Set-Covering Based Heuristic Approach for Bin-Packing Problems

Several combinatorial optimization problems can be formulated as large set-covering problems. In this work, we use the set-covering formulation to obtain a general heuristic algorithm for this type of problem, and describe our implementation of the algorithm for solving two variants of the well-known (one-dimensional) bin-packing problem: the two-constraint bin-packing problem and the basic version of the two-dimensional bin-packing problem, where the objects cannot be rotated and no additional requirements are imposed. In our approach, both the “column-generation” and the “column-optimization” phases are heuristically performed. In particular, in the first phase, we do not generate the entire set of columns, but only a small subset of it, by using greedy procedures and fast constructive heuristic algorithms from the literature. In the second phase, we solve the associated set-covering instance by means of a Lagrangian-based heuristic algorithm. Extensive computational results on test instances from the literature show that, for the two considered problems, this approach is competitive, with respect to both the quality of the solution and the computing time, with the best heuristic and metaheuristic algorithms proposed so far.