Efficient Pre-Solve Algorithms for the Schwerin and Falkenauer_U Bin Packing Benchmark Problems for Getting Optimal Solutions with High Probability

Abstract

Bin Packing is one of the research areas of Operations Research with many industrial applications, as well as rich theoretical impact. In this article, the authors deal with Bin Packing on the practical side: they consider two Bin Packing Benchmark classes. These benchmark problems are often used to check the “usefulness”, efficiency of algorithms. The problem is well-known to be NP-hard. Instead of introducing some exact, heuristic, or approximation method (as usual), the problem is attacked here with some kind of greedy algorithm. These algorithms are very fast; on the other hand, they are not always able to provide optimal solutions. Nevertheless, they can be considered as pre-processing algorithms for solving the problem. It is shown that almost all problems in the considered two benchmark classes are, in fact, easy to solve. In case of the Schwerin class, where there are 200 instances, it is obtained that all instances are solved by the greedy algorithm, optimally, in a very short time. The Falkenauer U class is a little bit harder, but, here, still more than 91% of the instances are solved optimally very fast, with the help of another greedy algorithm. Based on the above facts, the main contribution of the paper is to show that pre-processing is very useful for solving such kinds of problems.