General purpose heuristics for integer programming – Part I

In spite of the many special purpose heuristics for specific classes of integer programming (IP) problems, there are few developments that focus on general purpose integer programming heuristics. This stems partly from the perception that general purpose methods are likely to be less effective than specialized procedures for specific problems, and partly from the perception that there is no unifying theoretical basis for creating general purpose heuristics. Still, there is a general acknowledgment that methods which are not limited to solving IP problems on a ‘class by class’ basis, but which apply to a broader range of problems, have significant value. We show that certain ideas proposed in the 1970s, which are often overlooked, can be reformulated and linked with more recent developments to give a useful theoretical framework for generating general purpose IP heuristics. This framework, which has the appeal of being highly visual, makes use of cutting plane derivations that also give a natural basis for marrying heuristics with extra branch and cut methods for integer programming problems.