Exploiting the implications of choices in set partitioning

Computational experience so far has shown that on set partitioning problems of the scheduling type, forward checking considers far fewer partial solutions than does the Garfinkel and Nemhauser algorithm. However, since it seems unlikely that these algorithms could compete with mathematical programming methods when applied to problems of the size occurring in scheduling applications, the main interest in comparing the implicit enumeration and forward checking algorithms is in the differences they demonstrate between the OR and AI approaches. The OR methods concentrate on using the cost information, because of the emphasis on finding the minimum cost solution, whereas the AI approach sees this kind of problem in terms of searching a tree structure, and any kind of information which can prune the tree and so reduce the extent of the search is pressed into service