Nogood recording for valued constraint satisfaction problems

Abstract

In the frame of classical constraint satisfaction problems (CSPs), the backtrack tree search, combined with learning methods, presents a double advantage: for static solving, it improves the search speed by avoiding redundant explorations; for dynamic solving (after a slight change of the problem) it reuses the previous searches to build a new solution quickly. Backtrack reasoning concludes the rejection of certain combinatorial choices. Nogood Recording memorizes these choices in order to not reproduce. We aim to use Nogood Recording in the wider scope of the Valued CSP framework (VCSP) to enhance the branch and bound algorithm. Therefore, nogoods are used to increase the lower bound used by the branch and bound to prune the search. This issue leads to the definition of the "Valued Nogoods" and their use. This study focuses particularly on penalty and dynamic VCSPs which require special developments. However our results give an extension of the Nogood Recording to the general VCSP framework.