A Framework for Quasi-exact Optimization Using Relaxed Best-First Search

Abstract

Abstract. In this paper, a framework for previous and new quasi-exact extensions of the A * -algorithm is presented. In contrast to previous approaches, the new methods guarantee to expand every state at most once if guided by a socalled monotone heuristic. By that, they account more effectively for aspects of run time while still guaranteeing that the cost of the solution will not exceed the optimal cost by a certain factor. First a general upper bound for this factor is derived. This bound iswhere N is (an upper bound on) the maximum depth of the search. Next, we look at specific instances of the algorithm class described by our framework. For one of the new methods a linear, i.e. much tighter upper bound is obtained: the cost of the solution will not exceed the optimal cost by a factor greater than 1 + . The parameter ≥ 0 can be chosen by the user. Within a range of reasonable choices for , all new methods allow the user to trade off run time for solution quality. Besides that, the formal framework also serves for a comparison in terms of other algorithmic properties of interest, e.g. in terms of a necessary condition for state expansion. The results of experiments targeting the minimization of Binary Decision Diagrams (BDDs) demonstrate large reductions in run time when compared to the best known exact approach for BDD minimization and to previous relaxation methods. Moreover, the quality of the obtained solutions is often much better than the quality guaranteed by the theory.