Adaptive Domain Abstraction in a Soft-Constraint Message-Passing Algorithm

The computational tasks of model-based diagnosis and planning in embedded systems can be framed as soft-constraint optimization problems with planning costs or state transition probabilities as preferences. Running constraint optimization in embedded systems requires to reduce complexity, which can be achieved by combining dynamic programming message-passing algorithms with message approximation. We found that current approximation approaches such as Mini-Cluster Tree Elimination (MCTE) lack flexibility in adapting to resource limits such as limited memory, e.g. imposed by embedded controllers. We propose a new message approximation method based on the adaptive abstraction of domains and constraints, extending upon MCTE. We argue that our approach can be more flexibly adapted to imposed size limits when applied to constraint optimization problems with big constraints and big domains, which are typical for diagnosis and planning. It is further shown that the adaptation step is itself an optimization problem, which can be relaxed to and solved as a linear optimization problem. From preliminary empirical tests we conclude that the method has potential for diagnosis problems, but is probably limited with regard to binary constraint optimization problems.