New high performance algorithmic solution for diagnosis problem

We propose an algorithmic approach and present an algorithm for solving the diagnosis problem. We report the results of the performance tests of the new algorithm and compare them with the traditional and standard algorithms. These results show the strong performance of our new algorithm with more than ten times improvement over the traditional approach. The most widely used approach to model-based diagnosis consists of a two-step process: (1) generating conflict sets from symptoms; (2) calculating minimal diagnosis set from the conflicts. Here a conflict set is a set of assumption on the modes of some components that is not consistent with the model of the system and observations, and a minimal diagnosis is a set of the consistent assumptions of the modes of all components with minimal number of abnormal components. However, there are major drawbacks in the current model-based diagnosis techniques in efficiently performing the above two steps that severely limit their practical application to many systems of interest. For conflict generating problem, these techniques are usually based on different versions of truth maintenance method, which lead to an exhaustive search in the space of possible modes of the components. For finding minimal diagnosis from the conflicts, the most common is based on Reiter's algorithm, which requires both exponential time and exponential space (memory) for implementation. In this paper we address the problem of generating the minimal diagnosis from the conflicts. This problem can be formulated as the well-known hitting set problem. Our approach starts by mapping the hitting set problem onto the integer programming problem that enables us, for the first time, a priori determination of the lower and upper bounds on the size of the solution. Based on these bounds, we introduce a new concept of solution window for the problem. We also propose a new branch-and-bound technique that not only is faster than the current techniques in terms of number of operations (by exploiting the structure of the problem) but also, using the concept of window, allows a massive reduction (pruning) in the number of branches. Furthermore, as the branch-and-bound proceeds, the solution window is dynamically updated and narrowed to enable further pruning. We present the results of the performance of the new algorithm on a set of test cases. These results clearly show the advantage of our new algorithm over the traditional branch-and-bound algorithm; more specifically the new algorithm has achieved several orders of magnitude speedup over the standard algorithm. For example, for the systems with 40 components, the new algorithm, in average, solves the problem more than 300 times faster than the traditional algorithm