We consider the problem of constructing optimal and near-optimal multiple fault diagnosis (MFD) in bipartite systems with unreliable (imperfect) tests. It is known that exact computation of conditional probabilities for MFD is NP hard. The novel feature of our diagnostic algorithms is the use of Lagrangian relaxation and subgradient optimization methods to provide: 1) near optimal solutions for the MFD problem and 2) upper bounds for an optimal branch and bound algorithm. The proposed method is illustrated using several examples. Computational results indicate the following: 1) our algorithm has superior computational performance to the existing algorithms (approximately three orders of magnitude improvement over the algorithm by Z. Binglin et al. (1993)); 2) near optimal algorithm generates the most likely candidates with a very high accuracy; 3) our algorithm can find the most likely candidates in systems with as many as 1000 faults.
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