Reasoning and Facts Explanation in Valuation Based Systems
  In the literature, the optimization problem to identify a set of composite
hypotheses H, which will yield the $k$ largest $P(H|S_e)$ where a composite
hypothesis is an instantiation of all the nodes in the network except the
evidence nodes \cite{KSy:93} is of significant interest. This problem is called
"finding the $k$ Most Plausible Explanation (MPE) of a given evidence $S_e$ in
a Bayesian belief network".
  The problem of finding $k$ most probable hypotheses is generally NP-hard
\cite{Cooper:90}. Therefore in the past various simplifications of the task by
restricting $k$ (to 1 or 2), restricting the structure (e.g. to singly
connected networks), or shifting the complexity to spatial domain have been
investigated.
  A genetic algorithm is proposed in this paper to overcome some of these
restrictions while stepping out from probabilistic domain onto the general
Valuation based System (VBS) framework is also proposed by generalizing the
genetic algorithm approach to the realm of Dempster-Shafer belief calculus.
