The Complexity of Computing Optimal Assignments of Generalized   Propositional Formulae
  We consider the problems of finding the lexicographically minimal (or maximal) satisfying assignment of propositional formulae for different restricted formula classes. It turns out that for each class from our framework, the above problem is either polynomial time solvable or complete for OptP. We also consider the problem of deciding if in the optimal assignment the largest variable gets value 1. We show that this problem is either in P or P^NP complete. 
Steffen Reith and Heribert Vollmer