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In WDM rings, determining minimum number of ADMs is NP-hard. The best known algorithm namely, breadth first least interference (BFLI) heuristic gives optimal results in only 77% cases. In this paper, we analyze the problem and suggest a new set covering formulation for minimizing the number of ADMs in WDM rings and propose a new generic search algorithm namely uninformed best first search (UBFS) algorithm. UBFS always returns an optimal solution. We show through experiments that UBFS solves moderate sized problems in reasonable amount of execution time. We show that the output of BFLI heuristic is input order dependent. We make detailed error analysis of BFLI and suggest a modified BFLI which is input order independent and on the whole performs at least as good as BFLI.