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In this paper we present extensions to the original adaptive Parallel Tempering algorithm. Two different approaches are presented. In the first one we introduce state-dependent strategies using current information to perform a swap step. It encompasses a wide family of potential moves including the standard one and Equi-Energy type move, without any loss in tractability. In the second one, we introduce online trimming of the number of temperatures. Numerical experiments demonstrate the effectiveness of the proposed method.

State-dependent swap strategies and automatic reduction of number of temperatures in adaptive parallel tempering algorithm