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The Annealing Adaptive Search (AAS) algorithm searches the feasible region of an optimization problem by generating candidate solutions from a sequence of Boltzmann distributions. However, the difficulty of sampling from a Boltzmann distribution at each iteration of the algorithm limits its applications to practical problems. To address this difficulty, we propose an approximation of AAS, called Model-based Annealing Random Search (MARS), that samples solutions from a sequence of surrogate distributions that iteratively approximate the target Boltzmann distributions. We present the global convergence properties of MARS by exploiting its connection to the stochastic approximation method and report on numerical results.