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Translucent networks utilize sparse placements of optical-electronic-optical (O/E/O) 3R (reamplification, reshaping, and retiming) regenerators to improve the cost effectiveness and energy efficiency of wavelength-routed optical transport networks. In this paper, we show that the energy cost of a translucent network can be further reduced by leveraging the energy efficiency of all-optical 2R (reamplification and reshaping) regenerators. We propose a translucent network infrastructure that uses all-optical 2R regenerators to partially replace O/E/O 3R regenerators and implements mixed regenerator placements (MRP). We first consider the problem of MRP along a single given path, and propose three path-based impairment-aware MRP algorithms, based on periodic placement, genetic algorithm (GA), and ant colony optimization (ACO). We then address the offline network planning problem and develop a heuristic algorithm. By incorporating with one of the proposed MRP algorithms, the heuristic can achieve joint optimization of MRP and routing and wavelength assignment for high energy efficiency. We design simulations to compare the performance of different offline network planning scenarios and to see which one can provide the best balance between quality of transmission and energy cost. Simulation results show that the algorithm achieves 58.91-73.62% saving on regeneration energy, compared to the traditional scheme without all-optical 2R regenerators. The results also indicate that the joint optimization using the MRP-GA obtains the best network planning in terms of energy efficiency. Finally, we address the problem of online provisioning, and propose several algorithms to serve dynamic lightpath requests in translucent networks with MRP, and implement them in simulations to compare their performance in terms of blocking probability. Simulation results indicate that the online provisioning algorithm that utilizes the combination of the MRP-GA and a multiple MRP scheme achieves - he lowest blocking probability.