A replica exchange Markov Chain Monte Carlo (MCMC) engine is developed with automatic temperature adjustment for solving combinatorial optimization problems by minimizing the energy of the Ising model. The automatic temperature adjustment scheme ensures that the MCMC process is optimized at every stage of the execution. This approach is performed by dynamically adjusting temperatures of all replicas, based on the properties of any given problem, in addition to the capability of automatically inserting new replicas or removing any existing replicas to achieve the best possible resource efficiency and execution time. The proposed algorithm is integrated with parallel evaluation of energy increment and update scheme. The engine is implemented on the FPGA platform with a capacity of running up to 42 replicas in pipeline, each running 1024 fully-connected Ising spins in parallel. The performance of the hardware is examined with three different classes of problems, Vertex Cover, Maximum-Cut, and Travelling Salesman using the engine in three modes, simulated annealing, with replica exchange while the adjustments are turned on or off. Up to 16x speedup is observed by turning on the replica exchange capability in addition to the advantage of eliminating the challenging process of finding an optimal annealing schedule for simulated annealing process.

中文翻译：

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具有自动温度选择和并行试验的副本交换 MCMC 硬件

一个副本交换马尔可夫链蒙特卡罗 (MCMC) 引擎是通过自动温度调整开发的，用于通过最小化 Ising 模型的能量来解决组合优化问题。自动温度调节方案确保在执行的每个阶段优化 MCMC 过程。除了自动插入新副本或删除任何现有副本以实现最佳资源效率和执行时间的能力之外，该方法还通过基于任何给定问题的属性动态调整所有副本的温度来执行。所提出的算法与能量增量和更新方案的并行评估相结合。该引擎在 FPGA 平台上实现，最多可在流水线中运行 42 个副本，每个运行 1024 个完全连接的 Ising 并行自旋。硬件的性能通过三种不同类别的问题进行检查，即顶点覆盖、最大切割和旅行商，在三种模式下使用引擎，模拟退火，在打开或关闭调整时进行副本交换。除了消除为模拟退火过程寻找最佳退火时间表的挑战性过程之外，还可以通过打开副本交换功能观察到高达 16 倍的加速。