In this work, we explore the Ising spin glass model as a solution methodology for hard combinatorial optimization problems using the general purpose GPU (GPGPU). The Ising model is a mathematical model of ferromagnetism in statistical mechanics. Ising computing finds a minimum energy state for the Ising model which essentially corresponds to the expected optimal solution of the original problem. Ising computing is one of the proposed applications for quantum annealing computing and many combinatorial optimization problems can be mapped into the Ising model. In our work, we focus on the max-cut problem as it is relevant to many VLSI physical design problems. Our method is motivated by the observation that Ising computing by the annealing process is very amenable to fine-grain GPU based parallel computing. We will illustrate how the natural randomness of GPU thread scheduling can be exploited during the annealing process to create random update patterns and allow better GPU resource utilization. Furthermore, the proposed GPU-based Ising computing can handle any general Ising graph with arbitrary connections, which was shown to be difficult for existing FPGA and other hardware based implementation methods. Numerical results show that the proposed GPU Ising max-cut solver can deliver more than 2000X speedup over the CPU version of the algorithm on some large examples, which shows huge performance improvement potential for addressing many hard optimization algorithms for practical VLSI physical design.

翻译：在这项工作中,我们利用通用 GPU (GPGPU) 探索Ising 旋转玻璃模型,作为硬组合优化问题的解决方案。Ising 模型是统计机械中铁磁学的数学模型。Ising 计算为Ising 模型找到一个与最初问题的预期最佳解决方案基本相对应的最小能源状态。 计算是拟议中的量子反射计算应用之一, 许多组合优化问题可以映射到Ising 模型中。 在我们的工作中,我们侧重于与许多 VLSI 物理设计问题相关的最大切割问题。我们的方法动力是观察到用 Annealing 进程进行计算非常适合基于统计机械化的GPU的数学模型。 我们将说明如何利用GPU的自然随机性线列时间来创建随机更新模式,使GPU资源得到更好的利用。 此外,基于 GPU的Iing 计算可以处理任何带有任意连接的通用Ising 图表, 这对现有的 FPGA 和其他基于硬件的改进速度方法来说是困难的。