基于振荡器的MaxSAT求解器
An Oscillator-based MaxSAT solver
摘要：
对有效解决困难的组合优化问题的探索--对传统的数字计算机来说仍然是一个长期的挑战--激发了对许多替代计算模型和平台的探索。作为一个恰当的例子，振荡器网络提供了一个潜在的有前途的能源效率和可扩展的选择。然而，现有的基于振荡器的组合优化求解器主要集中在仅考虑振荡器之间的成对相互作用的二次组合优化问题上。在这项工作中，我们提出了一个新的计算模型的基础上的最大熵产生（MEP）原则，利用更高阶的振荡器之间的相互作用，并证明其在解决非二次最大可满足性（MaxSAT）问题的应用。我们证明了MaxSAT问题的解决方案可以直接映射到振荡器网络中的熵产生率，随后，提出了一种利用内存计算（CiM）原语的面积高效的硬件实现。使用实验与分析和电路模拟，我们阐明了所提出的方法在计算高质量的最佳/接近最佳的解决方案的MaxSAT问题的性能。我们的工作不仅揭示了如何振荡器可以解决非二次组合优化问题，如MaxSAT，但也扩展了应用这种基于动力系统的方法，可以很容易地分解到MaxSAT解决方案的更广泛的一类问题。
英文摘要：
The quest to solve hard combinatorial optimization problems efficiently -- still a longstanding challenge for traditional digital computers -- has inspired the exploration of many alternate computing models and platforms. As a case in point, oscillator networks offer a potentially promising energy efficient and scalable option. However, prior oscillator-based combinatorial optimization solvers have primarily focused on quadratic combinatorial optimization problems that consider only pairwise interaction among the oscillators. In this work, we propose a new computational model based on the maximum entropy production (MEP) principle that exploits higher order interactions among the oscillators, and demonstrate its application in solving the non-quadratic maximum satisfiability (MaxSAT) problem. We demonstrate that the solution to the MaxSAT problem can be directly mapped to the entropy production rate in the oscillator network, and subsequently, propose an area-efficient hardware implementation that leverages Compute-in-Memory (CiM) primitives. Using experiments along with analytical and circuit simulations, we elucidate the performance of the proposed approach in computing high-quality optimal / near-optimal solutions to the MaxSAT problem. Our work not only reveals how oscillators can solve non-quadratic combinatorial optimization problems such as MaxSAT but also extends the application of this dynamical system-based approach to a broader class of problems that can be easily decomposed to the MaxSAT solution.
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