超图上基于动力系统的组合优化计算模型
Dynamical system-based computational models for solving combinatorial optimization on hypergraphs
摘要：
动力系统的内禀能量最小化为组合优化中的计算难题的目标函数最小化提供了一个有价值的工具。然而，大多数现有工作集中于将这种动态映射到目标函数具有二次度的组合优化问题（例如，MaxCut）;这些问题可以使用图形来表示和分析。然而，开发这种模型的问题，需要的目标函数的程度大于2，随后，需要使用超图数据结构的工作，是相对稀疏的。在这项工作中，我们开发了动力系统启发的计算模型的几个这样的问题。具体来说，我们定义的“能量函数”的超图为基础的组合问题，从布尔SAT和它的变种，以整数分解，随后，定义所产生的系统动力学。我们还证明了该设计方法适用于二次优化问题，并使用它开发了一种新的动力系统公式来最小化伊辛汉密尔顿。我们的工作不仅扩大了可以直接映射到并使用物理模型解决的问题的范围，而且还为设计用于解决组合优化的高性能加速器创造了新的机会。
英文摘要：
The intrinsic energy minimization in dynamical systems offers a valuable tool for minimizing the objective functions of computationally challenging problems in combinatorial optimization. However, most prior works have focused on mapping such dynamics to combinatorial optimization problems whose objective functions have quadratic degree (e.g., MaxCut); such problems can be represented and analyzed using graphs. However, the work on developing such models for problems that need objective functions with degree greater than two, and subsequently, entail the use of hypergraph data structures, is relatively sparse. In this work, we develop dynamical system-inspired computational models for several such problems. Specifically, we define the 'energy function' for hypergraph-based combinatorial problems ranging from Boolean SAT and its variants to integer factorization, and subsequently, define the resulting system dynamics. We also show that the design approach is applicable to optimization problems with quadratic degree, and use it develop a new dynamical system formulation for minimizing the Ising Hamiltonian. Our work not only expands on the scope of problems that can be directly mapped to, and solved using physics-inspired models, but also creates new opportunities to design high-performance accelerators for solving combinatorial optimization.
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