[论文解读] A Tutorial on Formulating and Using QUBO Models

Fred Glover, Gary Kochenberger+1 more|arXiv (Cornell University)|Nov 13, 2018

Simulation Techniques and Applications参考文献 68被引用 177

一句话总结

论文解释如何将广泛的问题表述为 QUBO 模型，使用惩罚函数精确编码约束，并用简单数值示例进行说明，同时讨论现代求解创新及与量子和神经形态计算的联系。

ABSTRACT

The Quadratic Unconstrained Binary Optimization (QUBO) model has gained prominence in recent years with the discovery that it unifies a rich variety of combinatorial optimization problems. By its association with the Ising problem in physics, the QUBO model has emerged as an underpinning of the quantum computing area known as quantum annealing and has become a subject of study in neuromorphic computing. Through these connections, QUBO models lie at the heart of experimentation carried out with quantum computers developed by D-Wave Systems and neuromorphic computers developed by IBM. Computational experience is being amassed by both the classical and the quantum computing communities that highlights not only the potential of the QUBO model but also its effectiveness as an alternative to traditional modeling and solution methodologies. This tutorial discloses the basic features of the QUBO model that give it the power and flexibility to encompass the range of applications that have thrust it onto center stage of the optimization field. We show how many different types of constraining relationships arising in practice can be embodied within the "unconstrained" QUBO formulation in a very natural manner using penalty functions, yielding exact model representations in contrast to the approximate representations produced by customary uses of penalty functions. Each step of generating such models is illustrated in detail by simple numerical examples, to highlight the convenience of using QUBO models in numerous settings. We also describe recent innovations for solving QUBO models that offer a fertile avenue for integrating classical and quantum computing and for applying these models in machine learning.

研究动机与目标

• 将 QUBO 模型作为组合最优化的统一框架进行动机说明。
• 展示如何在不约束的 QUBO 形式中使用惩罚来编码约束关系。
• 提供逐步指导和简单数值示例以生成 QUBO 表示。
• 讨论最近在求解 QUBO 模型方面的创新及其与经典、量子和机器学习方法的整合。

提出的方法

• 描述 QUBO 模型的基本特征及其包含多样化应用的能力。
• 演示如何通过惩罚函数在无约束 QUBO 公式中体现各种约束。
• 表明基于惩罚的 QUBO 表示可以是精确的，与传统惩罚的近似相反。
• 用简单数值示例说明模型构建过程以突出其实用性。
• 讨论用于求解 QUBO 模型的最新创新及其在整合经典/量子计算和机器学习方面的潜力。

实验结果

研究问题

• RQ1 广泛的带约束的组合问题如何表示为无约束的 QUBO 模型？
• RQ2 在 QUBO 公式中通过惩罚函数如何能够精确编码约束？
• RQ3 从实际问题生成 QUBO 表示的逐步过程是什么？
• RQ4 有哪些关于 QUBO 模型的最新求解创新，以及它们如何连接经典、量子和机器学习方法？

主要发现

• QUBO 模型可以通过无约束的表述统一许多组合优化问题。
• 惩罚函数可以在 QUBO 中产生对约束的精确表示，从而实现精准建模。
• 教程提供了详细而简单的数值示例来说明 QUBO 构建。
• 最近的求解创新为将经典和量子计算以及机器学习与 QUBO 模型结合带来机会。