减少二次无约束二元优化问题规模和复杂性的逻辑和不等式蕴涵
Logical and Inequality Implications for Reducing the Size and Complexity of Quadratic Unconstrained Binary Optimization Problems
摘要：
二次无约束二进制优化（QUBO）问题出现在各种优化应用中，从伊辛自旋问题到图论中的经典问题和二进制离散优化。使用预处理将表示QUBO问题的图转换为较小的等效图对于提高精确算法和元启发式算法的解质量和时间是重要的，并且是将大规模QUBO映射到量子退火计算机中使用的硬件图的一步。在早期的一篇论文（Lewis和Glover，2016）中，引入了一组规则，通过计算测试验证，这些规则实现了显着的QUBO减少。在这里，这项工作扩展了额外的规则，提供了进一步的减少，成功地解决了10%的基准QUBO问题。算法和相关的数据结构，以有效地实现整个规则集的详细和计算实验的报告，证明其有效性。
英文摘要：
The quadratic unconstrained binary optimization (QUBO) problem arises in diverse optimization applications ranging from Ising spin problems to classical problems in graph theory and binary discrete optimization. The use of preprocessing to transform the graph representing the QUBO problem into a smaller equivalent graph is important for improving solution quality and time for both exact and metaheuristic algorithms and is a step towards mapping large scale QUBO to hardware graphs used in quantum annealing computers. In an earlier paper (Lewis and Glover, 2016) a set of rules was introduced that achieved significant QUBO reductions as verified through computational testing. Here this work is extended with additional rules that provide further reductions that succeed in exactly solving 10% of the benchmark QUBO problems. An algorithm and associated data structures to efficiently implement the entire set of rules is detailed and computational experiments are reported that demonstrate their efficacy.
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