In this paper, we present several new linearizations of a quadratic binary optimization problem (QBOP), primarily using the method of aggregations. Although aggregations were studied in the past in the context of solving system of Diophantine equations in non-negative variables, none of the approaches developed produced practical models, particularly due to the large size of associate multipliers. Exploiting the special structure of QBOP we show that selective aggregation of constraints provide valid linearizations with interesting properties. For our aggregations, multipliers can be any non-zero real numbers. Moreover, choosing the multipliers appropriately, we demonstrate that the resulting LP relaxations have value identical to the corresponding non-aggregated models. We also provide a review of existing explicit linearizations of QBOP and presents the first systematic study of such models. Theoretical and experimental comparisons of new and existing models are also provided.

翻译：本文提出了二次二元优化问题（QBOP）的几种新线性化方法，主要采用了聚合技术。尽管聚合方法过去曾被研究用于求解非负变量丢番图方程组，但由于关联乘数规模过大，现有方法均未能产生实用的模型。利用QBOP的特殊结构，我们证明对约束进行选择性聚合能够生成具有优良性质的可行线性化模型。对于所提出的聚合方法，乘数可为任意非零实数。进一步地，通过合理选择乘数，我们证明所得线性规划松弛的解值与非聚合模型相同。本文还系统回顾了QBOP已有的显式线性化方法，首次对该类模型进行了系统性研究，并提供了新旧模型的理论与实验对比分析。