A computational status update for exact rational mixed integer programming
改进了2013年提出的混合精度分支定界算法，集成符号预处理、精确修复启发式解、更快的有理线性规划求解器，并生成可验证的最优性证明，在MIPLIB 2017基准集上平均加速10.7倍。
Abstract The last milestone achievement for the roundoff-error-free solution of general mixed integer programs over the rational numbers was a hybrid-precision branch-and-bound algorithm published by Cook, Koch, Steffy, and Wolter in 2013. We describe a substantial revision and extension of this framework that integrates symbolic presolving, features an exact repair step for solutions from primal heuristics, employs a faster rational LP solver based on LP iterative refinement, and is able to produce independently verifiable certificates of optimality. We study the significantly improved performance and give insights into the computational behavior of the new algorithmic components. On the MIPLIB 2017 benchmark set, we observe an average speedup of 10.7x over the original framework and 2.9 times as many instances solved within a time limit of two hours.