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Preprocessing and Cutting Planes with Conflict Graphs
Computers & Operations Research ( IF 4.6 ) Pub Date : 2021-04-01 , DOI: 10.1016/j.cor.2020.105176
Samuel Souza Brito , Haroldo Gambini Santos

This paper addresses the development of conflict graph-based algorithms and data structures into the COIN-OR Branch-and-Cut (CBC) solver, including: $(i)$ an efficient infrastructure for the construction and manipulation of conflict graphs; $(ii)$ a preprocessing routine based on a clique strengthening scheme that can both reduce the number of constraints and produce stronger formulations; $(iii)$ a clique cut separator capable of obtaining dual bounds at the root node LP relaxation that are $19.65\%$ stronger than those provided by the equivalent cut generator of a state-of-the-art commercial solver, $3.62$ times better than those attained by the clique cut separator of the GLPK solver and $4.22$ times stronger than the dual bounds obtained by the clique separation routine of the COIN-OR Cut Generation Library; $(iv)$ an odd-cycle cut separator with a new lifting module to produce valid odd-wheel inequalities. The average gap closed by this new version of CBC was up to four times better than its previous version. Moreover, the number of mixed-integer programs solved by CBC in a time limit of three hours was increased by $23.53\%$.

中文翻译:

使用冲突图预处理和切割平面

本文讨论了基于冲突图的算法和数据结构在 COIN-OR Branch-Cut (CBC) 求解器中的发展,包括:$(ii)$ 基于集团强化方案的预处理例程,既可以减少约束的数量,又可以产生更强的公式;$(iii)$ 一个集团切割分离器,能够在根节点 LP 松弛处获得双重边界,比最先进的商业求解器的等效切割生成器提供的强 19.65\%$,$3.62$ 倍比 GLPK 求解器的 clique cut 分离器获得的更好,并且比 COIN-OR Cut Generation Library 的 clique 分离例程获得的双重边界强 4.22 倍;$(iv)$ 带有新提升模块​​的奇周期切割分离器,可产生有效的奇轮不等式。这个新版本的 CBC 缩小的平均差距比以前的版本好四倍。而且,CBC在三小时内解决的混合整数程序数量增加了$23.53\%$。
更新日期:2021-04-01
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