Smooth and Flexible Dual Optimal Inequalities

We address the problem of accelerating column generation (CG) for set-covering formulations via dual optimal inequalities (DOIs). study two novel classes DOIs, which are referred to as Flexible DOIs (F-DOIs) and Smooth-DOIs (S-DOIs), respectively (and jointly SF-DOIs). F-DOIs provide rebates covering items more than necessary. S-DOIs describe payment a penalty permit undercoverage in exchange overinclusion other items. Unlike from literature, rely on very little problem-specific knowledge and, such, have potential be applied vast number domains. In particular, we discuss application new three relevant problems: single-source capacitated facility location problem, p-median vehicle-routing problem. computational evidence strength by embedding them within column-generation solver these problems. Substantial speedups can observed when compared with nonstabilized variant same CG procedure achieve linear-relaxation lower bound problems dense columns structured assignment costs.