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Bundle-enhanced column-and-constraint generation method for solving two-stage robust optimization problems
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DOI：10.1016/j.cor.2026.107525.png)
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Abstract
En 中文
We propose a column-and-constraint generation framework enhanced with bundle techniques and a switching mechanism that dynamically alternates between lower- and upper-bound search strategies. Our approach uses geometric information on the master problem’s feasible region as a proxy for the missing dual information in both-stage mixed-integer programs, curbing master problem growth and mitigating structural tail-off. Because the framework requires solving nonlinear mixed-integer quadratic programs, we develop a tailored outer approximation method. We test it on a two-stage robust location-transportation problem with uncertain demands, common in logistics and distribution, where the goal is to locate capacitated facilities and plan transportation to meet uncertain customer demands at minimum total cost (facility installation, capacity utilization, and transportation). The problem is formulated as a two-stage robust mixed-integer bilevel nonconvex program: facilities are located in the first stage before demands are known, and transportation and capacity decisions are made in the second stage. Computational results show average solution time reductions of 50% over the original column-and-constraint generation method, outperforming existing approaches.
Keywords:
column-and-constraint generation
robust optimization
mixed-integer programming
bundle methods
two-stage optimization
Journal
C
IF:
4.3
Papers:
201
Citations:
0