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cloud.google.com·6h ago
Data Science
Towards Data Science·Aug 21·5 min read
How Benders Decomposition Works, Part II: Feasibility Cuts
TL;DR
Benders decomposition is enhanced by incorporating Farkas' lemma to generate feasibility cuts, specifically applied to the capacitated facility location problem. This approach improves the identification of infeasible solutions, leading to more efficient optimization.
✦ Why It Matters
Implement feasibility cuts in your optimization models to enhance solution efficiency and reduce computation time.
Key Takeaways
- Use feasibility cuts to handle infeasibility in optimization problems.
- Apply Farkas' lemma to generate certificates of infeasibility.
- Integrate feasibility cuts into Benders decomposition for better decision-making.
- Implement the complete algorithm in Python using Pyomo and HiGHS.
How It Works
Feasibility cuts restrict the master problem to decisions that allow for at least one feasible operational solution. By using Farkas' lemma, infeasibility is transformed into actionable constraints, guiding the master problem away from poor decisions.