An Extended C&CG Algorithm for Solving Two-Stage Robust Optimization of Economic and Feasible Scheduling

Ruibin Chen (), Zhejing Bao (), Lingxia Lu () and Miao Yu ()
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Ruibin Chen: Zhejiang University
Zhejing Bao: Zhejiang University
Lingxia Lu: Zhejiang University
Miao Yu: Zhejiang University

Journal of Optimization Theory and Applications, 2025, vol. 205, issue 2, No 5, 29 pages

Abstract: Abstract The extensively researched column-and-constraint-generation (C&CG) algorithm, which utilizes the KKT (Karush–Kuhn–Tucker) condition or duality theory to reformulate the subproblem, encounters challenges when solving two-stage robust optimization (TSRO) problems with extreme parameters that could adversely affect the feasibility of the second-stage decision. After the analysis of the original C&CG algorithm, an extended C&CG algorithm with multiple subproblems is proposed to overcome the challenges, which decompose a TSRO model into the master problem and several subproblems searching for the worst-case scenarios. A simple linear case is given to show the shortcoming of the traditional C&CG algorithm and the advantage of the extended C&CG algorithm. Then, a TSRO model for the scheduling optimization of electricity system considering the optimal power flow (OPF) is proposed, in order to explore the effectiveness of the extended C&CG algorithm in handling the general optimization problem while considering the feasibility. Finally, the proposed solving method is validated by case studies.

Keywords: Column and constraint generation; Two-stage robust optimization; Feasibility check; $$\varepsilon $$ ε -Constraint method; 90C30; 90C31; 90B06 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-025-02642-3

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