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

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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.

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Acknowledgements

This research was supported by Zhejiang Provincial Natural Science Foundation of China under Grant No. LGG22F030008

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Authors and Affiliations

  1. Zhejiang University, Hangzhou, China

    Ruibin Chen, Zhejing Bao, Lingxia Lu & Miao Yu

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  1. Ruibin Chen
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  2. Zhejing Bao
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Correspondence to Zhejing Bao.

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Communicated by Aviv Gibali.

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Chen, R., Bao, Z., Lu, L. et al. An Extended C&CG Algorithm for Solving Two-Stage Robust Optimization of Economic and Feasible Scheduling. J Optim Theory Appl 205, 24 (2025). https://doi.org/10.1007/s10957-025-02642-3

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  • DOI: https://doi.org/10.1007/s10957-025-02642-3

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