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<p>The extensively researched column-and-constraint-generation (C&amp;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&amp;CG algorithm, an extended C&amp;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&amp;CG algorithm and the advantage of the extended C&amp;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&amp;CG algorithm in handling the general optimization problem while considering the feasibility. Finally, the proposed solving method is validated by case studies.</p>

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

  • 期刊论文

  • 发表日期：

    2025年3月10日

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  • Ruibin Chen,
  • Zhejing Bao,
  • Lingxia Lu,
  • Miao Yu

摘要

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.