Solving two-stage robust optimization problems using a column-and-constraint generation method
Citations
414 citations
326 citations
Cites background or methods from "Solving two-stage robust optimizati..."
...Previous work has dealt with this problem using outer-approximation techniques [4] and exact methods based on mixed-integer programming (MIP) reformulations [12], [36], [40]....
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...Indeed, (13) can be efficiently solved by adding and the associated constraints iteratively [4], [36]....
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...[12], [36], [40]....
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...Efficient solution methods for the two-stage robust UC have been proposed [4], [12], [16], [36]....
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...The exact MIP method proposed in [36] is based on the KKT conditions, which are applicable to general polyhedral uncertainty sets....
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323 citations
Cites methods from "Solving two-stage robust optimizati..."
...The power system subproblem is solved by C&CG [18], and the nonlinear gas system subproblem is solved by converting into an MILP model....
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...The C&CG is implemented via a master-subproblem framework....
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...The power system subproblem is solved by C&CG, in which the identified worst case realizations are directly used in further iterations of ADMM to improve the computation speed....
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...The power system subproblem is solved by C&CG in a master-subproblem framework....
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...Solve power system subproblem: Solve (49) and (2)– (25) using the C&CG method in Section III-A.1, with given P̄ bit = P̂ g (r) it , P̄ b,ptg at = P̂ g ,ptg(r) at λp,it = λ (r) p,it , λp,at = λ (r) p,at , and the worst case natural gas usage cuts generated so far....
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307 citations
Cites methods from "Solving two-stage robust optimizati..."
...Details of this algorithm is reported in [36]....
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...The RUC-CEHN model is a typical two-stage RO that can be solved to global optimality with the column-and-constraint generation (C&CG) method [36]....
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290 citations
Cites background or methods from "Solving two-stage robust optimizati..."
...It was proven in [32] that given a finite binary set, the column-and-constraint generation method could converge in finite iterations to obtain a global optimal solution....
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...But the convergence performance of this method outperforms Bender’s algorithm [32], [33]....
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..., continuous reactive power compensators) are represented as the “wait-and-see” decisions that can be adjusted after the first stage decisions are determined and the wind power uncertainty is revealed, which essentially provides the decision maker a recourse opportunity [32], [33]....
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References
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3,359 citations
"Solving two-stage robust optimizati..." refers background in this paper
...Robust optimization (RO) [2, 3, 4, 11, 7, 8] is a recent optimization approach to deal with data uncertainty....
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2,501 citations
"Solving two-stage robust optimizati..." refers background in this paper
...Robust optimization (RO) [2, 3, 4, 11, 7, 8] is a recent optimization approach to deal with data uncertainty....
[...]
2,133 citations