Journal
OPTIMIZATION METHODS & SOFTWARE
Volume 34, Issue 2, Pages 406-436Publisher
TAYLOR & FRANCIS LTD
DOI: 10.1080/10556788.2017.1401069
Keywords
multilevel optimization; mixed-integer nonlinear optimization; graph partitioning; generalized Benders decomposition; electricity market design
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Funding
- 'Aufbruch Bayern (Bavaria on the move)' initiative of the state of Bavaria
- Emerging Field Initiative (EFI) of the Friedrich-Alexander-Universitat Erlangen-Nurnberg
- DFG [CRC TRR 154]
- ZISC
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Mathematical modelling of market design issues in liberalized electricity markets often leads to mixed-integer nonlinear multilevel optimization problems for which no general-purpose solvers exist and which are intractable in general. In this work, we consider the problem of splitting a market area into a given number of price zones such that the resulting market design yields welfare-optimal outcomes. This problem leads to a challenging multilevel model that contains a graph-partitioning problem with multi-commodity flow connectivity constraints and nonlinearities due to proper economic modelling. Furthermore, it has highly symmetric solutions. We develop different problem-tailored solution approaches. In particular, we present an extended Karush-Kuhn-Tucker (KKT) transformation approach as well as a generalized Benders approach that both yield globally optimal solutions. These methods, enhanced with techniques such as symmetry breaking and primal heuristics, are evaluated in detail on academic as well as on realistic instances. It turns out that our approaches lead to effective solution methods for the difficult optimization tasks presented here, where the problem-specific generalized Benders approach performs considerably better than the methods based on KKT transformation.
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