114. Piecewise linear modeling of head-dependent hydropower function on non-grid triangulation
Invited abstract in session WD-3: Mixed Integer Programming II, stream Discrete Optimization.
Wednesday, 12:00 - 13:30Room: C 104
Authors (first author is the speaker)
| 1. | Peter Dobrovoczki
|
| Engineering and Management Intelligence Research Laboratory, HUN-REN SZTAKI | |
| 2. | Tamas Kis
|
| Institute for Computer Science and Control |
Abstract
Modeling piecewise linear functions with mixed integer linear programming is a challenging problem with several applications. We present a novel method to construct efficient MILP representation of piecewise linear functions of two variable over non-grid triangulations. Our method consists of the construction of a novel heuristic to find biclique cover to derive an ideal formulation of combinatorial disjunctive constraints that are pairwise independent branching (IB) scheme representable. We extend our method for the case when the combinatorial disjunction is not IB-representable by coloring an auxiliary graph.
We apply our techniques for constructing a piecewise linear approximation of 2-variable (non-linear) functions. Firstly, we propose a fast heuristic algorithm to construct a piecewise linear approximation of a function over a bounded domain such that the approximation error is low in expectation. We apply our methods to model the head-dependent hydropower function in a hydropower plant scheduling application.
Keywords
- Optimization in industry, business and finance
- Linear and nonlinear optimization
- Mixed integer nonlinear optimization
Status: accepted
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