Convex Relaxations for Quadratic On/Off Constraints and Applications to Optimal Transmission Switching
This paper studies mixed-integer nonlinear programs featuring disjunctive constraints and trigonometric functions and presents a strengthened version of the convex quadratic relaxation of the optimal transmission switching problem. We first characterize the convex hull of univariate quadratic on/off...
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| Veröffentlicht in: | INFORMS journal on computing 2020-07, Vol.32 (3), p.682-696 |
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| container_title | INFORMS journal on computing |
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| creator | Bestuzheva, Ksenia Hijazi, Hassan Coffrin, Carleton |
| description | This paper studies mixed-integer nonlinear programs featuring disjunctive constraints and trigonometric functions and presents a strengthened version of the convex quadratic relaxation of the optimal transmission switching problem. We first characterize the convex hull of univariate quadratic on/off constraints in the space of original variables using perspective functions. We then introduce new tight quadratic relaxations for trigonometric functions featuring variables with asymmetrical bounds. These results are used to further tighten recent convex relaxations introduced for the optimal transmission switching problem in power systems. Using the proposed improvements, along with bound propagation, on 23 medium-sized test cases in the PGLib benchmark library with a relaxation gap of more than 1%, we reduce the gap to less than 1% on five instances. The tightened model has promising computational results when compared with state-of-the-art formulations. |
| doi_str_mv | 10.1287/ijoc.2019.0900 |
| format | Article |
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Using the proposed improvements, along with bound propagation, on 23 medium-sized test cases in the PGLib benchmark library with a relaxation gap of more than 1%, we reduce the gap to less than 1% on five instances. 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| identifier | ISSN: 1091-9856 |
| ispartof | INFORMS journal on computing, 2020-07, Vol.32 (3), p.682-696 |
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| language | eng |
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| source | INFORMS PubsOnLine |
| subjects | Computational geometry Computer Science Convex analysis Convexity Integer programming Mathematics MATHEMATICS AND COMPUTING Mixed integer Mixed-Integer Nonlinear Programming Nonlinear programming On/Off constraints Optimal Transmission Switching Perspective Relaxation Quadratic functions Relaxation methods (Mathematics) Switching Trigonometric Functions |
| title | Convex Relaxations for Quadratic On/Off Constraints and Applications to Optimal Transmission Switching |
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