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 constraints in the space of original variables using perspective functions. Next, we 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.
- Research Organization:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Sponsoring Organization:
- USDOE National Nuclear Security Administration (NNSA)
- Grant/Contract Number:
- 89233218CNA000001
- OSTI ID:
- 1688736
- Report Number(s):
- LA-UR-17-28336
- Journal Information:
- INFORMS Journal on Computing, Vol. 32, Issue 3; ISSN 1091-9856
- Publisher:
- INFORMSCopyright Statement
- Country of Publication:
- United States
- Language:
- English
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