TR2023-110
Tailored Presolve Techniques in Branch-and-Bound Method for Fast Mixed-Integer Optimal Control Applications
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- "Tailored Presolve Techniques in Branch-and-Bound Method for Fast Mixed-Integer Optimal Control Applications", Optimal Control Applications and Methods, DOI: 10.1002/oca.3030, Vol. 44, No. 6, pp. 3139-3167, August 2023.BibTeX TR2023-110 PDF
- @article{Quirynen2023aug2,
- author = {Quirynen, Rien and Di Cairano, Stefano},
- title = {Tailored Presolve Techniques in Branch-and-Bound Method for Fast Mixed-Integer Optimal Control Applications},
- journal = {Optimal Control Applications and Methods},
- year = 2023,
- volume = 44,
- number = 6,
- pages = {3139--3167},
- month = aug,
- doi = {10.1002/oca.3030},
- url = {https://www.merl.com/publications/TR2023-110}
- }
,
- "Tailored Presolve Techniques in Branch-and-Bound Method for Fast Mixed-Integer Optimal Control Applications", Optimal Control Applications and Methods, DOI: 10.1002/oca.3030, Vol. 44, No. 6, pp. 3139-3167, August 2023.
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Abstract:
Mixed-integer model predictive control (MI-MPC) can be a powerful tool for con- trolling hybrid systems. In case of a linear-quadratic objective in combination with linear or piecewise-linear system dynamics and inequality constraints, MI-MPC needs to solve a mixed-integer quadratic program (MIQP) at each sampling time step.
This paper presents a collection of exact block-sparse presolve techniques to effi- ciently remove decision variables, and to remove or tighten inequality constraints, tailored to mixed-integer optimal control problems. In addition, we describe a novel approach based on a heuristic presolve algorithm to compute a feasible but possibly suboptimal MIQP solution. We present benchmarking results for a C code imple- mentation of the proposed BB-ASIPM solver, including a branch-and-bound (B&B) method with the proposed tailored presolve techniques and an active-set based inte- rior point method (ASIPM), compared against multiple state-of-the-art MIQP solvers on a case study of motion planning with obstacle avoidance constraints. Finally, we demonstrate the feasibility and computational performance of the BB-ASIPM solver in embedded system on a dSPACE Scalexio real-time rapid prototyping unit for a second case study of stabilization for an underactuated cart-pole with soft contacts