TR2023-110

Tailored Presolve Techniques in Branch-and-Bound Method for Fast Mixed-Integer Optimal Control Applications


    •  Quirynen, R., Di Cairano, S., "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}
      • }
  • MERL Contact:
  • Research Areas:

    Control, Dynamical Systems, Optimization

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

 

  • Related Publication

  •  Quirynen, R., Di Cairano, S., "Tailored Presolve Techniques in Branch-and-Bound Method for Fast Mixed-Integer Optimal Control Applications", arXiv, November 2022.
    BibTeX arXiv
    • @article{Quirynen2022nov,
    • author = {Quirynen, Rien and Di Cairano, Stefano},
    • title = {Tailored Presolve Techniques in Branch-and-Bound Method for Fast Mixed-Integer Optimal Control Applications},
    • journal = {arXiv},
    • year = 2022,
    • month = nov,
    • url = {https://arxiv.org/abs/2211.12700}
    • }