Optimization

Efficient solutions to large-scale problems.

Much of MERL's research activity involves formulating scientific and engineering problems as optimizations, which can be solved in an efficient way. We have developed fundamental algorithms to better solve classic problems, such as quadratic programs and minimum-cost paths. Our work also involves developing theoretical bounds to understand performance limits.

  • Researchers

  • Awards

    •  AWARD   Best conference paper of IEEE PES-GM 2020
      Date: June 18, 2020
      Awarded to: Tong Huang, Hongbo Sun, K.J. Kim, Daniel Nikovski, Le Xie
      MERL Contacts: Kyeong Jin (K.J.) Kim; Daniel Nikovski; Hongbo Sun
      Research Areas: Data Analytics, Electric Systems, Optimization
      Brief
      • A paper on A Holistic Framework for Parameter Coordination of Interconnected Microgrids Against Natural Disasters, written by Tong Huang, a former MERL intern from Texas A&M University, has been selected as one of the Best Conference Papers at the 2020 Power and Energy Society General Meeting (PES-GM). IEEE PES-GM is the flagship conference for the IEEE Power and Energy Society. The work was done in collaboration with Hongbo Sun, K. J. Kim, and Daniel Nikovski from MERL, and Tong's advisor, Prof. Le Xie from Texas A&M University.
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  • News & Events

    •  NEWS   MERL researchers presented 10 papers at American Control Conference (ACC)
      Date: July 1, 2020 - July 3, 2020
      Where: Denver, Colorado (virtual)
      MERL Contacts: Mouhacine Benosman; Karl Berntorp; Ankush Chakrabarty; Claus Danielson; Stefano Di Cairano; Saleh Nabi; Rien Quirynen; Yebin Wang; Avishai Weiss
      Research Areas: Control, Machine Learning, Optimization
      Brief
      • At the American Control Conference, MERL presented 10 papers on subjects including autonomous-vehicle decision making and motion planning, nonlinear estimation for thermal-fluid models and GNSS positioning, learning-based reference governors and reference governors for railway vehicles, and fail-safe rendezvous control.
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    •  TALK   Universal Differential Equations for Scientific Machine Learning
      Date & Time: Thursday, May 7, 2020; 12:00 PM
      Speaker: Christopher Rackauckas, MIT
      MERL Host: Christopher Laughman
      Research Areas: Machine Learning, Multi-Physical Modeling, Optimization
      Brief
      • In the context of science, the well-known adage "a picture is worth a thousand words" might well be "a model is worth a thousand datasets." Scientific models, such as Newtonian physics or biological gene regulatory networks, are human-driven simplifications of complex phenomena that serve as surrogates for the countless experiments that validated the models. Recently, machine learning has been able to overcome the inaccuracies of approximate modeling by directly learning the entire set of nonlinear interactions from data. However, without any predetermined structure from the scientific basis behind the problem, machine learning approaches are flexible but data-expensive, requiring large databases of homogeneous labeled training data. A central challenge is reco nciling data that is at odds with simplified models without requiring "big data". In this talk we discuss a new methodology, universal differential equations (UDEs), which augment scientific models with machine-learnable structures for scientifically-based learning. We show how UDEs can be utilized to discover previously unknown governing equations, accurately extrapolate beyond the original data, and accelerate model simulation, all in a time and data-efficient manner. This advance is coupled with open-source software that allows for training UDEs which incorporate physical constraints, delayed interactions, implicitly-defined events, and intrinsic stochasticity in the model. Our examples show how a diverse set of computationally-difficult modeling issues across scientific disciplines, from automatically discovering biological mechanisms to accelerating climate simulations by 15,000x, can be handled by training UDEs.
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  • Internships

    • CA1401: Formal Synthesis for Planning and Control for Autonomous Systems

      The Control and Dynamical Systems (CD) group at MERL is seeking a highly motivated intern to conduct research on planning and control by formal methods, in particular temporal logics specifications and their synthesis by mixed-integer inequalities. The ideal candidate is enrolled in a PhD program in Electrical, Mechanical, Aerospace Engineering, Computer Science or related program, with focus on Control Theory. The ideal candidate will have experience in (one or more of) formal methods, particularly temporal logics and signal temporal logics, reachability analysis, abstractions of dynamical systems, hybrid predictive control, and mixed integer programming. Good programming skills in Matlab (or alternatively Python) are required, working knowledge of C/C++ is a plus. The expected duration of the internship is 3-6 months with flexible start date after April 1st, 2020.

    • SA1031: Distributed auctions for network welfare maximization

      We are looking for a talented individual to collaborate and facilitate research on new algorithms in mechanism design and distributed auctions. Responsibilities will include mathematical modeling, algorithm design, software prototyping, and running Monte Carlo simulations in a network traffic domain. Candidates should be strong scientific programmers and have some background in numerical optimization, simulation design, and auction theory.

    • MD1406: Numerical Analysis of Electric Machines

      MERL is seeking a motivated and qualified intern to conduct research in the design, modeling and optimization of electrical machines. The ideal candidate should have solid backgrounds in electromagnetic theory, electric machine design, and numerical modeling techniques (including model reduction), research experiences in electric, magnetic, and thermal modeling and analysis of electrical machines, and demonstrated capability to publish results in leading conferences/journals. Experience with ANSYS, COMSOL, and optimization techniques is a strong plus. Senior Ph.D. students in electrical or mechanical engineering with related expertise are encouraged to apply. Start date for this internship is flexible and the duration is 3-6 months.


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  • Recent Publications

    •  Aguilar Marsillach, D., Di Cairano, S., Weiss, A., "Fail-safe Rendezvous Control on Elliptic Orbits using Reachable Sets", American Control Conference (ACC), July 2020.
      BibTeX TR2020-098 PDF
      • @inproceedings{AguilarMarsillach2020jul,
      • author = {Aguilar Marsillach, Daniel and Di Cairano, Stefano and Weiss, Avishai},
      • title = {Fail-safe Rendezvous Control on Elliptic Orbits using Reachable Sets},
      • booktitle = {American Control Conference (ACC)},
      • year = 2020,
      • month = jul,
      • url = {https://www.merl.com/publications/TR2020-098}
      • }
    •  Greiff, M., Berntorp, K., "Optimal Measurement Projections with Adaptive Mixture Kalman Filtering for GNSS Positioning", American Control Conference (ACC), July 2020.
      BibTeX TR2020-097 PDF
      • @inproceedings{Greiff2020jul,
      • author = {Greiff, Marcus and Berntorp, Karl},
      • title = {Optimal Measurement Projections with Adaptive Mixture Kalman Filtering for GNSS Positioning},
      • booktitle = {American Control Conference (ACC)},
      • year = 2020,
      • month = jul,
      • url = {https://www.merl.com/publications/TR2020-097}
      • }
    •  Hansen, E., Wang, Y., "Improving Path Accuracy for Autonomous Parking Systems: An Optimal Control Approach", American Control Conference (ACC), July 2020.
      BibTeX TR2020-099 PDF
      • @inproceedings{Hansen2020jul,
      • author = {Hansen, Emma and Wang, Yebin},
      • title = {Improving Path Accuracy for Autonomous Parking Systems: An Optimal Control Approach},
      • booktitle = {American Control Conference (ACC)},
      • year = 2020,
      • month = jul,
      • url = {https://www.merl.com/publications/TR2020-099}
      • }
    •  Quirynen, R., Berntorp, K., Kambam, K., Di Cairano, S., "Integrated Obstacle Detection and Avoidance in Motion Planning and Predictive Control of Autonomous Vehicles", American Control Conference (ACC), July 2020.
      BibTeX TR2020-096 PDF
      • @inproceedings{Quirynen2020jul,
      • author = {Quirynen, Rien and Berntorp, Karl and Kambam, Karthik and Di Cairano, Stefano},
      • title = {Integrated Obstacle Detection and Avoidance in Motion Planning and Predictive Control of Autonomous Vehicles},
      • booktitle = {American Control Conference (ACC)},
      • year = 2020,
      • month = jul,
      • url = {https://www.merl.com/publications/TR2020-096}
      • }
    •  Sahin, Y.E., Quirynen, R., Di Cairano, S., "Autonomous Vehicle Decision-Making and Monitoring based on Signal Temporal Logic and Mixed-Integer Programming", American Control Conference (ACC), July 2020.
      BibTeX TR2020-095 PDF
      • @inproceedings{Sahin2020jul,
      • author = {Sahin, Yunus Emre and Quirynen, Rien and Di Cairano, Stefano},
      • title = {Autonomous Vehicle Decision-Making and Monitoring based on Signal Temporal Logic and Mixed-Integer Programming},
      • booktitle = {American Control Conference (ACC)},
      • year = 2020,
      • month = jul,
      • url = {https://www.merl.com/publications/TR2020-095}
      • }
    •  Vijayshankar, S., Nabi, S., Chakrabarty, A., Grover, P., Benosman, M., "Dynamic Mode Decomposition and Robust Estimation: Case Study of a 2D Turbulent Boussinesq Flow", American Control Conference (ACC), July 2020.
      BibTeX TR2020-091 PDF
      • @inproceedings{Vijayshankar2020jul,
      • author = {Vijayshankar, Sanjana and Nabi, Saleh and Chakrabarty, Ankush and Grover, Piyush and Benosman, Mouhacine},
      • title = {Dynamic Mode Decomposition and Robust Estimation: Case Study of a 2D Turbulent Boussinesq Flow},
      • booktitle = {American Control Conference (ACC)},
      • year = 2020,
      • month = jul,
      • url = {https://www.merl.com/publications/TR2020-091}
      • }
    •  Quirynen, R., Hespanhol, P., "Adjoint-based SQP Method with Block-wise quasi-Newton Jacobian Updates for Nonlinear Optimal Control", Journal of Optimization Methods and Software, June 2020.
      BibTeX TR2020-086 PDF
      • @article{Quirynen2020jun,
      • author = {Quirynen, Rien and Hespanhol, Pedro},
      • title = {Adjoint-based SQP Method with Block-wise quasi-Newton Jacobian Updates for Nonlinear Optimal Control},
      • journal = {Journal of Optimization Methods and Software},
      • year = 2020,
      • month = jun,
      • url = {https://www.merl.com/publications/TR2020-086}
      • }
    •  Romero, O., Benosman, M., "Time-Varying Continuous-Time Optimization with Pre-Defined Finite-Time Stability", International Journal of Control, June 2020.
      BibTeX TR2020-088 PDF
      • @article{Romero2020jun2,
      • author = {Romero, Orlando and Benosman, Mouhacine},
      • title = {Time-Varying Continuous-Time Optimization with Pre-Defined Finite-Time Stability},
      • journal = {International Journal of Control},
      • year = 2020,
      • month = jun,
      • url = {https://www.merl.com/publications/TR2020-088}
      • }
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