SCIP: global optimization of mixed-integer nonlinear programs in a branch-and-cut framework

Vigerske, Stefan; Gleixner, Ambros

doi:10.1080/10556788.2017.1335312

Cited by 160 publications

(133 citation statements)

References 60 publications

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“…According to Ref. [29], the general list of feasible nonconvex global MINLP solvers contains ANTIGONE [30], BARON [31], Couenne [32], LindoGlobal [33], and SCIP [34]. According to the results of the comparative solver study [26].…”

Section: Solvermentioning

confidence: 99%

Identifying Physico-Chemical Laws from the Robotically Collected Data

Cao¹,

Russo²,

Vassiliadis³

et al. 2019

Preprint

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A mixed-integer nonlinear programming (MINLP) formulation for symbolic regression was proposed to identify physical models from noisy experimental data. The formulation was tested using numerical models and was found to be more efficient than the previous literature example with respect to the number of predictor variables and training data points. The globally optimal search was extended to identify physical models and to cope with noise in the experimental data predictor variable. The methodology was coupled with the collection of experimental data in an automated fashion, and was proven to be successful in identifying the correct physical models describing the relationship between the shear stress and shear rate for both Newtonian and non-Newtonian fluids, and simple kinetic laws of reactions. Future work will focus on addressing the limitations of the formulation presented in this work, by extending it to be able to address larger complex physical models.

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Section: Solvermentioning

confidence: 99%

Identifying Physico-Chemical Laws from the Robotically Collected Data

Cao¹,

Russo²,

Vassiliadis³

et al. 2019

Preprint

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show abstract

“…The lower bounding scenario subproblems, however, remain nonconvex because we need to simultaneously handle the controller settings and the dynamic model response. This observation highlights that the decomposition scheme is limited by the scope of off‐the‐shelf global optimization solvers (such as SCIP and BARON) (which are needed to solve the scenario subproblems). We also highlight that a global optimization framework for SPs can also exploit more advanced techniques that handle differential equations in a simulation‐based setting .…”

Section: Computational Toolsmentioning

confidence: 99%

“…We now proceed to certify that the controller settings obtained with IPOPT are globally optimal (we recall that this is a local solver so there is no guarantee that the solution is globally optimal). To do this, we solve expected value problems with increasing number of scenarios with SNGO (which exploits the nearly separable structure of the problem) and with the off‐the‐shelf global solver SCIP . The results are presented in Table .…”

Section: Numerical Case Studiesmentioning

confidence: 99%

Optimal PID controller tuning using stochastic programming techniques

et al. 2017

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We argue that stochastic programming provides a powerful framework to tune and analyze the performance limits of controllers. In particular, stochastic programming formulations can be used to identify controller settings that remain robust across diverse scenarios (disturbances, set-points, and modeling errors) observed in real-time operations. We also discuss how to use historical data and sampling techniques to construct operational scenarios and inference analysis techniques to provide statistical guarantees on limiting controller performance. Under the proposed framework, it is also possible to use risk metrics to handle extreme (rare) events and stochastic dominance concepts to conduct systematic benchmarking studies. We provide numerical studies to illustrate the concepts and to demonstrate that modern modeling and local/global optimization tools can tackle large-scale applications. The proposed work also opens the door to data-based controller tuning strategies that can be implemented in real-time operations. V C 2017 American Institute of Chemical Engineers AIChE J, 00: 000-000, 2017

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“…Some softwares, implementing the methods described above, are available for solving (P ). See for instance Couenne 0.5 [11], Baron [51], Scip 3.2.1 [1,58]. Another frequently used technique to obtain convex relaxations of (P ) is semi-definite programming, see for example [5,52].…”

Section: Introductionmentioning

confidence: 99%

Global solution of non-convex quadratically constrained quadratic programs

Elloumi

Lambert

2017

Optimization Methods and Software

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The class of mixed-integer quadratically constrained quadratic programs (QCQP) consists of minimizing a quadratic function under quadratic constraints where the variables could be integer or continuous. On a previous paper we introduced a method called MIQCR for solving QC-QPs with the following restriction : all quadratic sub-functions of purely continuous variables are already convex. In this paper, we propose an extension of MIQCR which applies to any QCQP. Let (P) be a QCQP. Our approach to solve (P) is first to build an equivalent mixed-integer quadratic problem (P *). This equivalent problem (P *) has a quadratic convex objective function, linear constraints, and additional variables y that are meant to satisfy the additional quadratic constraints y = xx T , where x are the initial variables of problem (P). We then propose to solve (P *) by a branch-and-bound algorithm based on the relaxation of the additional quadratic constraints and of the integrality constraints. This type of branching is known as spatial branch-and-bound. Computational experiences are carried out on a total of 325 instances. The results show that the solution time of most of the considered instances is improved by our method in comparison with the recent implementation of QuadProgBB, and with the solvers Cplex, Couenne, Scip, BARON and GloMIQO.

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SCIP: global optimization of mixed-integer nonlinear programs in a branch-and-cut framework

Cited by 160 publications

References 60 publications

Identifying Physico-Chemical Laws from the Robotically Collected Data

Identifying Physico-Chemical Laws from the Robotically Collected Data

Optimal PID controller tuning using stochastic programming techniques

Global solution of non-convex quadratically constrained quadratic programs

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