# Learning Active Constraints to Efficiently Solve Bilevel Problems.

@article{Prat2020LearningAC, title={Learning Active Constraints to Efficiently Solve Bilevel Problems.}, author={El'ea Prat and Spyros Chatzivasileiadis}, journal={arXiv: Optimization and Control}, year={2020} }

Bilevel programming can be used to formulate many engineering and economics problems. However, solving such problems is hard, which impedes their implementation in real-life. In this paper, we propose to address this tractability challenge using machine learning classification techniques to learn the active constraints of the lower-level problem, in order to reduce it to those constraints only. Unlike in the commonly used reformulation of bilevel programs with the Karush-Kuhn-Tucker conditions…

## 5 Citations

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Mixed Integer Linear Programs (MILP) are well known to be NP-hard problems in general, and therefore, tackling and using their solution in online applications is a great challenge. Some Machine…

## References

SHOWING 1-10 OF 23 REFERENCES

Efficient Evolutionary Algorithm for Single-Objective Bilevel Optimization

- Computer ScienceArXiv
- 2013

This paper introduces bilevel evolutionary algorithm based on quadratic approximations (BLEAQ) of optimal lower level variables with respect to the upper level variables, capable of handling bileVEL problems with different kinds of complexities in relatively smaller number of function evaluations.

Efficiently solving linear bilevel programming problems using off-the-shelf optimization software

- Mathematics
- 2018

Many optimization models in engineering are formulated as bilevel problems. Bilevel optimization problems are mathematical programs where a subset of variables is constrained to be an optimal…

Solving Linear Bilevel Problems Using Big-Ms: Not All That Glitters Is Gold

- Mathematics, Computer ScienceIEEE Transactions on Power Systems
- 2019

It is shown, through a counterexample, that this widely used trial-and-error approach may lead to highly suboptimal solutions and further research is required to properly select big-M values to solve linear bilevel problems.

An Evolutionary Algorithm for Solving Bilevel Programming Problems Using Duality Conditions

- Mathematics
- 2012

Bilevel programming is characterized by two optimization problems located at different levels, in which the constraint region of the upper level problem is implicitly determined by the lower level…

Learning for Constrained Optimization: Identifying Optimal Active Constraint Sets

- MathematicsINFORMS Journal on Computing
- 2021

In many engineered systems, optimization is used for decision making at time scales ranging from real-time operation to long-term planning. This process often involves solving similar optimization…

Learning for DC-OPF: Classifying active sets using neural nets

- Computer Science2019 IEEE Milan PowerTech
- 2019

This paper proposes the use of classification algorithms to learn the mapping between the uncertainty realization and the active set of constraints at optimality, thus further enhancing the computational efficiency of the real-time prediction of the optimal power flow.

A new approach for solving linear bilevel problems using genetic algorithms

- Mathematics, Computer ScienceEur. J. Oper. Res.
- 2008

Technical Note - There's No Free Lunch: On the Hardness of Choosing a Correct Big-M in Bilevel Optimization

- Mathematics, Computer ScienceOper. Res.
- 2020

It is proved that verifying that a given big-M does not cut off any feasible vertex of the lower level's dual polyhedron cannot be done in polynomial time unless P=NP, and it is shown that verifying this fact is as hard as solving the original bilevel problem.

Bilevel programming approach to demand response management with day-ahead tariff

- Computer ScienceJournal of Modern Power Systems and Clean Energy
- 2019

The primal-dual reformulation is proposed in this paper to convert the bilevel optimization problem into a single-level quadratically constrained quadratic program (QCQP), and a successive linear programming (SLP) algorithm is applied to solve it.

Statistical Learning for DC Optimal Power Flow

- Mathematics, Computer Science2018 Power Systems Computation Conference (PSCC)
- 2018

An ensemble control policy is proposed that combines several basis policies to improve performance and is based on the observation that the OPF solution corresponding to a certain uncertainty realization is a basic feasible solution, which provides an affine control policy.