A robust approach for modeling limited observability in bilevel optimization

Beck, Yasmine; Schmidt, Martin

doi:10.1016/j.orl.2021.07.010

Cited by 6 publications

(1 citation statement)

References 26 publications

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“…Based on the above analysis, as a nonlinear optimization problem, robust bilevel optimization can also be transformed into a single-level optimization problem of the Mathematical program with equilibrium constraints (MPEC) by utilizing the Karush-Kuhn-Tucker (KKT) conditions to construct the Lagrangian function of the original model [35]. The robust model and the transformed lower-level problem are solved together as constraints in the MPEC, which can significantly reduce the difficulty and complexity of the solution.…”

Section: Robust Bilevel Modelmentioning

confidence: 99%

Robust Bilevel Optimal Dispatch of Park Integrated Energy System Considering Renewable Energy Uncertainty

Wang,

Zheng,

Diao

et al. 2023

Energies

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This paper focuses on optimizing the park integrated energy system (PIES) operation, and a robust bilevel optimal dispatch is proposed. Firstly, the robust uncertainty set is constructed based on the K-means++ algorithm to solve the uncertainty of renewable energy sources output in PIES. Then, the bi-level dispatch model is proposed, with the operator as the leader and consumers as the follower. The upper model establishes an electricity-heat-gas integrated energy network, and the lower model considers the demand response of consumers. Optimizing the pricing strategies of energy sources to determine the output of each energy conversion equipment and the demand response plan. Moreover, analyzing the decision-making process of the robust bi-level model and the solution method is given. Finally, case studies show that the proposed dispatch model can increase operator profits and reduce consumers’ energy costs. The in-sample and out-of-sample simulations demonstrate that the proposed ellipsoid uncertainty set possesses high compactness, good robustness, and low conservatism.

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Section: Robust Bilevel Modelmentioning

confidence: 99%

Robust Bilevel Optimal Dispatch of Park Integrated Energy System Considering Renewable Energy Uncertainty

Wang,

Zheng,

Diao

et al. 2023

Energies

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On convex lower-level black-box constraints in bilevel optimization with an application to gas market models with chance constraints

et al. 2022

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Bilevel optimization is an increasingly important tool to model hierarchical decision making. However, the ability of modeling such settings makes bilevel problems hard to solve in theory and practice. In this paper, we add on the general difficulty of this class of problems by further incorporating convex black-box constraints in the lower level. For this setup, we develop a cutting-plane algorithm that computes approximate bilevel-feasible points. We apply this method to a bilevel model of the European gas market in which we use a joint chance constraint to model uncertain loads. Since the chance constraint is not available in closed form, this fits into the black-box setting studied before. For the applied model, we use further problem-specific insights to derive bounds on the objective value of the bilevel problem. By doing so, we are able to show that we solve the application problem to approximate global optimality. In our numerical case study we are thus able to evaluate the welfare sensitivity in dependence of the achieved safety level of uncertain load coverage.

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Robust bilevel optimization for near-optimal lower-level solutions

Besançon,

Anjos,

Brotcorne

2024

J Glob Optim

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Bilevel optimization problems embed the optimality of a subproblem as a constraint of another optimization problem. We introduce the concept of near-optimality robustness for bilevel optimization, protecting the upper-level solution feasibility from limited deviations from the optimal solution at the lower level. General properties and necessary conditions for the existence of solutions are derived for near-optimal robust versions of general bilevel optimization problems. A duality-based solution method is defined when the lower level is convex, leveraging the methodology from the robust and bilevel literature. Numerical results assess the efficiency of exact and heuristic methods and the impact of valid inequalities on the solution time.

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A robust approach for modeling limited observability in bilevel optimization

Cited by 6 publications

References 26 publications

Robust Bilevel Optimal Dispatch of Park Integrated Energy System Considering Renewable Energy Uncertainty

Robust Bilevel Optimal Dispatch of Park Integrated Energy System Considering Renewable Energy Uncertainty

On convex lower-level black-box constraints in bilevel optimization with an application to gas market models with chance constraints

Robust bilevel optimization for near-optimal lower-level solutions

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