A survey on bilevel optimization under uncertainty

Beck, Yasmine; Ljubić, Ivana; Schmidt, Martin

doi:10.1016/j.ejor.2023.01.008

Cited by 46 publications

(6 citation statements)

References 142 publications

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“…When conducting energy transactions, the operator guides consumers to demand response by rationally allocating and scheduling various energy sources [24]. When the bi-level optimization model involves data uncertainty [25], combined with the robust optimization method described above, it forms a robust bi-level optimization problem. In that case, it will cause serious solution difficulties.…”

Section: Literature Reviewmentioning

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: Literature Reviewmentioning

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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“…The next step is to define the region k i as the union of all k i ( j); see (3). Using (4), we obtain a covering of the bounding box of x I i and via (5), we obtain bounds for x r i .…”

Section: Construction Of the Master Problem's Feasible Regionmentioning

confidence: 99%

A Successive Linear Relaxation Method for MINLPs with Multivariate Lipschitz Continuous Nonlinearities

Grübel¹,

Krug²,

Schmidt³

et al. 2023

J Optim Theory Appl

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We present a novel method for mixed-integer optimization problems with multivariate and Lipschitz continuous nonlinearities. In particular, we do not assume that the nonlinear constraints are explicitly given but that we can only evaluate them and that we know their global Lipschitz constants. The algorithm is a successive linear relaxation method in which we alternate between solving a master problem, which is a mixed-integer linear relaxation of the original problem, and a subproblem, which is designed to tighten the linear relaxation of the next master problem by using the Lipschitz information about the respective functions. By doing so, we follow the ideas of Schmidt, Sirvent, and Wollner (Math Program 178(1):449–483 (2019) and Optim Lett 16(5):1355-1372 (2022)) and improve the tackling of multivariate constraints. Although multivariate nonlinearities obviously increase modeling capabilities, their incorporation also significantly increases the computational burden of the proposed algorithm. We prove the correctness of our method and also derive a worst-case iteration bound. Finally, we show the generality of the addressed problem class and the proposed method by illustrating that both bilevel optimization problems with nonconvex and quadratic lower levels as well as nonlinear and mixed-integer models of gas transport can be tackled by our method. We provide the necessary theory for both applications and briefly illustrate the outcomes of the new method when applied to these two problems.

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“…At present, in order to develop the potential of related research in commercial applications, some work has integrated several independent works and established corresponding double-layer or multi-objective mathematical models, especially in the fields of robotics and automation [8][9][10]. The above research provides ideas for the establishment Unlike work [6], with the proposal and development of sustainable development goals, some research on logistics distribution issues has introduced carbon emissions during logistics transportation into the objective function [7].…”

Section: Introductionmentioning

confidence: 99%

“…At present, in order to develop the potential of related research in commercial applications, some work has integrated several independent works and established corresponding double-layer or multi-objective mathematical models, especially in the fields of robotics and automation [8][9][10]. The above research provides ideas for the establishment of a more comprehensive integrated model for multimodal transportation in cross-border e-commerce logistics distribution.…”

Section: Introductionmentioning

confidence: 99%

Improved Swarm Intelligence-Based Logistics Distribution Optimizer: Decision Support for Multimodal Transportation of Cross-Border E-Commerce

Xu,

Di Nardo,

Yin

2024

Mathematics

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Cross-border e-commerce logistics activities increasingly use multimodal transportation modes. In this transportation mode, the use of high-performance optimizers to provide decision support for multimodal transportation for cross-border e-commerce needs to be given attention. This study constructs a logistics distribution optimization model for cross-border e-commerce multimodal transportation. The mathematical model aims to minimize distribution costs, minimize carbon emissions during the distribution process, and maximize customer satisfaction as objective functions. It also considers constraints from multiple dimensions, such as cargo aircraft and vehicle load limitations. Meanwhile, corresponding improvement strategies were designed based on the Sand Cat Swarm Optimization (SCSO) algorithm. An improved swarm intelligence algorithm was proposed to develop an optimizer based on the improved swarm intelligence algorithm for model solving. The effectiveness of the proposed mathematical model and improved swarm intelligence algorithm was verified through a real-world case of cross-border e-commerce logistics transportation. The results indicate that using the proposed solution in this study, the cost of delivery and carbon emissions can be reduced, while customer satisfaction can be improved.

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A survey on bilevel optimization under uncertainty

Cited by 46 publications

References 142 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

A Successive Linear Relaxation Method for MINLPs with Multivariate Lipschitz Continuous Nonlinearities

Improved Swarm Intelligence-Based Logistics Distribution Optimizer: Decision Support for Multimodal Transportation of Cross-Border E-Commerce

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