Journal articles: 'Bilevel optimal control'

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Mehlitz, Patrick, and Gerd Wachsmuth. "Weak and strong stationarity in generalized bilevel programming and bilevel optimal control." Optimization 65, no. 5 (December 31, 2015): 907–35. http://dx.doi.org/10.1080/02331934.2015.1122007.

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Ye, Jane J. "Optimal Strategies For Bilevel Dynamic Problems." SIAM Journal on Control and Optimization 35, no. 2 (March 1997): 512–31. http://dx.doi.org/10.1137/s0363012993256150.

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Bonnel, Henri, and Jacqueline Morgan. "Semivectorial Bilevel Convex Optimal Control Problems: Existence Results." SIAM Journal on Control and Optimization 50, no. 6 (January 2012): 3224–41. http://dx.doi.org/10.1137/100795450.

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Dempe, S. "Computing optimal incentives via bilevel programming." Optimization 33, no. 1 (January 1995): 29–42. http://dx.doi.org/10.1080/02331939508844061.

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Ye, Jianxiong, and An Li. "Necessary optimality conditions for nonautonomous optimal control problems and its applications to bilevel optimal control." Journal of Industrial & Management Optimization 13, no. 5 (2017): 1–21. http://dx.doi.org/10.3934/jimo.2018101.

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Lin, Hongzhi. "Optimal Design of Cordon Sanitaire for Regular Epidemic Control." Advances in Civil Engineering 2021 (June 1, 2021): 1–11. http://dx.doi.org/10.1155/2021/5581758.

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The outbreak of COVID-19 has disrupted our regular life. Many state and local authorities have enforced a cordon sanitaire for the protection of sensitive areas. Travelers can only travel across the cordon after being qualified. This paper aims to propose a method to determine the optimal deployment of cordon sanitaire in terms of the number of parallel checkpoints at each entry link for regular epidemic control. A bilevel programming model is formulated where the lower-level is the transport system equilibrium with queueing to predict traffic inflow, and the upper-level is queueing network optimization, which is an integer nonlinear programming. The objective of this optimization is to minimize the total operation cost of checkpoints with a predetermined maximum waiting time. Note that stochastic queueing theory is used to represent the waiting phenomenon at each entry link. A heuristic algorithm is designed to solve the proposed bilevel model where the method of successive averages (MSA) is adopted for the lower-level model, and the genetic algorithm (GA) is adopted for the upper-level model. An experimental study is conducted to demonstrate the effectiveness of the proposed method and algorithm. The results show that the methods can find a good heuristic optimal solution. These methods are useful for policymakers to determine the optimal deployment of cordon sanitaire for hazard prevention and control.

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Atiya Wardil *, Othman, and Samera Khaleel Ibrahim. "The Bi-level Programming Approach to Improve the Inventory Control System with a Practical Application." Journal of Economics and Administrative Sciences 30, no. 142 (September 6, 2024): 509–31. http://dx.doi.org/10.33095/gd8dy062.

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In this research, we investigated addressing the challenges associated with the seasonal allergic medical drug inventory system. The focus was on determining the optimal demand by calculating the Economic Order Quantity (EOQ) and achieving the lowest cost within the Pharmaceutical Industries and Medical Supplies company in Samarra. The primary objective was to efficiently meet the demand for seasonal allergy medications by identifying the optimal demand for medical drugs. The study encompassed two types of seasonal allergy medications, namely Samatifen drink and VALIAPAM 2 pills. The calculation of the lowest cost involved two methods: the multi-component production model without deficit, with restrictions, the solution was done using the classical method (normal) and mathematical analyses, utilizing tools such as QM and Win Qsb. Additionally, linear quadratic bilevel programming (LQBP) was employed. The LQBP model comprised an upper-level decision maker (leader) and a lower-level decision maker (follower). The transformation of the bilevel model into a single-level model was accomplished through the application of Karush-Kuhn-Tucker (KKT) conditions, and the solution was obtained using the modified simplex algorithm. The study's findings underscore the effectiveness of the LQBP method in identifying the optimal solution for the inventory problem by calculating the lowest cost. This approach significantly reduced medical drug inventory-related costs, with a value of 1,496,700,000 Iraqi Dinars (ID) and a production of 1200,700 ID. Notably, this cost was considerably lower than the total cost value obtained using the classical method, which was 1,719,166 ID/year, with a production of 2526,1773 ID. Therefore, bilevel programming (BLPP) demonstrates superior efficiency, providing more accurate and cost-effective solutions. This research emphasizes the potential of bilevel programming in optimizing medical drug inventory systems and contributes to the advancement of operational research in the healthcare sector. Paper type: Research Paper

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Amouzegar, Mahyar A., and Khosrow Moshirvaziri. "Determining optimal pollution control policies: An application of bilevel programming." European Journal of Operational Research 119, no. 1 (November 1999): 100–120. http://dx.doi.org/10.1016/s0377-2217(98)00336-1.

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Knauer, Matthias. "Fast and save container cranes as bilevel optimal control problems." Mathematical and Computer Modelling of Dynamical Systems 18, no. 4 (August 2012): 465–86. http://dx.doi.org/10.1080/13873954.2011.642388.

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Chen, Yi, Kadhim Hayawi, Meikai Fan, Shih Yu Chang, Jie Tang, Ling Yang, Rui Zhao, Zhongqi Mao, and Hong Wen. "A Bilevel Optimization Model Based on Edge Computing for Microgrid." Sensors 22, no. 20 (October 11, 2022): 7710. http://dx.doi.org/10.3390/s22207710.

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With the continuous progress of renewable energy technology and the large-scale construction of microgrids, the architecture of power systems is becoming increasingly complex and huge. In order to achieve efficient and low-delay data processing and meet the needs of smart grid users, emerging smart energy systems are often deployed at the edge of the power grid, and edge computing modules are integrated into the microgrids system, so as to realize the cost-optimal control decision of the microgrids under the condition of load balancing. Therefore, this paper presents a bilevel optimization control model, which is divided into an upper-level optimal control module and a lower-level optimal control module. The purpose of the two-layer optimization modules is to optimize the cost of the power distribution of microgrids. The function of the upper-level optimal control module is to set decision variables for the lower-level module, while the function of the lower-level module is to find the optimal solution by mathematical methods on the basis of the upper-level and then feed back the optimal solution to the upper-layer. The upper-level and lower-level modules affect system decisions together. Finally, the feasibility of the bilevel optimization model is demonstrated by experiments.

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Lu, Zhichao, Kalyanmoy Deb, and Ankur Sinha. "Uncertainty Handling in Bilevel Optimization for Robust and Reliable Solutions." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 26, Suppl. 2 (December 2018): 1–24. http://dx.doi.org/10.1142/s0218488518400093.

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Uncertainties in variables and parameters cause optimization problems to move away from globally-optimal and uncertain solutions. Practitioners resort to finding robust and reliable solutions in such situations. Bilevel optimization problems involving a hierarchy of two nested optimization problems have received a growing attention in the recent past due to their relevance in practice. While a number of studies on bilevel solution methodologies and applications are available for a deterministic setup, but studies on uncertainties in bilevel optimization are rare. In this paper, we suggest methodologies for handling uncertainty in both lower and upper level variables that may occur from different practicalities. For the first time, we perform a systematic study demonstrating the effect of uncertainties in each level along with the definition of robustness and reliability in the context of bilevel optimization. The issues and complexities introduced due to such uncertainties are then studied through a number of test cases, for brevity, we only show results on three test cases. Finally, two real-world bilevel problems involving uncertainties in their variables are solved. The study provides foundations and demon- strates viable directions for further research in uncertainty-based bilevel optimization problems.

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Liang, Yongliang, Zhiqi Li, Yuchuan Li, Shuwen Leng, Hongmei Cao, and Kejun Li. "Bilevel Optimal Economic Dispatch of CNG Main Station Considering Demand Response." Energies 16, no. 7 (March 28, 2023): 3080. http://dx.doi.org/10.3390/en16073080.

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Compressed natural gas (CNG) main stations are critical components of the urban energy infrastructure for CNG distribution. Due to its high electrification and significant power consumption, researching the economic operation of the CNG main station in demand response (DR)-based electricity pricing environments is crucial. In this paper, the dehydration process is considered in the CNG main station energy consumption model to enhance its participation in DR. A bilevel economic dispatch model for the CNG main station is proposed, considering critical peak pricing. The upper-level and lower-level models represent the energy cost minimization problems of the pre-system and rear-system, respectively, with safety operation constraints. The bilevel programming model is solved using a genetic algorithm combined with a bilevel programming method, which has better efficiency and convergence. The proposed optimization scheme has better control performance and stability, reduces the daily electricity cost by approximately 21.04%, and decreases the compressor switching frequency by 50.00% without changing the CNG filling demand, thus significantly extending the compressor’s service life. Moreover, the average comprehensive power cost of processing one unit of CNG reduces 20.62%.

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Kalashnikov, Vyacheslav V., Francisco Benita, and Patrick Mehlitz. "The Natural Gas Cash-Out Problem: A Bilevel Optimal Control Approach." Mathematical Problems in Engineering 2015 (2015): 1–17. http://dx.doi.org/10.1155/2015/286083.

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The aim of this paper is threefold: first, it formulates the natural gas cash-out problem as a bilevel optimal control problem (BOCP); second, it provides interesting theoretical results about Pontryagin-type optimality conditions for a general BOCP where the upper level boasts a Mayer-type cost function and pure state constraints, while the lower level is a finite-dimensional mixed-integer programming problem with exactly one binary variable; and third, it applies these theoretical results in order to find possible local minimizers of the natural gas cash-out problem.

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Lobo Pereira, Fernando, and Nathalie T. Khalil. "A Maximum Principle for a Time-Optimal Bilevel Sweeping Control Problem." Journal of Optimization Theory and Applications 192, no. 3 (March 2022): 1022–51. http://dx.doi.org/10.1007/s10957-022-02004-3.

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Benita, F., and P. Mehlitz. "Bilevel Optimal Control With Final-State-Dependent Finite-Dimensional Lower Level." SIAM Journal on Optimization 26, no. 1 (January 2016): 718–52. http://dx.doi.org/10.1137/15m1015984.

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Liua, Yuquan, Yuehao Zhao, Ke Peng, Bingyin Xu, Li Wang, and Huangsheng Hua. "Bilevel optimal coordinated control strategy for park-level integrated energy system." Energy Procedia 145 (July 2018): 44–53. http://dx.doi.org/10.1016/j.egypro.2018.04.009.

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Kalashnikov, Vyacheslav, Stephan Dempe, Boris Mordukhovich, and Sergii V. Kavun. "Bilevel Optimal Control, Equilibrium, and Combinatorial Problems with Applications to Engineering." Mathematical Problems in Engineering 2017 (2017): 1–3. http://dx.doi.org/10.1155/2017/7190763.

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Lu, Ping, Sergio Sandoval, and Christopher Davami. "Fast and Robust Optimization of Full Trajectory from Entry Through Powered Descent." Journal of Guidance, Control, and Dynamics 47, no. 2 (February 2024): 203–16. http://dx.doi.org/10.2514/1.g007564.

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A high-mass Mars entry, descent, and landing (EDL) mission for cargo delivery or human exploration faces the challenge of a high propellant mass fraction requirement for powered descent. This work develops a novel method and the associated algorithm that utilize existing entry and propellant-optimal powered descent guidance algorithms for fast and robust optimization of the end-to-end EDL trajectory for achieving the overall optimized propellant efficiency. A bilevel optimization formulation aided by a predictive logic based on the optimal powered descent algorithm to determine the near-optimal transition from entry to powered descent allows the end-to-end trajectory to be optimized in a relatively simple manner. No new major software or algorithms are required other than the existing guidance algorithms. A solution to the bilevel optimization problem is shown to exist, and the convergence of the bilevel optimization algorithm is guaranteed under certain mild assumptions. The algorithm developed in this paper is able to find consistently an end-to-end near-optimal EDL trajectory in just over 10 s on a desktop computer, while general-purpose modern trajectory optimization software can take thousands of seconds. The effectiveness and robustness of the algorithm are demonstrated by successfully optimizing thousands of complete EDL trajectories efficiently and reliably from dispersed initial entry conditions.

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Shi, Shenglei, Youlun Xiong, Jiankui Chen, and Caihua Xiong. "A bilevel optimal motion planning (BOMP) model with application to autonomous parking." International Journal of Intelligent Robotics and Applications 3, no. 4 (November 12, 2019): 370–82. http://dx.doi.org/10.1007/s41315-019-00109-z.

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Abstract In this paper, we present a bilevel optimal motion planning (BOMP) model for autonomous parking. The BOMP model treats motion planning as an optimal control problem, in which the upper level is designed for vehicle nonlinear dynamics, and the lower level is for geometry collision-free constraints. The significant feature of the BOMP model is that the lower level is a linear programming problem that serves as a constraint for the upper-level problem. That is, an optimal control problem contains an embedded optimization problem as constraints. Traditional optimal control methods cannot solve the BOMP problem directly. Therefore, the modified approximate Karush–Kuhn–Tucker theory is applied to generate a general nonlinear optimal control problem. Then the pseudospectral optimal control method solves the converted problem. Particularly, the lower level is the $$J_2$$J2-function that acts as a distance function between convex polyhedron objects. Polyhedrons can approximate objects in higher precision than spheres or ellipsoids. As a result, a fast high-precision BOMP algorithm for autonomous parking concerning dynamical feasibility and collision-free property is proposed. Simulation results and experiment on Turtlebot3 validate the BOMP model, and demonstrate that the computation speed increases almost two orders of magnitude compared with the area criterion based collision avoidance method.

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Deb, Kalyanmoy, and Ankur Sinha. "An Efficient and Accurate Solution Methodology for Bilevel Multi-Objective Programming Problems Using a Hybrid Evolutionary-Local-Search Algorithm." Evolutionary Computation 18, no. 3 (September 2010): 403–49. http://dx.doi.org/10.1162/evco_a_00015.

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Bilevel optimization problems involve two optimization tasks (upper and lower level), in which every feasible upper level solution must correspond to an optimal solution to a lower level optimization problem. These problems commonly appear in many practical problem solving tasks including optimal control, process optimization, game-playing strategy developments, transportation problems, and others. However, they are commonly converted into a single level optimization problem by using an approximate solution procedure to replace the lower level optimization task. Although there exist a number of theoretical, numerical, and evolutionary optimization studies involving single-objective bilevel programming problems, not many studies look at the context of multiple conflicting objectives in each level of a bilevel programming problem. In this paper, we address certain intricate issues related to solving multi-objective bilevel programming problems, present challenging test problems, and propose a viable and hybrid evolutionary-cum-local-search based algorithm as a solution methodology. The hybrid approach performs better than a number of existing methodologies and scales well up to 40-variable difficult test problems used in this study. The population sizing and termination criteria are made self-adaptive, so that no additional parameters need to be supplied by the user. The study indicates a clear niche of evolutionary algorithms in solving such difficult problems of practical importance compared to their usual solution by a computationally expensive nested procedure. The study opens up many issues related to multi-objective bilevel programming and hopefully this study will motivate EMO and other researchers to pay more attention to this important and difficult problem solving activity.

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Minciardi, R., and M. Robba. "A Bilevel Approach for the Optimal Control of Flows Through a Network." IEEE Systems Journal 6, no. 3 (September 2012): 539–47. http://dx.doi.org/10.1109/jsyst.2012.2192059.

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Jiang, Nan. "Optimal Signal Design for Mixed Equilibrium Networks with Autonomous and Regular Vehicles." Journal of Advanced Transportation 2017 (2017): 1–13. http://dx.doi.org/10.1155/2017/5649823.

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A signal design problem is studied for efficiently managing autonomous vehicles (AVs) and regular vehicles (RVs) simultaneously in transportation networks. AVs and RVs move on separate lanes and two types of vehicles share the green times at the same intersections. The signal design problem is formulated as a bilevel program. The lower-level model describes a mixed equilibrium where autonomous vehicles follow the Cournot-Nash (CN) principle and RVs follow the user equilibrium (UE) principle. In the upper-level model, signal timings are optimized at signalized intersections to allocate appropriate green times to both autonomous and RVs to minimize system travel cost. The sensitivity analysis based method is used to solve the bilevel optimization model. Various signal control strategies are evaluated through numerical examples and some insightful findings are obtained. It was found that the number of phases at intersections should be reduced for the optimal control of the AVs and RVs in the mixed networks. More importantly, incorporating AVs into the transportation network would improve the system performance due to the value of AV technologies in reducing random delays at intersections. Meanwhile, travelers prefer to choose AVs when the networks turn to be congested.

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Calvete, Herminia I., Carmen Galé, Stephan Dempe, and Sebastian Lohse. "Bilevel problems over polyhedra with extreme point optimal solutions." Journal of Global Optimization 53, no. 3 (August 9, 2011): 573–86. http://dx.doi.org/10.1007/s10898-011-9762-6.

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Benita, F., S. Dempe, and P. Mehlitz. "Bilevel Optimal Control Problems with Pure State Constraints and Finite-dimensional Lower Level." SIAM Journal on Optimization 26, no. 1 (January 2016): 564–88. http://dx.doi.org/10.1137/141000889.

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Ko, J. H., S. S. Hong, and M. J. Youn. "New optimal predictive current mode control technique for bilevel quantum series resonant convertors." Electronics Letters 27, no. 5 (1991): 412. http://dx.doi.org/10.1049/el:19910261.

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Minciardi, Riccardo, and Michela Robba. "A Bilevel Approach for the Stochastic Optimal Operation of Interconnected Microgrids." IEEE Transactions on Automation Science and Engineering 14, no. 2 (April 2017): 482–93. http://dx.doi.org/10.1109/tase.2016.2620150.

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Zheng, Huankun, and Kaidi Yu. "An Optimization Control Method of IEH Considering User Thermal Comfort." Energies 17, no. 4 (February 18, 2024): 948. http://dx.doi.org/10.3390/en17040948.

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In this paper, a user thermal comfort criterion based on predicted mean vote (PMV) values is introduced to realize the optimal operation of an improved energy hub (IEH) while considering thermal inertia and user thermal behavior. A three-layer optimization model based on user thermal comfort is constructed which fully considers user thermal comfort demand, IEH operating costs, and energy network constraints. Moreover, since IEH optimization considering user thermal comfort is a multi-objective bilevel optimization (MNBO) problem, this paper proposes an improved multilayer nested quantum genetic algorithm (IMNQGA) to solve it. Finally, the effectiveness of the proposed optimization model and algorithm is verified through the analysis of the four modes. The examples show that the proposed optimal control method can reduce the system’s operating costs and improve energy efficiency while satisfying user thermal comfort demand.

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Ma, Zetao, Nikolce Murgovski, Bo Egardt, and Shumei Cui. "Convex modeling for optimal battery sizing and control of an electric variable transmission powertrain." Oil & Gas Science and Technology – Revue d’IFP Energies nouvelles 74 (2019): 25. http://dx.doi.org/10.2516/ogst/2018104.

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This paper provides convex modeling steps for the problem of optimal battery sizing and energy management of a plug-in hybrid electric vehicle with an electric variable transmission. Optimal energy management is achieved by a switched model control, with driving modes identified by the engine on/off state. In pure electric mode, convex optimization is used to find the optimal torque split between two electric machines, in order to maximize powertrain efficiency. In hybrid mode, optimization is performed in a bilevel program. One level optimizes speed of a compound unit that includes the engine and electric machines. Another level optimizes the power split between the compound unit and the battery. The proposed method is used to minimize the total cost of ownership of a passenger vehicle for a daily commuter, including costs for battery, fossil fuel and electricity.

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Li, Dawei, Yuchen Song, and Qiong Chen. "Bilevel Programming for Traffic Signal Coordinated Control considering Pedestrian Crossing." Journal of Advanced Transportation 2020 (February 13, 2020): 1–18. http://dx.doi.org/10.1155/2020/3987591.

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With the rapid development of the subway, more and more people choose it as the main method of transportation. However, practically, the large number of pedestrians near some large metro stations can also correspondingly affect the traffic of motor vehicles on the roads adjacent to the stations. In this study, coordinated control of the traffic signal which considers the pedestrian crossing delay is studied based on this background. Firstly, the model of progression band in adjacent intersections is analyzed comprehensively, and the calculation formulas of progression bandwidth and the delay of vehicles which are from the progression of traffic flow under different conditions are given. Secondly, five different models of pedestrian delay are analyzed. Under different conditions of motor vehicle and pedestrian traffic flow, the Vissim fitting and proofreading are carried out and the optimal models under different conditions are obtained. Finally, the bilevel programming problem which fuses the above two models is determined; by coding an algorithm, it can be resolved. Furthermore, taking eight signalized intersections from Jiming Temple to Daxinggong along Nanjing Metro Line 3 as the actual background, the calculation and optimization of coordinated control are carried out. It is found that at the expense of the traffic efficiency of large intersections to a certain extent, a wider progression band can be formulated on the roads between them, and pedestrian delays can be reduced in general.

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Penkovskii, Andrey. "Hierarchical management model of heat supply to consumers." E3S Web of Conferences 219 (2020): 03004. http://dx.doi.org/10.1051/e3sconf/202021903004.

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The article proposes a hierarchical management model for heat supply to consumers based on the method of bilevel programming. An organizational model of heat supply to consumers in the form of a Unified Heat Supply Organization in a two-tier control system is considered, when the regulators (regional tariff service) manages tariffs for consumers, and heat sources cover the given demand from consumers from the condition of obtaining maximum profit. With the help of bilevel approach, the technical and economic indicators of the district heating are calculated. The proposed mathematical model makes it possible to take into account the technical and economic characteristics of heat sources and heat networks, the interests of the participants in the process of heat supply to consumers and to determine the optimal conditions for controlling the functioning of district heating systems.

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Zeng, Bo, Houqi Dong, Fuqiang Xu, and Ming Zeng. "Bilevel Programming Approach for Optimal Planning Design of EV Charging Station." IEEE Transactions on Industry Applications 56, no. 3 (May 2020): 2314–23. http://dx.doi.org/10.1109/tia.2020.2973189.

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Dempe, S., and F. Mefo Kue. "Solving discrete linear bilevel optimization problems using the optimal value reformulation." Journal of Global Optimization 68, no. 2 (October 22, 2016): 255–77. http://dx.doi.org/10.1007/s10898-016-0478-5.

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Zou, Yuan, Dong-ge Li, and Xiao-song Hu. "Optimal Sizing and Control Strategy Design for Heavy Hybrid Electric Truck." Mathematical Problems in Engineering 2012 (2012): 1–15. http://dx.doi.org/10.1155/2012/404073.

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Due to the complexity of the hybrid powertrain, the control is highly involved to improve the collaborations of the different components. For the specific powertrain, the components' sizing just gives the possibility to propel the vehicle and the control will realize the function of the propulsion. Definitely the components' sizing also gives the constraints to the control design, which cause a close coupling between the sizing and control strategy design. This paper presents a parametric study focused on sizing of the powertrain components and optimization of the power split between the engine and electric motor for minimizing the fuel consumption. A framework is put forward to accomplish the optimal sizing and control design for a heavy parallel pre-AMT hybrid truck under the natural driving schedule. The iterative plant-controller combined optimization methodology is adopted to optimize the key parameters of the plant and control strategy simultaneously. A scalable powertrain model based on a bilevel optimization framework is built. Dynamic programming is applied to find the optimal control in the inner loop with a prescribed cycle. The parameters are optimized in the outer loop. The results are analysed and the optimal sizing and control strategy are achieved simultaneously.

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Fisch, F., J. Lenz, F. Holzapfel, and G. Sachs. "On the Solution of Bilevel Optimal Control Problems to Increase the Fairness in Air Races." Journal of Guidance, Control, and Dynamics 35, no. 4 (July 2012): 1292–98. http://dx.doi.org/10.2514/1.54407.

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Albrecht, Sebastian, Marion Leibold, and Michael Ulbrich. "A bilevel optimization approach to obtain optimal cost functions for human arm movements." Numerical Algebra, Control & Optimization 2, no. 1 (2012): 105–27. http://dx.doi.org/10.3934/naco.2012.2.105.

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Kis, Tamás, András Kovács, and Csaba Mészáros. "On Optimistic and Pessimistic Bilevel Optimization Models for Demand Response Management." Energies 14, no. 8 (April 9, 2021): 2095. http://dx.doi.org/10.3390/en14082095.

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This paper investigates bilevel optimization models for demand response management, and highlights the often overlooked consequences of a common modeling assumption in the field. That is, the overwhelming majority of existing research deals with the so-called optimistic variant of the problem where, in case of multiple optimal consumption schedules for a consumer (follower), the consumer chooses an optimal schedule that is the most favorable for the electricity retailer (leader). However, this assumption is usually illegitimate in practice; as a result, consumers may easily deviate from their expected behavior during realization, and the retailer suffers significant losses. One way out is to solve the pessimistic variant instead, where the retailer prepares for the least favorable optimal responses from the consumers. The main contribution of the paper is an exact procedure for solving the pessimistic variant of the problem. First, key properties of optimal solutions are formally proven and efficiently solvable special cases are identified. Then, a detailed investigation of the optimistic and pessimistic variants of the problem is presented. It is demonstrated that the set of optimal consumption schedules typically contains various responses that are equal for the follower, but bring radically different profits for the leader. The main procedure for solving the pessimistic variant reduces the problem to solving the optimistic variant with slightly perturbed problem data. A numerical case study shows that the optimistic solution may perform poorly in practice, while the pessimistic solution gives very close to the highest profit that can be achieved theoretically. To the best of the authors’ knowledge, this paper is the first to propose an exact solution approach for the pessimistic variant of the problem.

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Ni, Ya Qi, Jia Shi Yang, Dian Gang Wang, Cheng Wei Li, Jun Yong Liu, and Hui Gong. "Research of Electric Vehicles' Discharging Price." Applied Mechanics and Materials 543-547 (March 2014): 452–56. http://dx.doi.org/10.4028/www.scientific.net/amm.543-547.452.

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Through the vehicle to the network (V2G) control, the objective of the "load shifting" is possible. Reasonable charging and discharging price is the fundamental driving force for EV users to participate in V2G and the analysis of the game process of the grid company and the EV users becomes critical. A bilevel programming problem is established which makes company the largest gains and consumers the minimum cost. Through a control scheme whose purpose is minimizing the sample variance of load, the relationship of annual discharging electricity energy and peak load decrement is obtained. At last the optimal discharging price of power grid company and the corresponding proportion of EV participating in V2G is calculated by chaos algorithm. It provides a reference for company to formulate discharging price.

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Zheng, Guorong, and Mingyan Zhang. "Research on the Cooperative Control Method of Intermittent Bus Lane and Downstream Intersection." Mathematical Problems in Engineering 2022 (January 31, 2022): 1–7. http://dx.doi.org/10.1155/2022/5621301.

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Intermittent bus lane (IBL) used for bus priority is a lane in which the status of a given section changes according to the presence or absence of a bus in its spatial domain. Therefore, when bus services are not so frequent, general traffic will not suffer much, and bus priority can still be obtained. In order to further explore the road resource utilization, a signal timing optimization model was proposed considering coordinate intermittent bus lanes and downstream intersections. Firstly, the functional relationship was established between the general vehicle carrying capacity and the social vehicle arrival rates, the distribution of public transportation vehicles, and the downstream intersection timing plan; then, a bilevel programming model was built which maximizes the social vehicle carrying capacity and simultaneously minimizes the delay of general vehicle intersections. Finally, the optimal solution of carrying capacity under different scenarios was analyzed through experimental simulation, which effectively reduced the delay and proved the effectiveness of the proposed method.

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Wang, Puming, Liqin Zheng, Tianyi Diao, Shengquan Huang, and Xiaoqing Bai. "Robust Bilevel Optimal Dispatch of Park Integrated Energy System Considering Renewable Energy Uncertainty." Energies 16, no. 21 (October 27, 2023): 7302. http://dx.doi.org/10.3390/en16217302.

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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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Chen, Nathan, David Rey, and Lauren Gardner. "Multiscale Network Model for Evaluating Global Outbreak Control Strategies." Transportation Research Record: Journal of the Transportation Research Board 2626, no. 1 (January 2017): 42–50. http://dx.doi.org/10.3141/2626-06.

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High volumes of passenger air travel increase the risk of infectious disease epidemics and pandemics. Regional preparedness planning for large-scale outbreaks requires models that are able to capture outbreak dynamics within a control policy evaluation framework. Previous studies focused on either modeling outbreak dynamics or optimizing outbreak control decisions; this paper proposes an integrated approach that combines both aspects. A multiscale epidemic outbreak model is introduced that is designed to capture the infection dynamics at both the local (city) scale and the global (air travel) scale. A bilevel decision-making framework is then proposed to identify the optimal set of outbreak control policies, while accounting for local and global outbreak dynamics. The model is implemented for a case study in which a hypothetical epidemic outbreak is assumed to emerge from within the United States, and different control resource allocation strategies are explored and evaluated. The results highlight the importance of accounting for outbreak dynamics within the decision-making process and provide insight into the design and efficiency of a range of control strategies. This research is an initial effort to be followed by further research on the design of outbreak control strategies by using optimization algorithms under this framework.

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Christof, Constantin. "Gradient-Based Solution Algorithms for a Class of Bilevel Optimization and Optimal Control Problems with a Nonsmooth Lower Level." SIAM Journal on Optimization 30, no. 1 (January 2020): 290–318. http://dx.doi.org/10.1137/18m1225707.

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Hieu, Dang Van, Le Dung Muu, and Pham Kim Quy. "STRONG CONVERGENCE OF MULTI-PARAMETER PROJECTION METHODS FOR VARIATIONAL INEQUALITY PROBLEMS." Mathematical Modelling and Analysis 27, no. 2 (April 27, 2022): 242–62. http://dx.doi.org/10.3846/mma.2022.14479.

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In this paper, we introduce a multi-parameter projection method for solving a variational inequality problem, and establish its strong convergence in a Hilbert space under appropriate conditions. The method involves two projectionsteps with different variable stepsizes where one of them is computed explicitly on a specifically structural half-space. The proof of strong convergence of the method is based on the regularization solutions depending on parameters of the original problem. It turns out that the solution obtained by the method is the solution of a bilevel variational inequality problem whose constraint is the solution set of our considered problem. In order to support the obtained theoretical results, we perform some experiments on transportation equilibrium and optimal control problems, and also involve comparisons. Numerical results show the computational effectiveness and the fast convergence of the new method over some existing ones.

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Zhao, Yuehao, Ke Peng, Bingyin Xu, Huimin Li, Yuquan Liu, and Xinhui Zhang. "Bilevel Optimal Dispatch Strategy for a Multi-Energy System of Industrial Parks by Considering Integrated Demand Response." Energies 11, no. 8 (July 26, 2018): 1942. http://dx.doi.org/10.3390/en11081942.

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To combat energy shortage, the multi-energy system has gained increasing interest in contemporary society. In order to fully utilize adjustable multi-energy resources on the demand side and reduce interactive compensation, this paper presents an integrated demand response (IDR) model in consideration of conventional load-shedding and novel resource-shifting, due to the fact that participants in IDR can use more abundant resources to reduce the consumption of energy. In the proposed IDR, cooling, heating, electricity, gas and so forth are considered, which takes the connection between compensation and load reductions into consideration. Furthermore, a bilevel optimal dispatch strategy is proposed to decrease the difficulty in coordinated control and interaction between lower-level factories and upper-level multi-energy operators in industrial parks. In this strategy, resources in both multi-energy operator and user sides are optimally controlled and scheduled to maximize the benefits under peak shifting constraint. In the normal operation mode, this strategy can maximize the benefits to users and multi-energy operators. Particularly in heavy load conditions, compared to the conventional electricity demand response, there are more types of adjustable resources, more flexibility, and lower interactive compensations in IDR. The results indicate that optimal operation for factories and multi-energy operators can be achieved under peak shifting constraint and the overall peak power value in industrial park is reduced.

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Xu, Tao, He Meng, Jie Zhu, Wei Wei, He Zhao, Han Yang, Zijin Li, and Yuhan Wu. "Optimal Capacity Allocation of Energy Storage in Distribution Networks Considering Active/Reactive Coordination." Energies 14, no. 6 (March 14, 2021): 1611. http://dx.doi.org/10.3390/en14061611.

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Energy storage system (ESS) has been advocated as one of the key elements for the future energy system by the fast power regulation and energy transfer capabilities. In particular, for distribution networks with high penetration of renewables, ESS plays an important role in bridging the gap between the supply and demand, maximizing the benefits of renewables and providing various types of ancillary services to cope the intermittences and fluctuations, consequently improving the resilience, reliability and flexibility. To solve the voltage fluctuations caused by the high permeability of renewables in distribution networks, an optimal capacity allocation strategy of ESS is proposed in this paper. Taking the life cycle cost, arbitrage income and the benefit of reducing network losses into consideration, a bilevel optimization model of ESS capacity allocation is established, the coordination between active/reactive power of associate power conversion system is considered, and the large scale nonlinear programming problem is solved using genetic algorithm, simulated annealing and mixed integer second-order cone programming method. The feasibility and effectiveness of the proposed algorithm have been verified.

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Cai, Yongyang. "Computational Methods in Environmental and Resource Economics." Annual Review of Resource Economics 11, no. 1 (October 5, 2019): 59–82. http://dx.doi.org/10.1146/annurev-resource-100518-093841.

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Computational methods are required to solve problems without closed-form solutions in environmental and resource economics. Efficiency, stability, and accuracy are key elements for computational methods. This review discusses state-of-the-art computational methods applied in environmental and resource economics, including optimal control methods for deterministic models, advances in value function iteration and time iteration for general dynamic stochastic problems, nonlinear certainty equivalent approximation, robust decision making, real option analysis, bilevel optimization, solution methods for continuous time problems, and so on. This review also clarifies the so-called curse of dimensionality, and discusses some computational techniques such as approximation methods without the curse of dimensionality and time-dependent approximation domains. Many existing economic models use simplifying and/or unrealistic assumptions with an excuse of computational feasibility, but these assumptions might be able to be relaxed if we choose an efficient computational method discussed in this review.

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Joksimovic, Dusica, Michiel C. J. Bliemer, and Piet H. L. Bovy. "Optimal Toll Design Problem in Dynamic Traffic Networks with Joint Route and Departure Time Choice." Transportation Research Record: Journal of the Transportation Research Board 1923, no. 1 (January 2005): 61–72. http://dx.doi.org/10.1177/0361198105192300107.

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Road pricing is one of the market-based traffic control measures that can influence travel behavior to alleviate congestion on roads. This paper addresses the effects of uniform (constant, fixed) and time-varying (step) tolls on the travel behavior of users on the road network. The problem of determining optimal prices in a dynamic traffic network is considered by applying second-best tolling scenarios imposing tolls only to a subset of links on the network and considering elastic demand. The optimal toll design problem is formulated as a bilevel optimization problem with the road authority (on the upper level) setting the tolls and the travelers (on the lower level) who respond by changing their travel decisions (route and departure time choice). To formulate the optimal toll design problem, the so-called mathematical program with equilibrium constraints (MPEC) formulation was used, considering the dynamic nature of traffic flows on the one hand and dynamic pricing on the other. Until now, the MPEC formulation has been applied in static cases only. The model structure comprises three interrelated levels: (a) dynamic network loading, (b) route choice and departure time choice, and (c) road pricing level. For solving the optimal toll design problem in dynamic networks, a simple search algorithm is used to determine the optimal toll pattern leading to optimization of the objective function of the road authority subject to dynamic traffic assignment constraints. Nevertheless, uniform and time-varying pricing is analyzed, and a small hypothetical network is considered.

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Kozanidis, George, Eftychia Kostarelou, Panagiotis Andrianesis, and George Liberopoulos. "Mixed integer parametric bilevel programming for optimal strategic bidding of energy producers in day-ahead electricity markets with indivisibilities." Optimization 62, no. 8 (August 2013): 1045–68. http://dx.doi.org/10.1080/02331934.2013.801473.

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Li, Xu, Zimeng Liu, Qing Xu, Zhongyi Jiang, and Guoliang Ma. "Optimal Policy Mechanism Design for Cross-Sector and Multi-Stage Pollution Control with a Bilevel Model: Application to SO2 Emission in China." Environmental Modeling & Assessment 22, no. 3 (October 6, 2016): 243–55. http://dx.doi.org/10.1007/s10666-016-9533-3.

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Sund, Lennard, Saber Talari, and Wolfgang Ketter. "Stochastic Wind Power Generation Planning in Liberalised Electricity Markets within a Heterogeneous Landscape." Energies 15, no. 21 (October 31, 2022): 8109. http://dx.doi.org/10.3390/en15218109.

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Spatially separated locations may differ greatly with respect to their electricity demand, available space, and local weather conditions. Thus, the regions that are best suited to operating wind turbines are often not those where electricity is demanded the most. Optimally, renewable generation facilities are constructed where the maximum generation can be expected. With transmission lines limited in capacity though, it might be economically rational to install renewable power sources in geographically less favourable locations. In this paper, a stochastic bilevel optimisation is developed as a mixed-integer linear programme to find the socially optimal investment decisions for generation expansion in a multi-node system with transmission constraints under an emissions reduction policy. The geographic heterogeneity is captured by using differently skewed distributions as a basis for scenario generation for wind speeds as well as different opportunities to install generation facilities at each node. The results reinforce that binding transmission constraints can greatly decrease total economic and emissions efficiency, implying additional incentives to enhance transmission capacity between the optimal supplier locations and large demand centres.

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Li, Peixuan, Meilin Wen, Tianpei Zu, and Rui Kang. "A Joint Location–Allocation–Inventory Spare Part Optimization Model for Base-Level Support System with Uncertain Demands." Axioms 12, no. 1 (January 1, 2023): 46. http://dx.doi.org/10.3390/axioms12010046.

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This paper copes with a joint Location-Allocation-Inventory problem in a three-echelon base-level spare part support system with epistemic uncertainty in uncertain demands of bases. The aim of the paper is to propose an optimization model under the uncertainty theory to minimize the total cost, which integrates crucial characterizations of the inventory control decisions and the location-allocation scheme arrangement under a periodic review order-up-to-S (T, S) policy. Uncertainty theory is introduced in this paper to characterize epistemic uncertainty, where demands are treated as uncertain variables and stockout loss is represented by value-at-risk in uncertain measurement. To solve the original uncertain optimization model, an equivalent deterministic model is derived and addressed by an improved bilevel genetic algorithm. Moreover, the proposed models and algorithm are encoded into numerical examples for supply chain programming. The results highlight the applicability of the model and the algorithm’s effectiveness in approaching the optimal solution compared with traditional genetic algorithm. Sensitivity analyses are further made for the impacts of review time and inventory capacity on different cost components.

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Journal articles on the topic 'Bilevel optimal control'

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