Journal articles: 'Bilevel program'

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Xu, Yi, and Lili Han. "Quadratic Program on a Structured Nonconvex Set." Mathematical Problems in Engineering 2020 (March 12, 2020): 1–6. http://dx.doi.org/10.1155/2020/4318186.

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In this paper, we focus on a special nonconvex quadratic program whose feasible set is a structured nonconvex set. To find an effective method to solve this nonconvex program, we construct a bilevel program, where the low-level program is a convex program while the upper-level program is a small-scale nonconvex program. Utilizing some properties of the bilevel program, we propose a new algorithm to solve this special quadratic program. Finally, numerical results show that our new method is effective and efficient.

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Mitsos, Alexander, Panayiotis Lemonidis, and Paul I. Barton. "Global solution of bilevel programs with a nonconvex inner program." Journal of Global Optimization 42, no. 4 (December 5, 2007): 475–513. http://dx.doi.org/10.1007/s10898-007-9260-z.

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Aboussoror, Abdelmalek, Hicham Babahadda, and Abdelatif Mansouri. "Bilevel programs with extremal value function: global optimality." International Journal of Mathematics and Mathematical Sciences 2005, no. 3 (2005): 419–35. http://dx.doi.org/10.1155/ijmms.2005.419.

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For a bilevel program with extremal value function, a necessary and sufficient condition for global optimality is given, which reduces the bilevel program to amax-minproblem with linked constraints. Also, for the case where the extremal value function is polyhedral, this optimality condition gives the possibility of a resolution via a maximization problem of a polyhedral convex function over a convex set. Finally, this case is completed by an algorithm.

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Liao, Jiagen, and Zhongping Wan. "On the Karush-Kuhn-Tucker reformulation of the bilevel optimization problems on Riemannian manifolds." Filomat 36, no. 11 (2022): 3609–24. http://dx.doi.org/10.2298/fil2211609l.

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Bilevel programming problems are often reformulated using the Karush-Kuhn-Tucker conditions for the lower level problem resulting in a mathematical program with complementarity constraints (MPCC). First, we present KKT reformulation of the bilevel optimization problems on Riemannian manifolds. Moreover, we show that global optimal solutions of theMPCCcorrespond to global optimal solutions of the bilevel problem on the Riemannian manifolds provided the lower level convex problem satisfies the Slater?s constraint qualification. But the relationship between the local solutions of the bilevel problem and its corresponding MPCC is incomplete equivalent. We then also show by examples that these correspondences can fail if the Slater?s constraint qualification fails to hold at lower-level convex problem. In addition,M- and C-type optimality conditions for the bilevel problem on Riemannian manifolds are given.

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Lin, Gui-Hua, Mengwei Xu, and Jane J. Ye. "On solving simple bilevel programs with a nonconvex lower level program." Mathematical Programming 144, no. 1-2 (January 30, 2013): 277–305. http://dx.doi.org/10.1007/s10107-013-0633-4.

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Li, Hecheng, and Zhicang Wang. "An Evolutionary Algorithm Using Parameter Space Searching for Interval Linear Fractional Bilevel Programming Problems." International Journal of Pattern Recognition and Artificial Intelligence 30, no. 04 (April 12, 2016): 1659011. http://dx.doi.org/10.1142/s0218001416590114.

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Interval programming is one of main approaches treating imprecise and uncertain elements involved in optimization problems. In this paper, an interval linear fractional bilevel program is considered, which is characterized in that both objective coefficients and the right-hand side vector are interval numbers, and an evolutionary algorithm (EA) is proposed to solve the problem. First, the interval parameter space of the follower’s problem is taken as the search space of the proposed EA. For each individual, one can evaluate it by dealing with a simplified interval bilevel program in which only the leader’s objective involves interval parameters. In addition, the optimality conditions of linear fractional programs are applied to convert and solve the simplified problem. Finally, some computational examples were solved and the results show that the proposed algorithm is efficient and robust.

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Li, Hecheng, and Lei Fang. "An Evolutionary Algorithm Using Duality-Base-Enumerating Scheme for Interval Linear Bilevel Programming Problems." Mathematical Problems in Engineering 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/737515.

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Interval bilevel programming problem is hard to solve due to its hierarchical structure as well as the uncertainty of coefficients. This paper is focused on a class of interval linear bilevel programming problems, and an evolutionary algorithm based on duality bases is proposed. Firstly, the objective coefficients of the lower level and the right-hand-side vector are uniformly encoded as individuals, and the relative intervals are taken as the search space. Secondly, for each encoded individual, based on the duality theorem, the original problem is transformed into a single level program simply involving one nonlinear equality constraint. Further, by enumerating duality bases, this nonlinear equality is deleted, and the single level program is converted into several linear programs. Finally, each individual can be evaluated by solving these linear programs. The computational results of 7 examples show that the algorithm is feasible and robust.

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ALVIANO, MARIO, and RAFAEL PEÑALOZA. "Fuzzy answer sets approximations." Theory and Practice of Logic Programming 13, no. 4-5 (July 2013): 753–67. http://dx.doi.org/10.1017/s1471068413000471.

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AbstractFuzzy answer set programming (FASP) is a recent formalism for knowledge representation that enriches the declarativity of answer set programming by allowing propositions to be graded. To now, no implementations of FASP solvers are available and all current proposals are based on compilations of logic programs into different paradigms, like mixed integer programs or bilevel programs. These approaches introduce many auxiliary variables which might affect the performance of a solver negatively. To limit this downside, operators for approximating fuzzy answer sets can be introduced: Given a FASP program, these operators compute lower and upper bounds for all atoms in the program such that all answer sets are between these bounds. This paper analyzes several operators of this kind which are based on linear programming, fuzzy unfounded sets and source pointers. Furthermore, the paper reports on a prototypical implementation, also describing strategies for avoiding computations of these operators when they are guaranteed to not improve current bounds. The operators and their implementation can be used to obtain more constrained mixed integer or bilevel programs, or even for providing a basis for implementing a native FASP solver. Interestingly, the semantics of relevant classes of programs with unique answer sets, like positive programs and programs with stratified negation, can be already computed by the prototype without the need for an external tool.

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Naebi Toutounchi, A., SJ Seyed Shenava, SS Taheri, and H. Shayeghi. "MPEC approach for solving preventive maintenance scheduling of power units in a market environment." Transactions of the Institute of Measurement and Control 40, no. 2 (July 27, 2016): 436–45. http://dx.doi.org/10.1177/0142331216659336.

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Yearly preventive maintenance scheduling of generating units in a restructured power system is one of the most important problems that have to be solved in modern power systems. In this paper, a bilevel approach is used for modelling of the preventive maintenance scheduling problem. The upper level of this bilevel problem represents the revenue function of power units owned by a generation company (GENCO), whereas the lower-level problem represents the market-clearing process and is usually called the independent system operator (ISO) level. This bilevel problem is then formulated as a mathematical program with equilibrium constraints (MPEC) using the primal–dual theorem, which converts the problem into a single-level mixed-integer non-linear optimization problem that can be solved using programming software. Various case studies are conducted using the IEEE reliability test system (RTS) and the obtained results are compared.

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Scaparra, Maria P., and Richard L. Church. "A bilevel mixed-integer program for critical infrastructure protection planning." Computers & Operations Research 35, no. 6 (June 2008): 1905–23. http://dx.doi.org/10.1016/j.cor.2006.09.019.

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Li, He Cheng, and Yu Ping Wang. "A Genetic Algorithm for Solving Linear-Quadratic Bilevel Program-Ming Problems." Advanced Materials Research 186 (January 2011): 626–30. http://dx.doi.org/10.4028/www.scientific.net/amr.186.626.

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In this paper, we focus on a special linear-quadratic bilevel programming problem in which the follower’s problem is a convex-quadratic programming, whereas the leader’s functions are linear. At first, based on Karush-Kuhn-Tucher(K-K-T) conditions, the original problem is transformed into an equivalent nonlinear programming problem in which the objective and constraint functions are linear except for the complementary slack conditions. Then, a genetic algorithm is proposed to solve the equivalent problem. In the proposed algorithm, the individuals are encoded in two phases. Finally, the efficiency of the approach is demonstrated by an example.

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Vardanyan, Yelena, and Henrik Madsen. "Stochastic Bilevel Program for Optimal Coordinated Energy Trading of an EV Aggregator." Energies 12, no. 20 (October 9, 2019): 3813. http://dx.doi.org/10.3390/en12203813.

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Gradually replacing fossil-fueled vehicles in the transport sector with Electric Vehicles (EVs) may help ensure a sustainable future. With regard to the charging electric load of EVs, optimal scheduling of EV batteries, controlled by an aggregating agent, may provide flexibility and increase system efficiency. This work proposes a stochastic bilevel optimization problem based on the Stackelberg game to create price incentives that generate optimal trading plans for an EV aggregator in day-ahead, intra-day and real-time markets. The upper level represents the profit maximizer EV aggregator who participates in three sequential markets and is called a Stackelberg leader, while the second level represents the EV owner who aims at minimizing the EV charging cost, and who is called a Stackelberg follower. This formulation determines endogenously the profit-maximizing price levels constraint by cost-minimizing EV charging plans. To solve the proposed stochastic bilevel program, the second level is replaced by its optimality conditions. The strong duality theorem is deployed to substitute the complementary slackness condition. The final model is a stochastic convex problem which can be solved efficiently to determine the global optimality. Illustrative results are reported based on a small case with two vehicles. The numerical results rely on applying the proposed methodology to a large scale fleet of 100, 500, 1000 vehicles, which provides insights into the computational tractability of the current formulation.

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Крылатов, Александр Юрьевич, Alexandr Krylatov, Анастасия Павловна Раевская, and Anastasia Raevskaya. "Design of the feasible region for demand values in a congested urban road network." Mathematical Game Theory and Applications 14, no. 3 (January 18, 2023): 22–44. http://dx.doi.org/10.17076/mgta_2022_3_55.

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The present paper is devoted to the study of the feasible region for demand values in a congested urban road network. Travel demand estimation is considered to be the inverse of the traffic assignment problem, formulated as a congestion game. We show that the corresponding estimation problem has the form of a bilevel optimization program with a weak-defined feasible set of upper-level solution variables (even a trivial solution leads to the global optimum). However, we are lucky to prove that for any congested urban road network there is a polygon in the space of demand values, which significantly narrows the area of optimal solution search for the considering bilevel problem. Moreover, such a polygon appears to be easily designed for an arbitrary road network, using solely observed congestion as input data. Thus, the findings obtained in the paper contribute to the development of tools for travel demand estimation in a congested urban road network.

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Yang, Fan, Henry X. Liu, Rachel R. He, Xuegang Ban, and Bin Ran. "Bilevel Formulation for Optimal Traffic-Information Dissemination." Transportation Research Record: Journal of the Transportation Research Board 1836, no. 1 (January 2003): 21–28. http://dx.doi.org/10.3141/1836-04.

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With the fast-growing telematics market and maturing traffic-information services, telematics devices provide a feasible means with which to manage traffic more efficiently. The provision of traffic information to travelers usually involves different parties that have distinctive objectives: travelers are concerned with benefits of travel-time savings at an affordable service charge, private information service providers (ISPs) seek to provide marketable information services from which they can derive a profit, and traffic management centers (TMCs) have the responsibility to maintain and improve system performance, especially to minimize the total system travel time. How transportation system managers can analyze the trade-offs among these objectives and adjust this new traffic-information flow diagram to improve system performance remains an open question. The trade-offs needed among the conflicting multiple objectives of different parties are studied, and traffic system performance is analyzed. The complex traffic network is formulated as a bilevel program. The upper level can be formulated by using various objective functions, such as the objectives for ISP and TMC. The lower level is a multiclass dynamic traffic-assignment model, which determines dynamic traffic flows in the network by considering the information dissemination strategies provided by the upper-level model. Numerical results of a small network are provided to illustrate the behavior of this model, and they prove that when there is congestion in the dynamic transportation network, appropriate subscribed rates benefit both all travelers and system performance, while the ISPs’ information influences little without congestion in the transportation network.

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Dempe, S., and J. Dutta. "Is bilevel programming a special case of a mathematical program with complementarity constraints?" Mathematical Programming 131, no. 1-2 (February 25, 2010): 37–48. http://dx.doi.org/10.1007/s10107-010-0342-1.

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Momber, Ilan, Sonja Wogrin, and Tomas Gomez San Roman. "Retail Pricing: A Bilevel Program for PEV Aggregator Decisions Using Indirect Load Control." IEEE Transactions on Power Systems 31, no. 1 (January 2016): 464–73. http://dx.doi.org/10.1109/tpwrs.2014.2379637.

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Liu, Yi-Hsin, and Thomas H. Spencer. "Solving a bilevel linear program when the inner decision maker controls few variables." European Journal of Operational Research 81, no. 3 (March 1995): 644–51. http://dx.doi.org/10.1016/0377-2217(94)00005-w.

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Hong, Qiuyi, Fanlin Meng, and Jian Liu. "Customised Multi-Energy Pricing: Model and Solutions." Energies 16, no. 4 (February 20, 2023): 2080. http://dx.doi.org/10.3390/en16042080.

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With the increasing interdependence among energies (e.g., electricity, natural gas and heat) and the development of a decentralised energy system, a novel retail pricing scheme in the multi-energy market is demanded. Therefore, the problem of designing a customised multi-energy pricing scheme for energy retailers is investigated in this paper. In particular, the proposed pricing scheme is formulated as a bilevel optimisation problem. At the upper level, the energy retailer (leader) aims to maximise its profit. Microgrids (followers) equipped with energy converters, storage, renewable energy sources (RES) and demand response (DR) programs are located at the lower level and minimise their operational costs. Three hybrid algorithms combining metaheuristic algorithms (i.e., particle swarm optimisation (PSO), genetic algorithm (GA) and simulated annealing (SA)) with the mixed-integer linear program (MILP) are developed to solve the proposed bilevel problem. Numerical results verify the feasibility and effectiveness of the proposed model and solution algorithms. We find that GA outperforms other solution algorithms to obtain a higher retailer’s profit through comparison. In addition, the proposed customised pricing scheme could benefit the retailer’s profitability and net profit margin compared to the widely adopted uniform pricing scheme due to the reduction in the overall energy purchasing costs in the wholesale markets. Lastly, the negative correlations between the rated capacity and power of the energy storage and both retailer’s profit and the microgrid’s operational cost are illustrated.

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Pandžić, Kristina, Ivan Pavić, Ivan Andročec, and Hrvoje Pandžić. "Optimal Battery Storage Participation in European Energy and Reserves Markets." Energies 13, no. 24 (December 15, 2020): 6629. http://dx.doi.org/10.3390/en13246629.

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Battery energy storage is becoming an important asset in modern power systems. Considering the market prices and battery storage characteristics, reserve provision is a tempting play fields for such assets. This paper aims at filling the gap by developing a mathematically rigorous model and applying it to the existing and future electricity market design in Europe. The paper presents a bilevel model for optimal battery storage participation in day-ahead energy market as a price taker, and reserve capacity and activation market as a price maker. It uses an accurate battery charging model to reliably represent the behavior of real-life lithium-ion battery storage. The proposed bilevel model is converted into a mixed-integer linear program by using the Karush–Kuhn–Tucker optimality conditions. The case study uses real-life data on reserve capacity and activation costs and quantities in German markets. The reserves activation quantities and activation prices are modeled by a set of credible scenarios in the lower-level problem. Finally, a sensitivity analysis is conducted to comprehend to what extent do battery storage bidding prices affect its overall profit.

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Londono, Gloria, and Angelica Lozano. "A Bilevel Optimization Program with Equilibrium Constraints for an Urban Network Dependent on Time." Transportation Research Procedia 3 (2014): 905–14. http://dx.doi.org/10.1016/j.trpro.2014.10.070.

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Aussel, Didier, and Anton Svensson. "Is Pessimistic Bilevel Programming a Special Case of a Mathematical Program with Complementarity Constraints?" Journal of Optimization Theory and Applications 181, no. 2 (January 8, 2019): 504–20. http://dx.doi.org/10.1007/s10957-018-01467-7.

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Mojica-Nava, Eduardo, and Fredy Ruiz. "Stackelberg Population Dynamics: A Predictive-Sensitivity Approach." Games 12, no. 4 (November 19, 2021): 88. http://dx.doi.org/10.3390/g12040088.

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Hierarchical decision-making processes traditionally modeled as bilevel optimization problems are widespread in modern engineering and social systems. In this work, we deal with a leader with a population of followers in a hierarchical order of play. In general, this problem can be modeled as a leader–follower Stackelberg equilibrium problem using a mathematical program with equilibrium constraints. We propose two interconnected dynamical systems to dynamically solve a bilevel optimization problem between a leader and follower population in a single time scale by a predictive-sensitivity conditioning interconnection. For the leader’s optimization problem, we developed a gradient descent algorithm based on the total derivative, and for the followers’ optimization problem, we used the population dynamics framework to model a population of interacting strategic agents. We extended the concept of the Stackelberg population equilibrium to the differential Stackelberg population equilibrium for population dynamics. Theoretical guarantees for the stability of the proposed Stackelberg population learning dynamics are presented. Finally, a distributed energy resource coordination problem is solved via pricing dynamics based on the proposed approach. Some simulation experiments are presented to illustrate the effectiveness of the framework.

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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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Lin, Lai-Jiu, and Chih-Sheng Chuang. "Saddle Point Problems, Bilevel Problems, and Mathematical Program with Equilibrium Constraint on Complete Metric Spaces." Journal of Inequalities and Applications 2010 (2010): 1–14. http://dx.doi.org/10.1155/2010/306403.

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Campêlo, Manoel, and Susana Scheimberg. "A Simplex Approach for Finding Local Solutions of a Linear Bilevel Program by Equilibrium Points." Annals of Operations Research 138, no. 1 (September 2005): 143–57. http://dx.doi.org/10.1007/s10479-005-2450-5.

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Haghighi, Yadollah, Bahman Bahmani-Firouzi, and Mehdi Nafar. "A Partnership of Virtual Power Plant in Day-Ahead Energy and Reserve Markets Based on Linearized AC Network-Constrained Unit Commitment Model." International Transactions on Electrical Energy Systems 2022 (September 6, 2022): 1–16. http://dx.doi.org/10.1155/2022/5650527.

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This paper presents coordinated energy management as a virtual power plant (VPP) framework with a wind farm, a storage system, and a demand response program in the transmission network according to the cooperation of VPPs in day-ahead energy and reserve markets. This strategy is based on a bilevel method, where it maximizes the expected VPP revenue in the proposed markets subject to constraints of renewable and flexible sources and the VPP reserve model in the upper-level problem. Also, a market-clearing model based on network-constrained unit commitment (NCUC) is explained in the lower-level problem so that it minimizes the expected operating cost of generation units constrained to a linearized AC-NCUC model. The scenario-based stochastic programming (SBSP) models the uncertainties of loads and WF power generation. Then, the master/slave decomposition method solves the bilevel problem to achieve an optimal solution at a low computational time. Also, since the lower-level problem is mixed-integer linear programming, the Benders decomposition algorithm is adopted to solve this problem. Finally, the suggested approach is implemented on IEEE test networks in GAMS software, and numerical results confirm the efficiency of the coordinated VPP management in DA energy and reserve markets and its capabilities in improving network operation.

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Camacho Vallejo, José Fernando, and Rafael Muñoz Sánchez. "A Path Based Algorithm for Solve the Hazardous Materials Transportation Bilevel Problem." Applied Mechanics and Materials 253-255 (December 2012): 1082–88. http://dx.doi.org/10.4028/www.scientific.net/amm.253-255.1082.

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In this work we consider the problem of determining a set of optimal tolls on the arcs of a multicommodity transportation network. The problem is formulated as a bilevel mathematical program where the upper level consists in a government agency that regulate the traffic of the dangerous materials by imposing tolls on arcs of the network trying to minimize the risk for the population in the case when an accident occurs to the carriers, while the lower level is represented by a group of carriers traveling on shortest paths with respect to a generalized travel cost. So, the problem can be seen in a simplistic form as find the equilibrium between tolls that minimize the population exposure to the risk and tolls that are convenient for the shippers. The paper applies a path based algorithm to solve a bi-level multi-commodity optimal toll setting ‘hazmat’ problem. The algorithm consists in find upper bounds for the tolls considering the total cost and the risk associated to a particular path. We made several experiments and the results are shown in this work.

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Epshteyn, A., and G. DeJong. "Generative Prior Knowledge for Discriminative Classification." Journal of Artificial Intelligence Research 27 (September 25, 2006): 25–53. http://dx.doi.org/10.1613/jair.1934.

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We present a novel framework for integrating prior knowledge into discriminative classifiers. Our framework allows discriminative classifiers such as Support Vector Machines (SVMs) to utilize prior knowledge specified in the generative setting. The dual objective of fitting the data and respecting prior knowledge is formulated as a bilevel program, which is solved (approximately) via iterative application of second-order cone programming. To test our approach, we consider the problem of using WordNet (a semantic database of English language) to improve low-sample classification accuracy of newsgroup categorization. WordNet is viewed as an approximate, but readily available source of background knowledge, and our framework is capable of utilizing it in a flexible way.

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Ferris, Michael, and Henry X. Liu. "Numerical Studies on Reformulation Techniques for Continuous Network Design with Asymmetric User Equilibria." International Journal of Operations Research and Information Systems 1, no. 1 (January 2010): 52–72. http://dx.doi.org/10.4018/joris.2010101304.

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In this article, we aim to find the most effective reformulation techniques to solve the MPCC (mathematical program with complementarity constraints) model that we proposed recently for continuous network design problems under asymmetric user equilibria. The MPCC model is based on a link-node nonlinear complementarity formulation for asymmetric user equilibria. By applying various reformulation techniques for the lower level nonlinear complementarity, the original bilevel formulation can be converted to a single level nonlinear programming problem. We show that certain reformulations are more effective than others to solve the proposed MPCC model. Recommendations are thus provided on how to choose a reformulation of the continuous network design problem that can be solved effectively and/or efficiently.

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Lin, L. J. "Existence Theorems for Bilevel Problem with Applications to Mathematical Program with Equilibrium Constraint and Semi-Infinite Problem." Journal of Optimization Theory and Applications 137, no. 1 (December 7, 2007): 27–40. http://dx.doi.org/10.1007/s10957-007-9283-0.

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Nath, Hari Nandan, Urmila Pyakurel, Stephan Dempe, and Tanka Nath Dhamala. "Saving a Path and Maximizing Dynamic Contra ow: A Bilevel Programming Approach." GANIT: Journal of Bangladesh Mathematical Society 42, no. 1 (August 22, 2022): 010–24. http://dx.doi.org/10.3329/ganit.v42i1.60997.

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An important aspect of evacuation planning is to save human population by sending the people in dangerous areas (sources) to the safe places (sinks). Optimization models for evacuation planning focus on regulating the tra_c ow in urban road networks so as to maximize the number of evacuees reaching the safe places or to minimize the evacuation time of evacuees. Recent studies show that reversing the direction of the usual tra_c ow in necessary road segments increases the tra_c ow and decreases the evacuation time signi_cantly. However, this may block the ow of some necessary support towards the source. Based on network ow models, we consider the problem of saving a path from a given node to the source, in a single-source-single-sink network, as a bilevel program. With an objective to minimize a function depending on ow rate and the path chosen, the upper level selects a path from a given node to the source, and the lower level maximizes the dynamic ow allowing arc reversals in the resulting network within a given time horizon. We discuss a solution strategy based on replacing the lower level problem by the corresponding KKT conditions. GANIT J. Bangladesh Math. Soc. 42.1 (2022) 010- 024

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Cai, Yifei, Jun Chen, Da Lei, and Jiang Yu. "The Integration of Multimodal Networks: The Generalized Modal Split and Collaborative Optimization of Transportation Hubs." Journal of Advanced Transportation 2022 (December 13, 2022): 1–32. http://dx.doi.org/10.1155/2022/3442921.

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Integrated transportation is one of the most important methods to encourage the modal shift from car to public transportation (PT). However, as most cities have an existing multimodal network, it is difficult to expand the current networks by building more PT routes. Thus, integrating different modes through the optimization of hubs is a cost-efficient way to promote sustainable mobility. This paper develops a bilevel multimodal network design problem based on the collaborative optimization of urban transportation hubs. The upper-level problem is formulated as a mixed-integer nonlinear program to achieve a modal shift from congested subnetworks to underutilized subnetworks to realize a balanced use of the entire network. The decision variables are classified into location-based (hub locations) and route-based (route layouts and frequency setting) ones. The lower-level problem is a generalized modal split/traffic assignment problem (GMS/TAP), which captures the mode choices of all modes in the path set. The GMS/TAP is formulated as a nonlinear optimization problem (NLP) and is solved using a hybrid method of the successive average (MSA) algorithm. A hybrid genetic search with advanced diversity control (HGSADC) is developed to solve the bilevel model, where the exploration of the search space is expanded using the biased fitness function and diversification mechanism. The solution properties of the hybrid MSA and HGSADC are demonstrated in two modified nine-node networks. The model performance is illustrated in a real-size network in Jianye district, Nanjing. 9.2% decrease of travel time, 25.7% increase of service level, and a significant modal shift from car to PT are obtained.

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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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Meisel, David D., Kenneth F. Kinsey, and Charles H. Recchia. "Microcomputers in an Introductory College Astronomy Laboratory: A Software Development Project." International Astronomical Union Colloquium 105 (1990): 175–76. http://dx.doi.org/10.1017/s0252921100086656.

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We have developed software for the Apple IIe series of microcomputers for use in labs in an introductory astronomy course. This software emphasizes a toolkit approach to data analysis; it has been class tested with over 170 students and was a resounding success as a replacement for previously used graphical approximations. A unique feature of this software is the incorporation of image-processing techniques into a course designed for non-science majors.The five software packages are:(a)Datasheet - A six-column spreadsheet with columnwise operations, statistical functions, and double-high-resolution graphics.(b)Image-Processor Program - Allows 37 × 27 pixel × 8 bit video captured images to be manipulated using standard image-processing techniques such as low pass/high pass filtering and histogram equalization.(c)Picture-Processor Program - Allows 256 × 192 bilevel pictures to be manipulated and measured with functions that include calipers, odometer, planimeter, and protractor.(d)Orrery Program - Simulates planet configurations along the ecliptic. A movable cursor allows selection of specific configurations. Since both relative times and angular positions are given, students can deduce the scale of the solar system using simple trigonometry.(e)Plot Program - Allows orbital positions as observed from above the pole to be plotted on the screen. By entering trial values of elliptical orbit parameters, students obtain and the program plots the best fitting ellipse to the data. The sum of the squares of the residuals in the radial coordinate is given after each trial so that students can discover convergence more easily than by simple visual examination of a plot comparing the trial theoretical points with the raw data points.

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Towle, Eli, and James Luedtke. "Intersection Disjunctions for Reverse Convex Sets." Mathematics of Operations Research 47, no. 1 (February 2022): 297–319. http://dx.doi.org/10.1287/moor.2021.1132.

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We present a framework to obtain valid inequalities for a reverse convex set: the set of points in a polyhedron that lie outside a given open convex set. Reverse convex sets arise in many models, including bilevel optimization and polynomial optimization. An intersection cut is a well-known valid inequality for a reverse convex set that is generated from a basic solution that lies within the convex set. We introduce a framework for deriving valid inequalities for the reverse convex set from basic solutions that lie outside the convex set. We first propose an extension to intersection cuts that defines a two-term disjunction for a reverse convex set, which we refer to as an intersection disjunction. Next, we generalize this analysis to a multiterm disjunction by considering the convex set’s recession directions. These disjunctions can be used in a cut-generating linear program to obtain valid inequalities for the reverse convex set.

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Liu, Haoxiang, David Z. W. Wang, and Hao Yue. "Global Optimization for Transport Network Expansion and Signal Setting." Mathematical Problems in Engineering 2015 (2015): 1–18. http://dx.doi.org/10.1155/2015/385713.

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This paper proposes a model to address an urban transport planning problem involving combined network design and signal setting in a saturated network. Conventional transport planning models usually deal with the network design problem and signal setting problem separately. However, the fact that network capacity design and capacity allocation determined by network signal setting combine to govern the transport network performance requires the optimal transport planning to consider the two problems simultaneously. In this study, a combined network capacity expansion and signal setting model with consideration of vehicle queuing on approaching legs of intersection is developed to consider their mutual interactions so that best transport network performance can be guaranteed. We formulate the model as a bilevel program and design an approximated global optimization solution method based on mixed-integer linearization approach to solve the problem, which is inherently nnonlinear and nonconvex. Numerical experiments are conducted to demonstrate the model application and the efficiency of solution algorithm.

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Ding, Dong, and Bin Shuai. "A Traffic Restriction Scheme for Enhancing Carpooling." Discrete Dynamics in Nature and Society 2017 (2017): 1–9. http://dx.doi.org/10.1155/2017/9626938.

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For the purpose of alleviating traffic congestion, this paper proposes a scheme to encourage travelers to carpool by traffic restriction. By a variational inequity we describe travelers’ mode (solo driving and carpooling) and route choice under user equilibrium principle in the context of fixed demand and detect the performance of a simple network with various restriction links, restriction proportions, and carpooling costs. Then the optimal traffic restriction scheme aiming at minimal total travel cost is designed through a bilevel program and applied to a Sioux Fall network example with genetic algorithm. According to various requirements, optimal restriction regions and proportions for restricted automobiles are captured. From the results it is found that traffic restriction scheme is possible to enhance carpooling and alleviate congestion. However, higher carpooling demand is not always helpful to the whole network. The topology of network, OD demand, and carpooling cost are included in the factors influencing the performance of the traffic system.

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Gao, Hong, Kai Liu, Xinchao Peng, and Cheng Li. "Optimal Location of Fast Charging Stations for Mixed Traffic of Electric Vehicles and Gasoline Vehicles Subject to Elastic Demands." Energies 13, no. 8 (April 16, 2020): 1964. http://dx.doi.org/10.3390/en13081964.

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With the rapid development of electric vehicles (EVs), one of the urgent issues is how to deploy limited charging facilities to provide services for as many EVs as possible. This paper proposes a bilevel model to depict the interaction between traffic flow distribution and the location of charging stations (CSs) in the EVs and gasoline vehicles (GVs) hybrid network. The upper level model is a maximum flow-covering model where the CSs are deployed on links with higher demands. The lower level model is a stochastic user equilibrium model under elastic demands (SUE-ED) that considers both demands uncertainty and perceived path constraints, which have a significant influence on the distribution of link flow. Besides the path travel cost, the utility of charging facilities, charging speed, and waiting time at CSs due to space capacity restraint are also considered for the EVs when making a path assignment in the lower level model. A mixed-integer nonlinear program is constructed, and the equivalence of SUE-ED is proven, where a heuristic algorithm is used to solve the model. Finally, the network trial and sensitivity analysis are carried out to illustrate the feasibility and effectiveness of the proposed model.

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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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Deng, Hua, Yinxue Li, Zhaoman Wan, and Zhong Wan. "Partially Smoothing and Gradient-Based Algorithm for Optimizing the VMI System with Competitive Retailers under Random Demands." Mathematical Problems in Engineering 2020 (March 16, 2020): 1–18. http://dx.doi.org/10.1155/2020/3687471.

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Vendor managed inventory (VMI) is an improved sustainable inventory management system, but it is difficult to establish and solve an integrated Stackelberg game model under the complicated practical environment. In this paper, a bilevel programming model is proposed to formulate the VMI system by taking into account the uncertainty of demand, the competition among retailers, the cooperative advertising, the shortage and holding costs, and the practical constraints. For the established stochastic model being associated with continuously random demands, a deterministic mathematical program with complementarity constraints (MPCC) is first derived by expectation method and the first-order optimality conditions of the lower-level problem. Then, with a partially smoothing technique, the MPCC is solved by transforming it into a series of standard smooth optimization subproblems. Finally, owing to complexity caused by evaluating the integrals with unknown decision variables in the objective function, an efficient algorithm is developed to solve the problem based on the gradient information of model. Sensitivity analysis has been employed to reveal a number of managerial implications from the constructed model and algorithm. (1) The participation rate depends on advertising expenditures from both the manufacturer and the retailer. There exists an optimal threshold of participation rate for the manufacturer, which can be provided by the intersection point of the manufacturer and retailer’s cost-profit curves. (2) The manufacturer’s advertising policy is less sensitive to uncertainty of demand than the change of the retailer’s advertising policy. (3) The manufacturer in the VMI system should concern about the differences caused by symmetric or asymmetric retailers.

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Li, Gaoxi, Liping Tang, Yingquan Huang, and Xinmin Yang. "Stability for semivectorial bilevel programs." Journal of Industrial & Management Optimization 13, no. 5 (2017): 0. http://dx.doi.org/10.3934/jimo.2020161.

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Calvete, Herminia I., and Carmen Galé. "Solving linear fractional bilevel programs." Operations Research Letters 32, no. 2 (March 2004): 143–51. http://dx.doi.org/10.1016/j.orl.2003.07.003.

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Zemkoho, Alain B. "Solving Ill-posed Bilevel Programs." Set-Valued and Variational Analysis 24, no. 3 (April 26, 2016): 423–48. http://dx.doi.org/10.1007/s11228-016-0371-x.

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Fliege, Jörg, Andrey Tin, and Alain Zemkoho. "Gauss–Newton-type methods for bilevel optimization." Computational Optimization and Applications 78, no. 3 (January 10, 2021): 793–824. http://dx.doi.org/10.1007/s10589-020-00254-3.

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AbstractThis article studies Gauss–Newton-type methods for over-determined systems to find solutions to bilevel programming problems. To proceed, we use the lower-level value function reformulation of bilevel programs and consider necessary optimality conditions under appropriate assumptions. First, under strict complementarity for upper- and lower-level feasibility constraints, we prove the convergence of a Gauss–Newton-type method in computing points satisfying these optimality conditions under additional tractable qualification conditions. Potential approaches to address the shortcomings of the method are then proposed, leading to alternatives such as the pseudo or smoothing Gauss–Newton-type methods for bilevel optimization. Our numerical experiments conducted on 124 examples from the recently released Bilevel Optimization LIBrary (BOLIB) compare the performance of our method under different scenarios and show that it is a tractable approach to solve bilevel optimization problems with continuous variables.

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Edmunds, T. A., and J. F. Bard. "Algorithms for nonlinear bilevel mathematical programs." IEEE Transactions on Systems, Man, and Cybernetics 21, no. 1 (1991): 83–89. http://dx.doi.org/10.1109/21.101139.

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Kalashnikov, Vyacheslav V., Stephan Dempe, Gerardo A. Pérez-Valdés, Nataliya I. Kalashnykova, and José-Fernando Camacho-Vallejo. "Bilevel Programming and Applications." Mathematical Problems in Engineering 2015 (2015): 1–16. http://dx.doi.org/10.1155/2015/310301.

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A great amount of new applied problems in the area of energy networks has recently arisen that can be efficiently solved only as mixed-integer bilevel programs. Among them are the natural gas cash-out problem, the deregulated electricity market equilibrium problem, biofuel problems, a problem of designing coupled energy carrier networks, and so forth, if we mention only part of such applications. Bilevel models to describe migration processes are also in the list of the most popular new themes of bilevel programming, as well as allocation, information protection, and cybersecurity problems. This survey provides a comprehensive review of some of the above-mentioned new areas including both theoretical and applied results.

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Nie, Jiawang, Li Wang, and Jane J. Ye. "Bilevel Polynomial Programs and Semidefinite Relaxation Methods." SIAM Journal on Optimization 27, no. 3 (January 2017): 1728–57. http://dx.doi.org/10.1137/15m1052172.

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Allende, Gemayqzel Bouza, and Georg Still. "Solving bilevel programs with the KKT-approach." Mathematical Programming 138, no. 1-2 (April 3, 2012): 309–32. http://dx.doi.org/10.1007/s10107-012-0535-x.

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Ye, Jane J. "Necessary Optimality Conditions for Multiobjective Bilevel Programs." Mathematics of Operations Research 36, no. 1 (February 2011): 165–84. http://dx.doi.org/10.1287/moor.1100.0480.

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Mao, Wei, Feifei Qin, Yihong Hu, and Zhijia Tan. "Joint Implementation of Signal Control and Congestion Pricing in Transportation Network." Journal of Applied Mathematics 2013 (2013): 1–6. http://dx.doi.org/10.1155/2013/315752.

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The policy of jointly implementing signal control and congestion pricing in the transportation network is investigated. Bilevel programs are developed to model the simultaneous optimization of signal setting and congestion toll. The upper level aims to maximize the network reserve capacity or minimize the total travel time, subject to signal setting and toll constraints. The lower level is a deterministic user equilibrium problem given a plan of signal setting and congestion charge. Then the bilevel programs are transferred into the equivalent single level programs, and the solution methods are discussed. Finally, a numerical example is presented to illustrate the concepts and methods, and it is shown that the joint implementation policy can achieve promising results.

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Journal articles on the topic 'Bilevel program'

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