Bi-level model for shared parking decision-making based on parking lot assignment simulation

In order to carry out comprehensive decision-making of multi-class shared parking measures within a region, a bilevel model assisting decision-making is proposed. The upper level selects parkers＇ average satisfaction and the violation rate during peak hours as indices in object function, and sets probability distribution models describing dynamic parking demand of each site, the feasibility of shared parking scenarios and occupancy requirements during peak hours of each parking lot as restrictions. The simulation model in the lower level sets up rules to assign each parker in the random parking demand series to the proper parking lot. An iterative method is proposed to confirm the state of each parking lot at the start of formal simulations. Besides, two patterns linking initialization and formal simulation are presented to acquire multiple solutions. The results of the numerical examples indicate the effectiveness of the model and solution methods.

Creation method for bi-level positive airway pressure based on pressure and flow feedback

An airway pressure and flow data acquisition system is developed to investigate the approach to building the bi-level positive airway pressure BiPAP in a ventilator.A number of experiments under different breathing situations and states are conducted and the experimental data are recorded.According to the data from these experiments the variation characteristics of the pressure and flow are analyzed using Matlab. The data analysis results show that the pressure increases while the flow decreases in the expiratory phase contrarily the pressure decreases while the flow increases in the inspiratory phase during the apnea state both the pressure and the flow remain unchanged. According to the above variation characteristics of breath a feedback-based method for creating bi-level positive airway pressure is proposed. Experiments are implemented to verify the BiPAP model. Results demonstrate that the proposed method works effectively in following respiration and caters well to most polypnea and apnea events.

Bi-level programming model and algorithm for optimizing headway of public transit line

Due to the fact that headway is a key factor to be considered in bus scheduling, this paper proposes a bi-level programming model for optimizing bus headway in public transit lines. In this model, with the interests of bus companies and passengers in mind, the upper-level model＇s objective is to minimize the total cost, which is affected by frequency settings, both in time and economy in the transit system. The lower-level model is a transit assignment model used to describe the assignment of passengers＇ trips to the network based on the optimal bus headway. In order to solve the proposed model, a hybrid genetic algorithm, namely the genetic algorithm and the simulated annealing algorithm （GA-SA）, is designed. Finally, the model and the algorithm are tested against the transit data, by taking some of the bus lines of Changzhou city as an example. Results indicate that the proposed model allows supply and demand to be linked, which is reasonable, and the solving algorithm is effective.

Flexible Load Participation in Peaking Shaving and Valley Filling Based on Dynamic Price Incentives

Considering the widening of the peak-valley difference in the power grid and the difficulty of the existing fixed time-of-use electricity price mechanism in meeting the energy demand of heterogeneous users at various moments or motivating users,the design of a reasonable dynamic pricing mechanism to actively engage users in demand response becomes imperative for power grid companies.For this purpose,a power grid-flexible load bilevel model is constructed based on dynamic pricing,where the leader is the dispatching center and the lower-level flexible load acts as the follower.Initially,an upper-level day-ahead dispatching model for the power grid is established,considering the lowest power grid dispatching cost as the objective function and incorporating the power grid-side constraints.Then,the lower level comprehensively considers the load characteristics of industrial load,energy storage,and data centers,and then establishes a lower-level flexible load operation model with the lowest user power-consuming cost as the objective function.Finally,the proposed method is validated using the IEEE-118 system,and the findings indicate that the dynamic pricing mechanism for peaking shaving and valley filling can effectively guide users to respond actively,thereby reducing the peak-valley difference and decreasing users’purchasing costs.

Bi-level programming model for reconstruction of urban branch road network

Considering the decision-making variables of the capacities of branch roads and the optimization targets of lowering the saturation of arterial roads and the reconstruction expense of branch roads, the bi-level programming model for reconstructing the branch roads was set up. The upper level model was for determining the enlarged capacities of the branch roads, and the lower level model was for calculating the flows of road sections via the user equilibrium traffic assignment method. The genetic algorithm for solving the bi-level model was designed to obtain the reconstruction capacities of the branch roads. The results show that by the bi-level model and its algorithm, the optimum scheme of urban branch roads reconstruction can be gained, which reduces the saturation of arterial roads apparently, and alleviates traffic congestion. In the data analysis the arterial saturation decreases from 1.100 to 0.996, which verifies the micro-circulation transportation's function of urban branch road network.

Bi-level hybrid local search approach for three-dimensional loading problem with balancing constraints

This paper presents a bi-level hybrid local search(BHLS)algorithm for the three-dimensional loading problem with balancing constraints(3DLP-B),where several rectangular boxes with even densities but different sizes are loaded into a single cubic bin to meet the requirements of the space or capacity utilization and the balance of the center of gravity.The proposed algorithm hybridizes a novel framed-layout procedure in which the concept of the core block and its generation strategy are introduced.Once the block-loading sequence has been determined,we can load one block at a time by the designed construction heuristic.Then,the double-search is introduced;its external search procedure generates a list of compact packing patterns while its internal search procedure is used to search the core-block frames and their best distribution locations.The approach is extensively tested on weakly to strongly heterogeneous benchmark data.The results show that it has better performance in improving space utilization rate and balanced condition of the placement than existed techniques:the overall averages from 79.85%to 86.45%were obtained for the balanced cases and relatively high space-usage rate of 89.44%was achieved for the unbalanced ones.

Multidisciplinary Design Optimization of A Human Occupied Vehicle Based on Bi-Level Integrated System Collaborative Optimization

The design of Human Occupied Vehicle （HOV） is a typical multidisciplinary problem, but heavily dependent on the experience of naval architects at present engineering design. In order to relieve the experience dependence and improve the design, a new Multidisciplinary Design Optimization （MDO） method ＂Bi-Level Integrated System Collaborative Optimization （BLISCO）＂ is applied to the conceptual design of an HOV, which consists of hull module, resistance module, energy module, structure module, weight module, and the stability module. This design problem is defined by 21 design variables and 23 constraints, and its objective is to maximize the ratio of payload to weight. The results show that the general performance of the HOV can be greatly improved by BLISCO.

Algorithm for solving the bi-level decision making problem with continuous variables in the upper level based on genetic algorithm

Based on genetic algorithms, a solution algorithm is presented for the bi-level decision making problem with continuous variables in the upper level in accordance with the bi-level decision making principle. The algorithm is compared with Monte Carlo simulated annealing algorithm, and its feasibility and effectiveness are verified with two calculating examples.

COVID-19 and Unemployment: A Novel Bi-Level Optimal Control Model

Since COVID-19 was declared as a pandemic in March 2020,the world’s major preoccupation has been to curb it while preserving the economy and reducing unemployment.This paper uses a novel Bi-Level Dynamic Optimal Control model(BLDOC)to coordinate control between COVID-19 and unemployment.The COVID-19 model is the upper level while the unemployment model is the lower level of the bi-level dynamic optimal control model.The BLDOC model’s main objectives are to minimize the number of individuals infected with COVID-19 and to minimize the unemployed individuals,and at the same time minimizing the cost of the containment strategies.We use the modified approximation Karush–Kuhn–Tucker(KKT)conditions with the Hamiltonian function to handle the bi-level dynamic optimal control model.We consider three control variables:The first control variable relates to government measures to curb the COVID-19 pandemic,i.e.,quarantine,social distancing,and personal protection;and the other two control variables relate to government interventions to reduce the unemployment rate,i.e.,employment,making individuals qualified,creating new jobs reviving the economy,reducing taxes.We investigate four different cases to verify the effect of control variables.Our results indicate that rather than focusing exclusively on only one problem,we need a balanced trade-off between controlling each.

A Lagrange Relaxation Based Approach to Solve a Discrete-Continous Bi-Level Model

In this work we propose a solution method based on Lagrange relaxation for discrete-continuous bi-level problems, with binary variables in the leading problem, considering the optimistic approach in bi-level programming. For the application of the method, the two-level problem is reformulated using the Karush-Kuhn-Tucker conditions. The resulting model is linearized taking advantage of the structure of the leading problem. Using a Lagrange relaxation algorithm, it is possible to find a global solution efficiently. The algorithm was tested to show how it performs.

Bi-Level Energy Management Model of Grid-Connected Microgrid Community

As the proportion of renewable energy power generation continues to increase,the number of grid-connected microgrids is gradually increasing,and geographically adjacent microgrids can be interconnected to form a Micro-Grid Community(MGC).In order to reduce the operation and maintenance costs of a single micro grid and reduce the adverse effects caused by unnecessary energy interaction between the micro grid and the main grid while improving the overall economic benefits of the micro grid community,this paper proposes a bi-level energy management model with the optimization goal of maximizing the social welfare of the micro grid community and minimizing the total electricity cost of a single micro grid.The lower-level model optimizes the output of each equipment unit in the system and the exchange power between the system and the external grid with the goal of minimizing the operating cost of each microgrid.The upper-level model optimizes the goal ofmaximizing the socialwelfare of themicrogrid.Taking amicrogrid community with four microgrids as an example,the simulation analysis shows that the proposed optimization model is beneficial to reduce the operating cost of a single microgrid,improve the overall revenue of the microgrid community,and reduce the power interaction pressure on the main grid.

An Alternative Approach for Solving Bi-Level Programming Problems

An algorithm is proposed in this paper for solving two-dimensional bi-level linear programming problems without making a graph. Based on the classification of constraints, algorithm removes all redundant constraints, which eliminate the possibility of cycling and the solution of the problem is reached in a finite number of steps. Example to illustrate the method is also included in the paper.

Bi-Level Programming for the Optimal Nonlinear Distance-Based Transit Fare Structure Incorporating Principal-Agent Game

The urban transit fare structure and level can largely affect passengers’travel behavior and route choices.The commonly used transit fare policies in the present transit network would lead to the unbalanced transit assignment and improper transit resources distribution.In order to distribute transit passenger flow evenly and efficiently,this paper introduces a new distance-based fare pattern with Euclidean distance.A bi-level programming model is developed for determining the optimal distance-based fare pattern,with the path-based stochastic transit assignment(STA)problem with elastic demand being proposed at the lower level.The upper-level intends to address a principal-agent game between transport authorities and transit enterprises pursing maximization of social welfare and financial interest,respectively.A genetic algorithm(GA)is implemented to solve the bi-level model,which is verified by a numerical example to illustrate that the proposed nonlinear distance-based fare pattern presents a better financial performance and distribution effect than other fare structures.

Clinical Analysis of Early Application of Bi-level Positive Airway Pressure ventilation in the Treatment of COPD with Type II Respiratory Failure

Objective:To analyze the clinical efficacy of early application of bi-level positive airway pressure ventilation in the treatment of COPD with type II respiratory failure.Method:A total of 58 patients with COPD and type II respiratory failure admitted to our hospital from January 2017 to January 2019 were randomly divided into observation group and control group,with 29 cases in each group.Among them,the control group was received routine treatment while the observation group was treated with bi-level positive pressure airway ventilation in addition of conventional treatment.The arterial blood gas analysis,mortality rate and hospitalization time of these two groups before and after treatment were compared.Result:The blood pH,partial pressure of oxygen(PaO2)and arterial oxygen saturation(SaO2)of these two groups were significantly higher after the treatment while PaO2 alone was decreased.The difference was statistically significant(P<0.05).The results of arterial blood gas analysis in the observation group were significantly improved compared with those before treatment.The mortality rate and hospitalization time were significantly less than the control group,and the difference was statistically significant(P<0.05).Conclusion:Early clinical application of bi-level positive airway pressure ventilation in the treatment of COPD with type II respiratory failure has a significant clinical effect in reducing the mortality rate and hospitalization time of patients,and thus it is worthy of clinical application.

Optimization of the bioconversion of glycerol to ethanol using Escherichia coli by implementing a bi-level programming framework for proposing gene transcription control strategies based on genetic algorithms

In silico approaches for metabolites optimization have been derived from the flood of sequenced and annotated genomes. However, there exist still numerous degrees of freedom in terms of optimization algorithm approaches that can be exploited in order to enhance yield of processes which are based on biological reactions. Here, we propose an evolutionary approach aiming to suggest different mutant for augmenting ethanol yield using glycerol as substrate in Escherichia coli. We found that this algorithm, even though is far from providing the global optimum, is able to uncover genes that a global optimizer would be incapable of. By over-expressing accB, eno, dapE, and accA mutants in ethanol production was augmented up to 2 fold compared to its counterpart E. coli BW25113.

Student Performance Prediction Using A Cascaded Bi-level Feature Selection Approach

Features in educational data are ambiguous which leads to noisy features and curse of dimensionality problems.These problems are solved via feature selection.There are existing models for features selection.These models were created using either a single-level embedded,wrapper-based or filter-based methods.However single-level filter-based methods ignore feature dependencies and ignore the interaction with the classifier.The embedded and wrapper based feature selection methods interact with the classifier,but they can only select the optimal subset for a particular classifier.So their selected features may be worse for other classifiers.Hence this research proposes a robust Cascade Bi-Level(CBL)feature selection technique for student performance prediction that will minimize the limitations of using a single-level technique.The proposed CBL feature selection technique consists of the Relief technique at first-level and the Particle Swarm Optimization(PSO)at the second-level.The proposed technique was evaluated using the UCI student performance dataset.In comparison with the performance of the single-level feature selection technique the proposed technique achieved an accuracy of 94.94%which was better than the values achieved by the single-level PSO with an accuracy of 93.67%for the binary classification task.These results show that CBL can effectively predict student performance.

Efficient Origin-Destination Estimation Using Microscopic Traffic Simulation with Restricted Rerouting

Traffic simulators are utilized to solve a variety of traffic-related problems.For such simulators,origin-destination(OD)traffic volumes as mobility demands are required to input,and we need to estimate them.The authors regard an OD estimation as a bi-level programming problem,and apply a microscopic traffic simulation model to it.However,the simulation trials can be computationally expensive if full dynamic rerouting is allowed,when employing multi-agent-based models in the estimation process.This paper proposes an efficient OD estimation method using a multi-agent-based simulator with restricted dynamic rerouting to reduce the computational load.Even though,in the case of large traffic demand,the restriction on dynamic rerouting can result in heavier congestion.The authors resolve this problem by introducing constraints of the bi-level programming problem depending on link congestion.Test results show that the accuracy of the link traffic volume reproduced with the proposed method is virtually identical to that of existing methods but that the proposed method is more computationally efficient in a wide-range or high-demand context.

A Novel Stackelberg-Game-Based Energy Storage Sharing Scheme Under Demand Charge

Demand response(DR)using shared energy storage systems(ESSs)is an appealing method to save electricity bills for users under demand charge and time-of-use(TOU)price.A novel Stackelberg-game-based ESS sharing scheme is proposed and analyzed in this study.In this scheme,the interactions between selfish users and an operator are characterized as a Stackelberg game.Operator holds a large-scale ESS that is shared among users in the form of energy transactions.It sells energy to users and sets the selling price first.It maximizes its profit through optimal pricing and ESS dispatching.Users purchase some energy from operator for the reduction of their demand charges after operator's selling price is announced.This game-theoretic ESS sharing scheme is characterized and analyzed by formulating and solving a bi-level optimization model.The upper-level optimization maximizes operator's profit and the lower-level optimization minimizes users'costs.The bi-level model is transformed and linearized into a mixed-integer linear programming(MILP)model using the mathematical programming with equilibrium constraints(MPEC)method and model linearizing techniques.Case studies with actual data are carried out to explore the economic performances of the proposed ESS sharing scheme.

Gradient-based algorithms for multi-objective bi-level optimization

Multi-objective bi-level optimization(MOBLO)addresses nested multi-objective optimization problems common in a range of applications.However,its multi-objective and hierarchical bi-level nature makes it notably complex.Gradient-based MOBLO algorithms have recently grown in popularity,as they effectively solve crucial machine learning problems like meta-learning,neural architecture search,and reinforcement learning.Unfortunately,these algorithms depend on solving a sequence of approximation subproblems with high accuracy,resulting in adverse time and memory complexity that lowers their numerical efficiency.To address this issue,we propose a gradient-based algorithm for MOBLO,called gMOBA,which has fewer hyperparameters to tune,making it both simple and efficient.Additionally,we demonstrate the theoretical validity by accomplishing the desirable Pareto stationarity.Numerical experiments confirm the practical efficiency of the proposed method and verify the theoretical results.To accelerate the convergence of gMOBA,we introduce a beneficial L2O(learning to optimize)neural network(called L2O-gMOBA)implemented as the initialization phase of our gMOBA algorithm.Comparative results of numerical experiments are presented to illustrate the performance of L2O-gMOBA.

Bi-level ramp merging coordination for dense mixed traffic conditions

Connected and Autonomous Vehicles(CAVs)hold great potential to improve traffic efficiency,emissions and safety in freeway on-ramp bottlenecks through coordination between mainstream and on-ramp vehicles.This study proposes a bi-level coordination strategy for freeway on-ramp merging of mixed traffic consisting of CAVs and human-driven vehicles(HDVs)to optimize the overall traffic efficiency and safety in congested traffic scenarios at the traffic flow level instead of platoon levels.The macro level employs an optimization model based on fundamental diagrams and shock wave theories to make optimal coordination decisions,including optimal minimum merging platoon size to trigger merging coordination and optimal coordination speed,based on macroscopic traffic state in mainline and ramp(i.e.,traffic volume and penetration rates of CAVs).Furthermore,the micro level determines the real platoon size in each merging cycle as per random arrival patterns and designs the coordinated trajectories of the mainline facilitating vehicle and ramp platoon.A receding horizon scheme is implemented to accommodate human drivers’stochastics as well.The developed bi-level strategy is tested in terms of improving efficiency and safety in a simulation-based case study under various traffic volumes and CAV penetration rates.The results show the proposed coordination addresses the uncertainties in mixed traffic as expected and substantially improves ramp merging operation in terms of merging efficiency and traffic robustness,and reducing collision risk and emissions,especially under high traffic volume conditions.