Search NASA⌕ Search

SEARCH · Search NASA

Results for “Vehicle assignment”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

A real-time energy and cost efficient vehicle route assignment neural recommender system

Here, this paper presents a neural network recommender system algorithm for assigning vehicles to routes based on energy and cost criteria. In this work, we applied this new approach to efficiently identify the most cost-effective medium and heavy duty truck (MDHDT) powertrain technology, from a total cost of ownership (TCO) perspective, for given trips. We employ a machine learning based approach to efficiently estimate the energy consumption of various candidate vehicles over given routes, defined as sequences of links (road segments), with little information known about internal dynamics, i.e. using high level macroscopic route information. A complete recommendation logic is then developed to allow for real-time optimum assignment for each route, subject to the operational constraints of the fleet. We show how this framework can be used to (1) efficiently provide a single trip recommendation with a top-k vehicles star ranking system, and (2) engage in more general assignment problems where n vehicles need to be deployed over m (m ≤ n) trips. This new assignment system has been deployed and integrated into the POLARIS. Transportation System Simulation Tool for use in research conducted by the Department of Energy's Systems and Modeling for Accelerated Research in Transportation (SMART) Mobility Consortium (SMART, 2024).

Energy consumption↗
DOE OSTI2022

Data-Driven Prediction and Optimization of Energy Use for Transit Fleets of Electric and ICE Vehicles

Due to the high upfront cost of electric vehicles, many public transit agencies can afford only mixed fleets of internal combustion and electric vehicles. Optimizing the operation of such mixed fleets is challenging because it requires accurate trip-level predictions of electricity and fuel use as well as efficient algorithms for assigning vehicles to transit routes. We present a novel framework for the data-driven prediction of trip-level energy use for mixed-vehicle transit fleets and for the optimization of vehicle assignments, which we evaluate using data collected from the bus fleet of CARTA, the public transit agency of Chattanooga, TN. We first introduce a data collection, storage, and processing framework for system-level and high-frequency vehicle-level transit data, including domain-specific data cleansing methods. We train and evaluate machine learning models for energy prediction, demonstrating that deep neural networks attain the highest accuracy. Based on these predictions, we formulate the problem of minimizing energy use through assigning vehicles to fixed-route transit trips. We propose an optimal integer program as well as efficient heuristic and meta-heuristic algorithms, demonstrating the scalability and performance of these algorithms numerically using the transit network of CARTA.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2021

Minimizing Energy Use of Mixed-Fleet Public Transit for Fixed-Route Service

Affordable public transit services are crucial for communities since they enable residents to access employment, education, and other services. Unfortunately, transit services that provide wide coverage tend to suffer from relatively low utilization, which results in high fuel usage per passenger per mile, leading to high operating costs and environmental impact. Electric vehicles (EVs) can reduce energy costs and environmental impact, but most public transit agencies have to employ them in combination with conventional, internal-combustion engine vehicles due to the high upfront costs of EVs. To make the best use of such a mixed fleet of vehicles, transit agencies need to optimize route assignments and charging schedules, which presents a challenging problem for large transit networks. We introduce a novel problem formulation to minimize fuel and electricity use by assigning vehicles to transit trips and scheduling them for charging, while serving an existing fixed-route transit schedule. We present an integer program for optimal assignment and scheduling, and we propose polynomial-time heuristic and meta-heuristic algorithms for larger networks. We evaluate our algorithms on the public transit service of Chattanooga, TN using operational data collected from transit vehicles. Our results show that the proposed algorithms are scalable and can reduce energy use and, hence, environmental impact and operational costs. For Chattanooga, the proposed algorithms can save $145,635 in energy costs and 576.7 metric tons of CO 2 emission annually.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2021

Optimizing Vehicle Fleet and Assignment for Concentrating Solar Power Plant Heliostat Washing

Concentrating solar power central-receiver plants use thousands of sun-tracking mirrors, i.e., heliostats, to reflect sunlight to a central receiver, which collects and uses the heat to generate electricity. Over time, soiling reduces the reflectivity of the heliostats and, therefore, the efficiency of the system. Current industry practice sends vehicles to wash heliostats in an ad hoc fashion. We present a mixed-integer nonlinear program that determines wash vehicle fleet size, mix, and assignment of wash crews to heliostats to minimize the sum of (i) the revenues lost due to heliostat soiling, (ii) the costs of hiring wash crews and operating the vehicles, and (iii) the costs of purchasing wash vehicles. We establish conditions for convexity of the objective function, and then propose a decomposition method that enables near-optimal solutions to the wash vehicle fleet sizing and assignment problem on the order of a couple of minutes. Furthermore, these solutions yield hundreds of thousands of dollars in savings per year over current industry practices.

14 SOLAR ENERGY↗
DOE OSTI2021

High-dimensional Data-driven Energy optimization for Multi-Modal Transit Agencies (HD-EMMA) (Final Technical Report)

Public bus transit services in the U.S. are responsible for at least 19.7 million metric tons of CO 2 emission annually. Electric vehicles (EVs) can have a much lower environmental impact than comparable internal combustion engine vehicles (ICEVs), especially in urban areas. Unfortunately, EVs are also much more expensive than ICEVs. As a result, many public transit agencies can afford only mixed fleets of transit vehicles, consisting of EVs, hybrids (HEVs), and ICEVs. Transit agencies that operate such mixed fleets of vehicles face a challenging optimization problem: these agencies need to decide which vehicles are assigned to serving which transit trips. Since the advantage of EVs over ICEVs varies depending on the route and time of day (e.g., the benefit of EVs is higher in slower traffic with frequent stops and lower on highways), the assignment can have a significant effect on energy use and, hence, environmental impact. Through this project, we have developed reference data about energy collections and constructed a set of machine learning models that can accurately predict the energy consumption for the whole fleet at the level of each trip. We have used these models to develop a scheduling and assignment strategy that can rotate the different vehicle types across the transit agencies’ routes. The optimization algorithm ensures that the vehicles are matched to trips considering weather patterns, expected congestion, and road gradients to minimize the overall energy usage. We list the key observations from our project for other practitioners below. Details are available in the report, and the list of source code and our publications are included in the appendix. 1. We have demonstrated the feasibility of collecting, merging and analyzing large volumes of high-resolution real-world telemetry data from a mixed vehicle fleet. To mitigate the inherent noise of the recorded GPS points, the team developed an algorithm that filters data and maps the points onto a street. The algorithm considers previous and subsequent location measurements and different characteristics of nearby streets to determine how likely the vehicle travels on them. Then, the team segmented the time series into disjoint contiguous samples based on adjacent road segments and repeated the outlier detection and removal. For each data point, the team added features corresponding to elevation changes within the samples, weather features, such as temperature, and traffic data, such as speed ratio between actual speed and free-flow speed. 2. We have developed two forms of machine learning models that be used to understand and analyze the energy operations of a mixed vehicle transit fleet. The micro prediction model provides estimates of instantaneous energy prediction for all types of buses (diesel, hybrid, and electric). Such a model is important in evaluating the energy impacts of real-time bus operation strategies, but it is challenging due to diversified driving cycles of transit buses. The model can help the drivers understand the impact of their driving behaviors and short-term congestions. The macro prediction models estimate average energy consumption across the whole trip considering the features: distance traveled, various road-type features, elevation change, day of the week, time of day, various weather features (temperature, humidity, etc.), and traffic features (speed ratio and jam factor). 3. We have demonstrated that it is possible to transfer the machine learning models we have developed in this project to other teams and cities by using inductive transfer learning. We also showed that the performance of the macro energy prediction models can be improved using a multi-task learning approach where the learning parameters are shared between the models being developed for different vehicle types. The advantage of this approach is improved learning performance as the models can exploit common spatio-temporal and environmental characteristics. 4. Finally, we have developed trip and vehicle assignment and scheduling algorithms that use the energy prediction models and develop a trip to vehicle type (diesel, electric, hybrid) assignment for the whole operation to reduce overall emissions and cost. We have shown through simulations that the proposed algorithms can save $\$$ 48,910 in energy costs and 175 metric tons of CO 2 emission annually for CARTA.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2023

Intelligent driving passive pedal control

A method for assignment of vehicle control includes receiving route data indicating a route between a starting location of a vehicle and a destination location, and determining an optimal vehicle configuration for the route based on a target vehicle speed and a hybrid torque split. The method further includes receiving a driver requested torque value and determining a passive pedal torque value based on the route data and vehicle powertrain data. The method further includes selectively assigning control of the vehicle to a vehicle system or to a driver of the vehicle based on the driver requested torque value and the passive pedal torque value.

Aggoune, Karim↗
DOE OSTI2021

Energy and Emission Prediction for Mixed-Vehicle Transit Fleets Using Multi-task and Inductive Transfer Learning

Public transit agencies are focused on making their fixed-line bus systems more energy efficient by introducing electric (EV) and hybrid (HV) vehicles to their fleets. However, because of the high upfront cost of these vehicles, most agencies are tasked with managing a mixed-fleet of internal combustion vehicles (ICEVs), EVs, and HVs. In managing mixed-fleets, agencies require accurate predictions of energy use for optimizing the assignment of vehicles to transit routes, scheduling charging, and ensuring that emission standards are met. The current state-of-the-art is to develop separate neural network models to predict energy consumption for each vehicle class. Although different vehicle classes’ energy consumption depends on a varied set of covariates, we hypothesize that there are broader generalizable patterns that govern energy consumption and emissions. In this paper, we seek to extract these patterns to aid learning to address two problems faced by transit agencies. First, in the case of a transit agency which operates many ICEVs, HVs, and EVs, we use multi-task learning (MTL) to improve accuracy of forecasting energy consumption. Second, in the case where there is a significant variation in vehicles in each category, we use inductive transfer learning (ITL) to improve predictive accuracy for vehicle class models with insufficient data. As this work is to be deployed by our partner agency, we also provide an online pipeline for joining the various sensor streams for fixed-line transit energy prediction. Here, we find that our approach outperforms vehicle-specific baselines in both the MTL and ITL settings.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

High-Dimensional Data-Driven Energy Optimization for MultiModal Transit Agencies

Transportation accounts for 28% of the total energy use in the United States and as such, it is responsible for immense environmental impact, including urban air pollution and greenhouse gas emissions, and may pose a severe threat to energy security. As we encourage mode shift from personal vehicles to public transit, it is important to consider that public transit systems still require substantial amounts of energy; for example, public bus transit services in the U.S. are responsible for at least 19.7 million metric tons of CO 2 emission annually. As such it is absolutely crucial that we study the bottlenecks to energy efficiency in public transit and develop new algorithms that can help the public transit agencies, especially those that are still operating mixed fleets, which may consist of Electric vehicles (EVs), hybrids (HEVs), and internal combustion engine vehicles (ICEVs), optimize the operations by deciding which vehicles are assigned to serving which transit trips.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2026

2011 Atlanta, Georgia, Regional Travel Survey

The 2011 Regional Travel Survey collected trip data from households across 20 counties in and around Atlanta, Georgia, to improve regional travel demand forecasts. The survey was conducted by PTV NuStats, GeoStats, and PG Americas Inc. on behalf of the Atlanta Regional Commission. The goal was to collect trip data from a minimum of 10,000 households with a subsample of 1,000 households providing global positioning system (GPS) data. The GPS add-on consisted of two sample groups. The first sample group was provided with GPS devices to install in their personal vehicles (797 vehicles) to collect the speed and location of a vehicle during an assigned study period. The second sample group (1,653 participants) was provided with a wearable GPS device to collect the speed and location of an individual during an assigned study period. People participating in the wearable add-on part of the study were chosen because their travel diaries reported use of public transit in day-to-day travel. Each GPS participant was grouped into either the spring phase (March to May 2011) or the fall phase (July to September 2011), and data were recorded for a maximum of seven days for vehicle units and three days for wearable units.

1Hz data↗
DOE OSTI2020

Optimal assignment for the single-household shared autonomous vehicle problem

Autonomous vehicles have the potential to transform the way people are transported. While driverless technology may mean fewer vehicles are required to transport people to and from their daily activities, such changes may result in increased congestion or total miles traveled. In this study, we solve the single-household shared autonomous vehicle problem to identify cost-optimal routings of vehicles throughout the day. Such a tool will be useful for consumers seeking to minimize cost and for regulators seeking to understand and predict how people may behave in different scenarios. Here, we provide a thorough literature review and construct a mixed-integer linear program to minimize the daily travel cost of a household attending a given set of activities. Since solution time is a determinant for applicability of such a model, we present the model in a component-wise fashion. This approach allows us to understand which features most affect the problem complexity and solution time. We note that modeling carpooling is the feature that most increases time to find an optimal solution, and we therefore propose a novel modeling technique for carpooling two people. We illustrate the performance of our model by comparing it with other models from the literature and note that our model can solve significantly larger problem instances and in a time that is short enough to facilitate real-time scheduling. We also highlight the utility of our model for regulators, who can use it to analyze quickly produced optimal routes under different cost/tax scenarios.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2024

Technology progress and clean vehicle policies on fleet turnover and equity: insights from household vehicle fleet micro-simulations with $\text{ATLAS}$

This paper documents the design and application of ATLAS (Automobile and Technology Lifecycle-Based ASsignment), a comprehensive household vehicle transaction and technology adoption micro-simulator in the San Francisco Bay Area. ATLAS evolves the fleet mix of individual households by simulating the vehicle transaction and choice decisions in response to co-evolving demographics, land use, and vehicle technology simulations. While most existing literature has focused on the aggregate clean vehicle uptake, this paper differentiates distributional effects and decomposes the underlying mechanisms across heterogeneous sub-populations of households. Using scenarios and sensitivity simulations that vary vehicle technology and policy assumptions, we find that Zero Emission Vehicles (ZEVs) penetrate into higher income groups at a faster rate than into lower income groups, which is intuitive and aligns with expectations. Interestingly, the relative income disparity in ZEV ownership shrinks over time across all scenarios, with a ZEV mandate coupled with declining battery cost leading to the greatest reduction in disparity of ZEV ownership by 2050. Federal, state, and local financial incentives influence the redistribution of ZEV uptake across income groups and contribute to narrowing income disparity. Vehicle transaction frequency and new versus used market dynamics are found to be important factors contributing to the income disparity.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2024

"Traffic Control via Connected and Automated Vehicles: An Open-Road Field Experiment with 100 CAVs"

The CIRCLES project aims to reduce instabilities in traffic flow, which are naturally occurring phenomena due to human driving behavior. These "phantom jams" or "stop-and-go waves,"are a significant source of wasted energy. Toward this goal, the CIRCLES project designed a control system referred to as the MegaController by the CIRCLES team, that could be deployed in real traffic. Our field experiment leveraged a heterogeneous fleet of 100 longitudinally-controlled vehicles as Lagrangian traffic actuators, each of which ran a controller with the architecture described in this paper. The MegaController is a hierarchical control architecture, which consists of two main layers. The upper layer is called Speed Planner, and is a centralized optimal control algorithm. It assigns speed targets to the vehicles, conveyed through the LTE cellular network. The lower layer is a control layer, running on each vehicle. It performs local actuation by overriding the stock adaptive cruise controller, using the stock on-board sensors. The Speed Planner ingests live data feeds provided by third parties, as well as data from our own control vehicles, and uses both to perform the speed assignment. The architecture of the speed planner allows for modular use of standard control techniques, such as optimal control, model predictive control, kernel methods and others, including Deep RL, model predictive control and explicit controllers. Depending on the vehicle architecture, all onboard sensing data can be accessed by the local controllers, or only some. Control inputs vary across different automakers, with inputs ranging from torque or acceleration requests for some cars, and electronic selection of ACC set points in others. The proposed architecture allows for the combination of all possible settings proposed above. Most configurations were tested throughout the ramp up to the MegaVandertest.

Lee, Jonathan↗
DOE OSTI2025

Traffic Control via Connected and Automated Vehicles (CAVs): An Open-Road Field Experiment with 100 CAVs

The CIRCLES project aims to reduce instabilities in traffic flow, which are naturally occurring phenomena due to human driving behavior. Also called “phantom jams” or “stop-and-go waves,” these instabilities are a significant source of wasted energy. Toward this goal, the CIRCLES project designed a control system, referred to as the MegaController by the CIRCLES team, that could be deployed in real traffic. Our field experiment, the MegaVanderTest (MVT), leveraged a heterogeneous fleet of 100 longitudinally controlled vehicles as Lagrangian traffic actuators, each of which ran a controller with the architecture described in this article. The MegaController is a hierarchical control architecture that consists of two main layers. The upper layer is called the Speed Planner and is a centralized optimal control algorithm. It assigns speed targets to the vehicles, conveyed through the LTE cellular network. The lower layer is a control layer, running on each vehicle. It performs local actuation by overriding the stock adaptive cruise controller, using the stock onboard sensors. The Speed Planner ingests live data feeds provided by third parties as well as data from our own control vehicles and uses both to perform the speed assignment. The architecture of the Speed Planner allows for the modular use of standard control techniques, such as optimal control, model predictive control (MPC), kernel methods, and others. The architecture of the local controller allows for the flexible implementation of local controllers. Corresponding techniques include deep reinforcement learning (RL), MPC, and explicit controllers. Depending on the vehicle architecture, all onboard sensing data can be accessed by the local controllers or only some. Likewise, control inputs vary across different automakers, with inputs ranging from torque or acceleration requests for some cars to electronic selection of adaptive cruise control (ACC) setpoints in others. The proposed architecture technically allows for the combination of all possible settings proposed previously, that is {Speed Planner algorithms} × {local Vehicle Controller algorithms} × {full or partial sensing} × {torque or speed control}. As a result, most configurations were tested throughout the ramp up to the MegaVandertest (MVT).

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2024

Automobile and Technology Lifecycle-Based Assignment (ATLAS) v2.0.12

ATLAS is a comprehensive vehicle transaction and technology adoption microsimulator. ATLAS evolves the fleet mix of individual households by simulating the transaction (vehicle addition, disposal, and replacement) and choice (vehicle type, vintage, powertrain, and tenure) decisions in response to the co-evolving demographics, land use, and vehicle technology simulations. Different from the existing vehicle models that are either static or aggregated (e.g. stock model), ATLAS is fully disaggregated and dynamic following a sequential and circumstantial decision-making trajectory. This fine-grained approach not only enhances the realism of the simulation but also provides a nuanced understanding of the dynamics inherent in vehicle fleet evolution. ATLAS outputs are fully compatible with subsequent agent-based transportation modeling system and can enable distributional effect analysis regarding the fleet turnover among heterogeneous populations. ATLAS expands the typical new sale focused vehicle choice modeling to including used vehicle transactions that are of increasing interests to understanding the vehicle adoption behavior among lower income households.

Jin, Ling↗
DOE OSTI2020

Impacts of Distributed Speed Harmonization and Optimal Maneuver Planning on Multi-Lane Roads

A commonly proposed method for improving traffic flow on freeways is speed harmonization. The effectiveness of current speed harmonization approaches, such as variable speed limits, is extremely reliant on human driver compliance. Connected and automated vehicles (CAVs) are expected to come to market within this decade, offering the opportunity to eliminate or reduce the reliance on human compliance. However, extending current roadside infrastructure-based approaches of assigning centrally computed harmonization speeds to individual vehicles is, costly. An alternative approach is to have individual vehicles estimate the traffic state on-board and make distributed decisions to achieve the harmonization goal autonomously. In this work, we present a distributed algorithm for estimating the current average speed of traffic. We couple this with a distributed 2D maneuver planning approach. Then, we study the impact on traffic efficiency in terms of energy consumption and travel time at varying CAV penetration rates.

Goulet, Nathan↗
DOE OSTI2023

Minimal Energy Routing of a Leader and a Wingmate with Periodic Connectivity

We consider a route planning problem in which two unmanned vehicles are required to complete a set of tasks present at distinct locations, referred to as targets, with minimum energy consumption. The mission environment is hazardous, and to ensure a safe operation, the UVs are required to communicate with each other at every target they visit. The problem objective is to determine the allocation of the tasks to the UVs and plan tours for the UVs to visit the targets such that the weighted sum of the distances traveled by the UVs and the distances traveled by the communicating signals between them is minimized. We formulate this problem as an Integer program and show that naively solving the problem using commercially available off-the-shelf solvers is insufficient in determining scalable solutions efficiently. To address this computational challenge, we develop an approximation and a heuristic algorithm, and employ them to compute high-quality solutions to a special case of the problem where equal weights are assigned to the distances traveled by the vehicles and the communicating signals. For this special case, we show that the approximation algorithm has a fixed approximation ratio of 3.75. We also develop lower bounds to the optimal cost of the problem to evaluate the performance of these algorithms on large-scale instances. We demonstrate the performance of these algorithms on 500 randomly generated instances with the number of targets ranging from 6 to 100, and show that the algorithms provide high-quality solutions to the problem swiftly; the average computation time of the algorithmic solutions is within a fraction of a second for instances with at most 100 targets. Finally, we show that the approximation ratio has a variable ratio for the weighted case of the problem. Specifically, if ρ denotes the ratio of the weights assigned to the distances representing the communication and travel costs, the algorithm has an a posteriori ratio of $3 + \frac{3ρ}{4}$ when ρ ≥ 1, and $\frac{3}{ρ}$ + $\frac{3}{4}$ when ρ ≤ 1.

42 ENGINEERING↗
DOE OSTI2020

Refueling infrastructure planning in intercity networks considering route choice and travel time delay for mixed fleet of electric and conventional vehicles

The range anxiety has been a major factor that affects the market acceptance of electric vehicles. Even with the recent development of battery technologies, a lack of charging stations and range anxiety are still significant concerns, specifically for intercity trips. This calls for more investments in building charging stations and advancing battery technologies to increase the market share of electric vehicles and improve sustainability. This study suggests a configuration for plug-in electric vehicle charging infrastructure to support long-distance intercity trips of electric vehicles at the network level. A model is proposed to minimize the total system cost including infrastructure investment (building charging stations/spots) and travel time delays (charging time, waiting time in the queue, and detour time to access charging stations). This study fills existing gaps in the literature by capturing realistic patterns of travel demand and considering flow-dependent charging delays at charging stations. Furthermore, the proposed model, which is formulated as a mixed-integer program with nonlinear constraints, solves the optimization problem at the network level. At the network level, impacts of charging station locations on the traffic assignment problem with a mixed fleet of electric and conventional vehicles need to be considered. To this end, a traffic assignment module is integrated with a simulated annealing algorithm. The numerical experiments show a satisfactory application of the model for a full-scale case study (intercity network in Michigan). The solution quality and efficiency of the proposed solution algorithm are evaluated against those of an enumeration approach for a small case study. The results suggest that even for the current market share and charging stations’ setting, a significant investment is needed to support intercity trips without range anxiety issues and with acceptable delays. Additionally, through sensitivity analyses, the required infrastructure and battery investments to support intercity trips with acceptable delays are established for hypothetical increased market shares and battery size in the future.

42 ENGINEERING↗
DOE OSTI2020

Joint Planning of EV Fast Charging Stations and Power Distribution Systems With Balanced Traffic Flow Assignment

To tackle the challenges introduced by the fast-growing charging demand of electric vehicles (EVs), the power distribution systems (PDSs) and fast charging stations (FCSs) of EVs should be planned and operated in a more coordinated fashion. However, existing planning approaches generally aim to minimize investment costs in PDSs while ignoring the risk of worsening traffic conditions. To overcome this research gap, this article integrates the interests of traffic networks into PDS and FCS joint planning model to mitigate negative impacts on traffic conditions caused by installing FCSs. First, a novel microscopic method that is different from traditional assignment methods is proposed to simulate the influences of FCSs on traffic flows and EV charging loads. Then, a multiobjective joint planning model is developed to minimize both the planning costs and unbalanced traffic flows. A new bilayer Benders decomposition algorithm is designed to solve the proposed joint planning model. Numerical results on two practical systems in China validate the feasibility of our microscopic method by comparing the simulated results with real data. Compared with existing approaches, it is also demonstrated that the proposed joint planning approach helps to balance traffic flow assignments and relieve traffic congestion.

bilayer expanded Benders decomposition↗