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Road traffic networks are chaotic and highly complex systems. In this paper, we introduce a dynamic gravity model that characterizes the behaviors of the O-D (origin-destination) traffic, such as equilibrium, period-doubling, chaos, and fractal in discrete time. In cases where the original cost function is used, the trip distribution model might degenerate into an all-or-nothing problem without the capacity constraints. To address this shortcoming, we propose substituting the original cost function with an improved conical volume-delay function. This new function retains some of the properties of the original cost function, and its parameters have the same meaning as those in the original function. Our analysis confirms that the double-constrained dynamic gravity model successfully characterizes complex traffic behavior because of the improved conical volume-delay function. Our analysis further shows that the three-parameter bifurcation diagram based on the period characteristics provides deep insight into the actual state of the road traffic networks. Investigating the properties of the model solutions, we further show that the new model is more effective in addressing the all-or-nothing problem.

In China, the transportation capacity of high-speed railways is gradually sufficient to provide services for high-value express freight besides meeting passenger demands. However, similar as the passengers, express freight demands fluctuate and show clear peak and trough periods daily. Therefore, optimizing running numbers of express freight trains on high-speed railway by periods is quite necessary to guarantee the revenues of railway industry and to meet the various requirements of all consignees simultaneously. First, a space-period-pattern three-dimensional network with virtual arcs is built to describe the departure period selection and the stopping or skip-stopping operations. Second, by constructing the arcs' impedance function, the user equilibrium principle is introduced to optimize the express freight flow distribution for each pattern in each period. To elaborate the comprehensive goal of balancing the relationship between profits and the flow distribution, a bi-level programming model is established. The upper model addresses the railway industry's maximum profits, and the lower model addresses the minimum and similar impedance values of the final express freight flow distribution. Finally, through the use of a hybrid algorithm that combines the heuristic genetic algorithm with the Frank-Wolfe algorithm, an experimental case of 10 stations on the Beijing-Xi'an high-speed railway corridor is used to validate the study. The results show that the express freight volume is reasonably distributed to each kind of virtual arc, the impedance value of each pattern is minimized and almost equalized, and the profits of railway industry are maximized by optimizing the number and departure time of trains by each pattern in each period on the basis of meeting all the express freight demands.

Taxi is an important part of urban passenger transportation system. The research and analysis of taxi trip behavior is the key to meet the demand of urban passenger transport and solve the traffic congestion problem. Based on the GPS data of taxis in Nanjing, the statistical method is used to analyze the taxi characteristics of the average number of passengers, the average passenger time, the no-load distance and the passenger distance. By using the double logarithmic coordinate, the trip distance and trip time of taxi passengers are analyzed, it is found that the average trip distance of taxi passengers is mainly concentrated in 3-20km, and the average trip time of taxi passengers is mainly concentrated in 10-30 minutes. Using the information entropy theory to construct the equilibrium model of taxi passenger-carrying point, and analyze the spatial distribution of taxi, it is found that the distribution of urban taxi is unbalanced. The peak clustering algorithm is used to determine the location of passenger gathering points, and the hot spot of taxi trip is analyzed, it is found that the hot spots of taxi trip are mainly concentrated in the central city of Nanjing. Combined with the results of urban taxi trip analysis, from the perspective of taxi and passenger, we found that the number of urban taxis, the passenger carrying rate of taxis, the duration period of passenger trip, the duration and distance of passenger trip and the location of passenger trip points will have an impact on the urban taxi carpooling in Nanjing. By using the probability model of urban taxi carpooling, this paper discusses and analyzes the influence of these factors on urban taxi carpooling. The research in this paper can provide a reference for the effective implementation of urban taxi carpooling policy.

Vehicle delay and stops at intersections are considered targets for optimizing signal timing for an isolated intersection to overcome the limitations of the linear combination and single objective optimization method. A multi-objective optimization model of a fixed-time signal control parameter of unsaturated intersections is proposed under the constraint of the saturation level of approach and signal time range. The signal cycle and green time length of each phase were considered decision variables, and a non-dominated sorting artificial bee colony (ABC) algorithm was used to solve the multi-objective optimization model. A typical intersection in Lanzhou City was used for the case study. Experimental results showed that a single-objective optimization method degrades other objectives when the optimized objective reaches an optimal value. Moreover, a reasonable balance of vehicle delay and stops must be achieved to flexibly adjust the signal cycle in a reasonable range. The convergence is better in the non-dominated sorting ABC algorithm than in non-dominated sorting genetic algorithm II, Webster timing, and weighted combination methods. The proposed algorithm can solve the Pareto front of a multi-objective problem, thereby improving the vehicle delay and stops simultaneously.

This paper builds a multiobjective optimization model for solving the taxi carpooling with detour problem and designs a genetic algorithm to determine a fair pricing scheme for riders and drivers. The researches show that it is feasible to share a taxi with detour. It is the key to determine appropriate carpooling payment ratio and detour carpooling payment ratio. The ratio of detour distance to travel distance has an important influence on detour carpooling. It should be limited to less than certain values. Payment ratios and the maximum value of the ratio of detour distance to travel distance are determined by the method proposed in this paper. The method can ensure benefits of passengers and drivers, which makes detour carpooling a reality. These conclusions and the method have a certain guiding significance for formulating taxi policy.

For the problem of taxi carpooling detour, this paper studies driver strategy choice with carpooling detour. The model of taxi driver strategy evolution with carpooling detour is built based on prospect theory and evolution game theory. Driver stable strategies are analyzed under the conditions of complaint mechanism and absence of mechanism, respectively. The results show that passenger’s complaint mechanism can effectively decrease the phenomenon of driver refusing passengers with carpooling detour. When probability of passenger complaint reaches a certain level, the stable strategy of driver is to take carpooling detour passengers. Meanwhile, limiting detour distance and easing traffic congestion can decrease the possibility of refusing passengers. These conclusions have a certain guiding significance to formulating taxi policy.

To identify electrical vehicle (EV) distribution paths with high robustness, insensitivity to uncertainty factors, and detailed road-by-road schemes, optimization of the distribution path problem of EV with multiple distribution centers and considering the charging facilities is necessary. With the minimum transport time as the goal, a robust optimization model of EV distribution path with adjustable robustness is established based on Bertsimas' theory of robust discrete optimization. An enhanced three-segment genetic algorithm is also developed to solve the model, such that the optimal distribution scheme initially contains all road-by-road path data using the three-segment mixed coding and decoding method. During genetic manipulation, different interlacing and mutation operations are carried out on different chromosomes, while, during population evolution, the infeasible solution is naturally avoided. A part of the road network of Xifeng District in Qingyang City is taken as an example to test the model and the algorithm in this study, and the concrete transportation paths are utilized in the final distribution scheme. Therefore, more robust EV distribution paths with multiple distribution centers can be obtained using the robust optimization model.

The problem that passengers are hard to take taxis while empty driving rate is high widely exists under the traditional taxi operation mode. The implementation of taxi carpooling mode can alleviate the problem in a certain extent. The objective of this study is to optimize the taxi carpooling path. Firstly, the taxi carpooling path optimization model with single objective and its extended model with multiple objectives are built respectively. Then, the single objective path optimization model of taxi carpooling is solved based on the improved single objective genetic algorithm, and the multiple-objective path optimization model of taxi carpooling is solved based on the improved multiple-objective genetic algorithm. Finally, a case study is carried out based on a road network with 24 nodes. The case study results show the path optimization models and algorithms of taxi carpooling proposed in the paper can quickly get the taxi carpooling path, and can increase the income of taxi driver while reduce the cost for passengers.

Aiming at route optimization problem of hazardous materials transportation in uncertain environment, this paper presents a multiobjective robust optimization model by taking robust control parameters into consideration. The objective of the model is to minimize not only transportation risk but also transportation time, and a robust counterpart of the model is introduced through applying the Bertsimas-Sim robust optimization theory. Moreover, a fuzzy C-means clustering-particle swarm optimization (FCMC-PSO) algorithm is designed, and the FCMC algorithm is used to cluster the demand points. In addition the PSO algorithm with the adaptive archives grid is used to calculate the robust optimization route of hazmat transportation. Finally, the computational results show the multiobjective route robust optimization model with 3 centers and 20 demand points’ sample studied and FCMC-PSO algorithm for hazmat transportation can obtain different robustness Pareto solution sets. As a result, this study will provide basic theory support for hazmat transportation safeguarding.

An extended car-following model is proposed on the basis of experimental analysis to improve the performance of the traditional car-following model and simulate a microscopic car-following behaviour at signalised intersections. The new car-following model considers vehicle gather and dissipation. Firstly, the parameters of optimal velocity, generalised force and full velocity difference models are calibrated by measured data, and the problems and causes of the three models are analysed with a realistic trajectory simulation as an evaluation criterion. Secondly, an extended car-following model based on the full optimal velocity model is proposed by considering the vehicle gather and dissipation. The parameters of the new car-following model are calibrated by the measured data, and the model is compared with comparative models on the basis of isolated point data and the entire car-following process. Simulation results show that the optimal velocity, generalised force, and full velocity difference models cannot effectively simulate a microscopic car-following behaviour at signalised intersections, whereas the new car-following model can avoid a collision and has a high fit degree for simulating the measured data of the car-following behaviour at signalised intersections.

Mathematical models for path planning and vehicle scheduling for logistic distribution of hazardous materials in full container load (FCL) are established, with their problem-solving methods proposed. First, a two-stage multiobjective optimization algorithm is designed for path planning. In the first stage, pulse algorithm is used to obtain the Pareto paths from the distribution center to each destination. In the second stage, a multiobjective optimization method based on Nondominated Sorting Genetic Algorithm II (NSGA-II) is designed to obtain candidate transport paths. Second, with analysis on the operating process of vehicles with hazardous materials in FCL, the vehicle scheduling problem is converted to Vehicle Routing Problem with Time Windows (VRPTW). A problem-solving method based on estimation of distribution is adopted. A transport timetable for all vehicles based on their transport paths is calculated, with participation of the decision-makers. A visual vehicle scheduling plan is presented for the decision-makers. Last, two examples are used to test the method proposed in this study: distribution of hazardous materials in a small-scale test network and distribution of oil products for sixteen gas stations in the main districts of Lanzhou city. In both examples, our method is used to obtain the path selection and vehicle scheduling plan, proving that validity of our method is verified.

For the problem of route choice in taxi carpooling detour, considering the uncertainty of traffic and the characteristic of passengers’ noncomplete rationality, an evolutionary game model of taxi carpooling detour route is built, in which prospect theory is introduced and revenue of strategy is replaced by prospect value. The model reflects more really decision-making psychology of passengers. Then the stable strategies of the model are studied, and the influences of detour distance and traffic congestion on detour carpooling success are analyzed, respectively. The results show that when at least one route of which prospect values for two passenger sides are both positive exists, carpooling route can reach an agreement. The route is stable strategy of evolutionary game, and the passengers requiring short travel time tend to select the nondetour route. With the increase of detour distance and traffic congestion rate, the possibility of reaching an agreement decreases gradually; that is, possibility of carpooling failure increases. So taxi carpooling detour is possible under the certain condition, but some measures must be carried out such as constraints of detour distance and mitigation of traffic congestion to improve carpooling success probability. These conclusions have a certain guiding significance to the formulation of taxi carpooling policy.

The real-time dynamic coupling under the virtual-coupling technology guarantees running multi-group trains in different sections based on passenger flow's spatial and temporal distribution characteristics. It enables more flexible transport organization modes such as full-length and short-turn routing and the express/local stop mode. Utilizing the redundant capacity of the airport line to carry out coordinated transportation of passengers and goods is an essential means of relieving urban traffic pressure, saving energy, and protecting the environment. To promote urban rail transit to achieve the goal of "double-carbon," the optimization of passenger and freight cooperative transport schemes based on the virtual coupling technology for the airport line of the rail transit is investigated. Based on the train operation of full-length and short-turn routing under the virtual-coupling technology, according to the unbalanced distribution characteristics of passenger and freight flows in urban rail transit, this paper constructs an optimization model of urban rail transit capacity allocation to minimize passenger travel costs, enterprise operation costs, and carbon emission costs, and considering the constraints of the carbon emission policy, with the constraints such as the train operation safety, the constraints of the balance of the passenger flow and freight flow loading. The multi-objective model to solve the optimization problem has been designed. Given the complexity of the multi-objective model solution, an improved nondominated sorting genetic algorithm is designed, and the algorithm makes use of the screening function of the constraints during the initial population generation process, which effectively balances the relationship between the whole process of screening and time-consumption of the NSGA-II algorithm. Taking Wuxi Metro Line 3 as an example, the results show that: (i) Compared with the traditionally large and small crossing mode, full-length and short-turn routing of virtual coupling Trains proposed in this paper can reduce the average waiting time of passengers by about 2.01min, the cost of carbon emission by 15.7% and the cost of enterprise operation by 20.2%, and at the same time, improve the average total rate by about 50%, which verifies that the virtual formation technology is conducive to improving the efficiency of passenger travel and reducing the operating cost and the carbon cost. It is also beneficial for improving passenger traveling efficiency. (ii)The single-alignment fixed configuration mode, compared with the single-flow mode, can increase the average full-load rate by 26.6% while increasing the passenger travel cost by only 0.98% and reducing the carbon emission cost by a small margin; the virtual configuration technology based-on the large and smallalignment operation and transport scheme increases the passenger travel cost by about 0.3% and further reduces the carbon emission cost by 1.9%. They further reduced the carbon emission cost by 1.9% while increasing the average total occupancy rate by about 5.8%. The proposed models and algorithms provide some decision support for urban rail transit operators to optimize transport schemes under different carbon emission policies and the virtual coupling operation mode. [ABSTRACT FROM AUTHOR]

Regarding alleviating urban traffic pressure and conserving environmental energy, it is essential to utilize the redundant capacity of urban rail transit during non-peak hours for passenger-freight collaborative transportation. In order to achieve the "dual carbon" goals in urban rail transit, a study has been conducted on the coordinated transportation of passengers and goods, which can adapt to the evolving carbon emission policies. A method for calculating the waiting time that allows passengers to queue for a second time has been proposed by studying the queue of passengers. A multiobjective optimization model for urban rail transit passenger-freight collaborative transportation has been constructed, with the objectives of minimizing carbon emissions and passenger waiting time, considering constraints such as carbon emission policy, train operation safety, passenger and freight loading balance, and train formation scheme. An improved nondominated sorting genetic algorithm (NSGA-II) has been designed to deal with the complexity of solving the multiobjective model. The algorithm utilizes the filtering function of the constraint conditions during the initial population generation process, effectively balancing the relationship between the filtering and time consumption of the NSGA-II algorithm. Taking the Wuxi Metro Line 3 as an example for analysis, the results show that: ① Although the average passenger waiting time increases by about 0.53 minutes in this method, the carbon emissions of the trains decrease by approximately 21.3%. Meanwhile, the average seating rate of the optimized solution is 5%~15% higher than the traditional transportation scheme used by Wuxi Metro Line 3. The superiority of urban rail transportation for passenger-freight collaborative transportation has been verified. ② With the mandatory control of carbon emission control, the passengerfreight collaborative optimization scheme is not affected by different carbon emission limits. Under the carbon tax policy, transportation schemes are less affected by different carbon tax levels. Transportation schemes remain consistent under the different limits of carbon trading policies. The proposed model and algorithm provide decision-making support for urban rail transit operators to optimize transportation plans under different carbon emission policies. [ABSTRACT FROM AUTHOR]

Urban rail transit has the potential to utilize surplus capacity to carry out urban freight transportation during off-peak periods. Based on the characteristics of virtual coupling operation and organization mode, this paper comprehensively considers the competition between passenger flow and freight flow, takes the train stopping plan and train carriage allocation as the main decision variables, and takes the minimization of passenger waiting time and the maximization of average full load rate as dual objectives to construct a multi-objective optimization model of passengerfreight collaborative transport scheme of urban rail transit under virtual coupling conditions. The multi-objective optimization model is developed to obtain the system optimization of the train stopping plan, running plan, carriage allocation plan, and passenger-freight collaborative transport plan. Numerical experiments are designed to verify the model's validity, using Wuxi Metro Line 3 as an example, and the NSGA-II algorithm solves all experiments. The results of the algorithm show that, compared to the traditional single passenger transport with a fixed large coupling, the scheme in this paper can simultaneously improve the average full capacity of the whole line by about 38.5% during the study period with only 0.65 minutes increase in the average passenger waiting time for the same number of rolling stocks, which can effectively shorten passenger travel time and improve the quality of passenger service in urban rail transit while ensuring transport efficiency. [ABSTRACT FROM AUTHOR]