A pure electric bus line network planning method considering fairness

Abstract

The application belongs to the technical field of urban traffic planning, and relates to a pure electric bus line network planning method considering fairness, comprising the following steps: obtaining site distribution and site distance of a design area to obtain a road network structure diagram of the design area; constructing an objective function of a fairness model of a pure electric bus system with the minimum traffic Gini coefficient as the target and constructing an objective function of a total cost model of a pure electric bus line network with the minimum total social travel cost as the target, and further constructing a pure electric bus line network double-target nonlinear programming model; adopting an NAGS-II genetic algorithm, setting constraint conditions of the pure electric bus line network double-target nonlinear programming model, solving the pure electric bus line network double-target nonlinear programming model, and obtaining a pure electric bus planning line network. The method can reduce the traffic Gini coefficient while making the total travel cost as small as possible, effectively improves the fairness of the bus line network design scheme under the premise of controlling the total cost, and has important reference significance.

Description

Technical Field

[0001] This invention belongs to the field of urban transportation planning technology and relates to a pure electric bus network planning method that takes fairness into account. Background Technology

[0002] With the increasing number of motor vehicles, urban congestion has become increasingly prominent, affecting not only citizens' lives and work but also exacerbating urban environmental pollution. The widespread adoption and electrification of public transportation can effectively alleviate these problems. Transit Network Design (TRNDP) is a crucial aspect of rationally planning public transportation systems. While large-scale urban rail transit has somewhat squeezed passenger traffic from traditional surface public transport, conventional buses remain the mainstay of public transportation in most cities due to their advantages in accessibility and flexibility. Therefore, optimizing transit network design is essential for promoting the development of conventional public transport systems and enhancing their competitiveness.

[0003] As people's awareness of fairness increases, the issue of transportation equity is gradually gaining attention. Transportation equity indicators are mainly established around horizontal or vertical equity, that is, inequality between different individuals in the same region or residents of different regions, but they rarely consider the equity between different modes of transportation. This means that people prioritize the mode of transportation with the highest personal utility, leading to a greater preference for private cars. The dramatic increase in private car use has squeezed out a large amount of road space and time resources, reducing the attractiveness of other low-carbon and affordable transportation modes, which will seriously undermine transportation equity and increase environmental pollution. Therefore, it is necessary to reduce the gap in travel utility between different modes of transportation.

[0004] The fairness of public transportation systems refers to optimizing and improving the public transportation network to enable public transportation users to access more road traffic resources, thereby improving the overall accessibility of the public transportation system, narrowing the gap between public transportation users and those choosing other modes of transportation, and ultimately ensuring that public transportation users have the same opportunities to participate in social activities as other travel groups. Conventional public transportation network design problems often fail to incorporate the concept of transportation fairness or establish transportation fairness indicators as constraints in the model, only considering the network's own passenger attraction and operating costs, which has little impact on improving the public transportation modal share. Furthermore, in actual public transportation network design problems, the fairness of public transportation resource allocation among different travelers is often overlooked. Current network planning methods that favor economic utility can easily lead to situations where public transportation is not covered in some urban fringe areas with relatively low demand, while resources are surplus in areas with high demand, resulting in excessive route duplication. The significantly longer travel time, longer walking distances, and poorer accessibility of public transportation trips between some origin-destination (OD) areas compared to those between other OD areas are a concentrated manifestation of public transportation unfairness, which to some extent limits the public service nature of the public transportation system. Therefore, considering the fairness of the public transport system in the design of public transport networks is an effective way to reduce the differences in travel costs among different groups of public transport users and to improve the attractiveness of public transport.

[0005] With the continuous advancement of pure electric bus technology, the driving range and charging speed have achieved a qualitative leap, and their application scale has greatly expanded. However, most current measures to improve fairness are based on accessibility, which is a rather one-sided approach, and there is a lack of research on bus network design specifically for pure electric buses. Therefore, to achieve more efficient and wider application of pure electric buses, it is essential to develop a bus network design method based on fairness for pure electric buses.

[0006] In 2019, Iliopoulou et al. proposed a comprehensive route design model for the operation of pure electric buses, aiming to minimize user costs and optimize charging station locations. The model was solved using a multi-objective particle swarm optimization algorithm (Electric Transit Route Network Design Problem: Model and Application[J]. Transportation Research Record: Journal of the Transportation Research Board2673 (8): 264-274). In 2020, Liu et al. proposed an improved artificial fish-swarm algorithm (AFSA) based on crossover and mutation operators to optimize bus route layout, number of buses, and charging station locations (Electric transit network design by an improved artificial Fish-Swarm algorithm[J]. Journal of Transportation Engineering, Part A: Systems 146 (8)). In 2021, Iliopoulou et al. proposed a design framework for pure electric public transportation networks, studying the design of opportunistic charging electric bus networks under conditions of power supply variations and queuing for charging. They employed a robust optimization method to address the location problem of charging infrastructure (Robust electric transit route network design problem (RE-TRNDP) with delay considerations: Model and application [J]. Transportation Research Part C: Emerging Technologies 129: 103255). However, these studies did not consider the number of charging facilities and the associated costs during the design and optimization process. Furthermore, most studies on the fairness of public transportation systems are based on accessibility measures, resulting in a somewhat one-sided approach to fairness, and there is a lack of research specifically on pure electric buses. Summary of the Invention

[0007] This invention addresses the aforementioned technical problems by providing a pure electric bus network planning method that considers fairness. This method minimizes the total travel cost while reducing the traffic Gini coefficient, effectively improving the fairness of bus network design schemes under the premise of controlling total cost, and has significant reference value.

[0008] To achieve the above objectives, the present invention adopts the following technical solution:

[0009] This invention provides a pure electric bus network planning method that considers fairness, comprising the following steps:

[0010] Step 1: Obtain the distribution of stations and the distances between stations in the design area to obtain the road network structure map of the design area;

[0011] Step 2: Based on passenger travel-related parameters, construct the objective function of a fairness model for a pure electric bus system with the goal of minimizing the traffic Gini coefficient;

[0012] Step 3: Considering passenger travel time costs and pure electric bus operating costs, construct an objective function for the total cost model of the pure electric bus network with the goal of minimizing the total social travel cost;

[0013] Step 4: Based on the objective function of the fairness model of the pure electric bus system and the objective function of the total cost model of the pure electric bus network, construct a bi-objective nonlinear programming model for the pure electric bus network;

[0014] Step 5: Using the NSGA-II genetic algorithm, based on the number of pure electric bus routes, route length, departure frequency, operating mileage, and route non-linearity coefficient, set the constraints of the bi-objective nonlinear programming model of the pure electric bus network, solve the bi-objective nonlinear programming model of the pure electric bus network, and obtain the planned pure electric bus network.

[0015] The passenger travel-related parameters described in the technical solution of this invention include passenger walking speed, walking time, waiting time, and time spent in the vehicle.

[0016] The objective function of the fairness model for the pure electric bus system described in the technical solution of this invention is as follows:

[0017] ,

[0018] Where: G is the traffic Gini coefficient. This represents the cumulative proportion of the population variable. , , ; This is the cumulative ratio of public transportation travel time to private driving travel time. , .

[0019] The passenger travel time cost mentioned in the technical solution of this invention includes the passenger walking and waiting time cost and the passenger on-vehicle time cost; the pure electric bus operating cost includes charging cost, charging equipment construction cost, vehicle purchase cost and vehicle maintenance cost.

[0020] The objective function of the total cost model for the pure electric bus network described in the technical solution of this invention is as follows:

[0021] ,

[0022] Where: C represents the total social travel cost. The daily travel time cost for passengers. ;

[0023] Cost of daily passenger walking and waiting time. In the formula The unit cost of passenger walking and waiting time is expressed in yuan / hour. The distance (in km) from the passenger's starting point to the boarding station i is the walking distance. The distance (in km) is the distance a passenger walks from their alighting point (j) to their final destination. Let be the passenger's walking speed, in km / h; E is the set of all pure electric bus routes stopping at stations i and j. The departure frequency of the all-electric bus route from station i to station j is vehicles / hour. The passenger flow from station i to station j is expressed in people / hour. This indicates the conversion factor for passenger flow during peak periods;

[0024] Cost of daily passenger time on the vehicle In the formula Cost per unit of passenger time in the vehicle, in yuan / hour; To from the site Arrive at the station The distance of the shortest path s in time, in km; The operating speed of the pure electric bus is in km / h; To from the site Arrive at the station The total number of paths;

[0025] The daily operating cost of pure electric buses, In the formula The daily charging cost for pure electric buses, , Let X be the charging price, in yuan / (kw·h); X is the set of all pure electric bus routes, and the number of elements in the set is K, that is, K is the number of pure electric bus routes. The energy consumption per kilometer for a pure electric bus is expressed in kWh / km. For the line The departure frequency of pure electric buses, vehicles / hour; For the line The length, in km; The construction cost of a single charging device is RMB per unit. The design lifespan of the charging equipment is [number] days. The number of charging facilities built; In the formula The battery capacity of a pure electric bus is expressed in kWh. The charging efficiency of the charging equipment; The charging power of the charging device, in kW;

[0026] The daily purchase cost and maintenance cost of pure electric buses, In the formula The purchase cost of a pure electric bus is yuan per vehicle. The lifespan of a pure electric bus is [number] days. The price for a single maintenance service for a pure electric bus is [amount in yuan]. The maintenance cycle for pure electric buses is times per year. The number of vehicles required to ensure the normal operation of a pure electric bus network. In the formula This refers to the total travel time of a pure electric bus operating in one direction.

[0027] The bi-objective nonlinear programming model for the pure electric bus network described in the technical solution of this invention is as follows:

[0028] ,

[0029] Where S is the solution set of the bi-objective nonlinear programming model of the pure electric bus network, x is the optimal solution, G is the objective function of the fairness model of the pure electric bus system, and C is the objective function of the total cost model of the pure electric bus network.

[0030] The constraints described in the technical solution of this invention are as follows:

[0031] ,

[0032] in, and The lines are respectively Minimum and maximum length; and These are the minimum and maximum values ​​of the number K of pure electric bus routes, respectively. For the line The straight-line distance between the starting station and the ending station; This represents the maximum value of the non-linear coefficient; For the line The frequency of departures for pure electric buses; For the line The set consisting of all cross-sections; and The lines are respectively upper section Passenger flow in both upward and downward directions; This represents the maximum passenger capacity of a pure electric bus. Energy consumption per kilometer for pure electric buses; The number of runs completed before charging; The charging power of the charging device; This refers to the charging time. The charging efficiency of the charging device.

[0033] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0034] Compared to conventional pure electric bus network design, this invention's fairness-based pure electric bus network planning method can, on the one hand, enhance the attractiveness of public transportation, reduce cost differences among different travelers, and improve the fairness of bus network design; on the other hand, operating pure electric buses can effectively reduce environmental pollution caused by car and bus emissions, while alleviating traffic congestion. Therefore, this invention has significant reference value for effectively improving the fairness of public transportation network design while minimizing total travel costs and reducing the traffic Gini coefficient, thus controlling total costs. Attached Figure Description

[0035] Figure 1 This invention relates to the Lorenz curve, which reflects the allocation of public transport resources.

[0036] Figure 2 This is a road network structure diagram of a city's trunk road network in an example of the present invention.

[0037] Figure 3 This is a public transport network planning scheme for a certain city obtained in an example of the present invention. Detailed Implementation

[0038] The following embodiments are used to illustrate the present invention, but are not intended to limit the scope of protection of the present invention. Unless otherwise specified, the technical means used in the embodiments are conventional means well known to those skilled in the art. Unless otherwise specified, the test methods in the following embodiments are conventional methods.

[0039] Example 1

[0040] The main differences between pure electric buses and traditional fuel-powered buses lie in their unique energy replenishment process, which can easily lead to range anxiety. The limited battery capacity restricts their daily operating mileage. Because pure electric buses face difficulties in replenishing energy during operation, they can only be charged after completing their scheduled transport services. During operation, it is crucial to ensure that the remaining battery power is always sufficient to maintain the route's operation, resulting in relatively high investment in the number of vehicles required for pure electric bus systems. Solving the design problems of pure electric bus networks requires addressing two issues: firstly, reducing passenger travel costs while meeting passenger travel needs; and secondly, minimizing the scale of charging infrastructure to reduce operator costs while ensuring that route transport requirements are met. Therefore, this invention makes the following reasonable assumptions regarding the above problems:

[0041] (1) All buses in the public transport system are fast-charging pure electric buses, and the average operating speed of different routes is relatively stable;

[0042] (2) In the system, the arrival times of passengers at all stops on the bus routes follow a uniform distribution.

[0043] (3) Electric buses must be fully charged before the start of operation each day and must only be charged at the starting and ending points, not at intermediate stops.

[0044] This invention provides a method for planning a pure electric bus network that considers fairness, comprising the following steps:

[0045] Step 1: Obtain the distribution of stations and the distances between stations in the design area to obtain the road network structure map of the design area.

[0046] Step 2: Based on passenger travel-related parameters, including passenger walking speed, walking time, waiting time, and time on the bus, construct the objective function of a fairness model for a pure electric bus system with the goal of minimizing the traffic Gini coefficient.

[0047] Travel time is the most direct indicator reflecting the quality of public transport services received by travelers. However, due to significant differences in travel distance among different travelers, the absolute value of travel time is insufficient to directly reflect the differences in public transport service levels among different travelers. Therefore, this invention selects a relative indicator to reflect the differences in public transport service levels among different travelers, namely the ratio of public transport travel time between OD pairs to driving time of the shortest path between OD pairs. Furthermore, the cumulative proportion of this relative indicator is mapped to the cumulative proportion of ranked travelers, thereby creating a Lorenz curve reflecting the allocation of public transport resources, as shown below. Figure 1 As shown, Figure 1The horizontal axis represents the cumulative percentage of public transport users, the vertical axis represents the cumulative percentage of the ratio of public transport to private car travel time, the solid arc line represents the Lorenz curve, and the dashed line represents the absolute fairness curve. Therefore, the fairness of public transport allocation is determined by the proximity of the Lorenz curve to the dashed line; that is, the smaller the area enclosed by the Lorenz curve and the dashed line, the smaller the traffic Gini coefficient, and the higher the actual fairness of public transport allocation. The traffic Gini coefficient G is represented by the proportion of the area enclosed by the dashed line and the Lorenz curve to the total area under the dashed line.

[0048] ,

[0049] Where G is the traffic Gini coefficient. Let be the area enclosed by the dashed line and the Lorentz curve. Let be the integral of the Lorentz curve along the horizontal axis. Approximately, Differential along the horizontal axis If there is a trapezoid, then The calculation formula is as follows:

[0050] ,

[0051] in, This represents the cumulative proportion of the population variable. , , , This is the cumulative ratio of public transportation travel time to private driving travel time. , .

[0052] Furthermore, the higher the Gini coefficient of traffic, the higher the fairness of the pure electric bus system. Therefore, the objective function of the fairness model for the pure electric bus system is as follows:

[0053] ,

[0054] Where: G is the traffic Gini coefficient. This represents the cumulative proportion of the population variable. , , ; This is the cumulative ratio of public transportation travel time to private driving travel time. , .

[0055] Step 3: Considering passenger travel time costs and the operating costs of pure electric buses, the passenger travel time cost in this invention... Cost of passenger walking and waiting time Composition of passenger time cost Operating costs of pure electric buses Due to charging costs (Including the cost of building charging equipment), vehicle purchase cost, and vehicle maintenance cost) The objective function for constructing a total cost model for a pure electric bus network, with the goal of minimizing the total social travel cost C, is as follows:

[0056] ,

[0057] Where: C represents the total social travel cost. The daily travel time cost for passengers. ;

[0058] Cost of daily passenger walking and waiting time. In the formula The unit cost of passenger walking and waiting time is expressed in yuan / hour. The distance (in km) from the passenger's starting point to the boarding station i is the walking distance. The distance (in km) is the distance a passenger walks from their alighting point (j) to their final destination. Let be the passenger's walking speed, in km / h; E is the set of all pure electric bus routes stopping at stations i and j. The departure frequency of the all-electric bus route from station i to station j is vehicles / hour. The passenger flow from station i to station j is expressed in people / hour. This indicates the conversion factor for passenger flow during peak periods;

[0059] Cost of daily passenger time on the vehicle In the formula Cost per unit of passenger time in the vehicle, in yuan / hour; To from the site Arrive at the station The distance of the shortest path s in time, in km; The operating speed of the pure electric bus is in km / h; To from the site to station The total number of paths;

[0060] The daily operating cost of pure electric buses In the formula The daily charging cost for pure electric buses, , Let X be the charging price, in yuan / (kw·h); X is the set of all pure electric bus routes, and the number of elements in the set is K, that is, K is the number of pure electric bus routes. The energy consumption per kilometer for a pure electric bus is expressed in kWh / km. For the line The departure frequency of pure electric buses, vehicles / hour; For the line The length, in km; The construction cost of a single charging device is RMB per unit. The design lifespan of the charging equipment is [number] days. The number of charging facilities built; In the formula The battery capacity of a pure electric bus is expressed in kWh. The charging efficiency of the charging equipment; The charging power of the charging device, in kW;

[0061] The daily purchase cost and maintenance cost of pure electric buses, In the formula The purchase cost of a pure electric bus is yuan per vehicle. The lifespan of a pure electric bus is [number] days. The price for a single maintenance service for a pure electric bus is [amount in yuan]. The maintenance cycle for pure electric buses is times per year. The number of vehicles required to ensure the normal operation of a pure electric bus network. In the formula This refers to the total travel time of a pure electric bus operating in one direction.

[0062] It is worth noting that the present invention adopts a uniform distribution for the waiting time of travelers at the station; the on-vehicle time mainly covers the parking delay at intersections and the segment travel time of buses, and the calculation of on-vehicle time mainly utilizes the average travel speed of the route.

[0063] Step 4: Based on the objective function of the fairness model of the pure electric bus system and the objective function of the total cost model of the pure electric bus network, construct the following bi-objective nonlinear programming model for the pure electric bus network:

[0064] ,

[0065] Where S is the solution set of the bi-objective nonlinear programming model of the pure electric bus network, x is the optimal solution, G is the objective function of the fairness model of the pure electric bus system, and C is the objective function of the total cost model of the pure electric bus network.

[0066] Step 5: Using the NSGA-II genetic algorithm, based on the number of pure electric bus routes, route length, departure frequency, operating mileage, and route non-linearity coefficient, set the constraints of the bi-objective nonlinear programming model of the pure electric bus network, solve the bi-objective nonlinear programming model of the pure electric bus network, and obtain the planned pure electric bus network.

[0067] (1) Regarding line length constraints

[0068] Bus route length is typically related to city size and passenger travel distances; routes should not be too long or too short. If routes are too long, travel time is excessive, affecting the flexibility of the route network and increasing the number of vehicles required. Conversely, if routes are too short, an excessive number of routes may be deployed, increasing system operating costs and potentially leading to more transfers and a lower level of public transport service. Therefore, it is necessary to set a reasonable range for bus route lengths based on different operating conditions. Thus, the constraints on route length are as follows:

[0069] ,

[0070] in, and The lines are respectively The minimum and maximum length values.

[0071] (2) Regarding the constraints on the number of lines

[0072] To facilitate residents' travel while controlling operating costs, the number of pure bus routes in the network should be kept within a reasonable integer range. Therefore, the constraints on the number of routes are as follows:

[0073] ,

[0074] in, and These are the minimum and maximum values ​​of the number K of pure electric bus routes, respectively.

[0075] (3) Regarding the constraint on nonlinear coefficients

[0076] The non-linearity coefficient refers to the ratio of the route length to the straight-line distance between the first and last stops of a bus route. For the bus network, reducing bus route detours can, to some extent, lower passenger travel costs and improve passenger satisfaction. Therefore, the constraints on the non-linearity coefficient are as follows:

[0077] ,

[0078] in, For the line The straight-line distance between the starting station and the ending station; This represents the maximum value of the non-linear coefficient.

[0079] (4) Regarding departure frequency constraints

[0080] When designing a pure public transport network, it is essential to meet the travel needs of individuals within the study area. The frequency of departures determines the transport capacity of each bus route, which should satisfy the public transport demand at all cross-sections in both directions. Therefore, based on the cross-section with the highest passenger flow in the passenger flow distribution results, the following constraints are set for the route's departure frequency:

[0081] ,

[0082] in, For the line The frequency of departures for pure electric buses; For the line The set consisting of all cross-sections; and The lines are respectively upper section Passenger flow in both upward and downward directions; This represents the maximum passenger capacity of a pure electric bus.

[0083] (5) Regarding mileage constraints

[0084] Pure electric buses are vehicles that rely entirely on power batteries for energy. During daily operation, the power battery maintains a constant state of charge; that is, after each charge, the bus's state of charge is 1%. The amount of electricity consumed by the bus during operation between two consecutive charges is equal to the amount of electricity charged during each charge. Therefore, the constraints on operating mileage are as follows:

[0085] ,

[0086] in, Energy consumption per kilometer for pure electric buses; The number of runs completed before charging; The charging power of the charging device; This refers to the charging time. The charging efficiency of the charging device.

[0087] Because solving the bus network design problem involves nondeterministic polynomial time complexity (NP-hard), heuristic search algorithms have become the mainstream method for solving this problem in recent years. However, many traditional heuristic algorithms often have poor global convergence, and sometimes the quality of the final result depends heavily on the initial solution. Currently, commonly used heuristic algorithms for bus network design problems include genetic algorithms, ant colony algorithms, and simulated annealing algorithms. These methods solve multi-objective programming models by selecting weights to transform the multi-objective function into a single objective for solution. However, the weight values ​​for each objective are subjective and can affect the reliability of the results. Non-dominated genetic algorithm II (NSGA-II) is one of the most effective algorithms for solving multi-objective problems. Its main processes include fast non-dominated sorting, congestion calculation, and population selection based on an elite strategy. The solution process of the bi-objective nonlinear programming model for the pure electric bus network of this invention is as follows:

[0088] S1: Input algorithm initialization parameters and set the population size. Number of iterations Set the number of routes, generate an initial population, and initialize the departure frequency of each route. Set the number of iterations. .

[0089] S2: Calculate the shortest path based on the shortest path algorithm, allocate travel demand to the public transport network, calculate the maximum flow of each road segment, and determine the new departure frequency for each route.

[0090] S3: Based on the newly determined departure frequency and the bus network, calculate the objective function value and determine the fitness value.

[0091] S4: Perform fast non-dominated sorting based on the objective function value, assign levels, and calculate the crowding degree of individuals in each level.

[0092] S5: Use a tournament strategy to select the parent generation. Randomly select two individuals each time, prioritizing individuals with higher ranking. If the ranking is the same, prioritize individuals with higher crowding.

[0093] S6: Perform a crossover operation on the selected parent population. For each individual, randomly select two different lines and swap them.

[0094] S7: Randomly select a parent individual, perform mutation operation on its line, and then merge the crossover and mutated offspring individuals with the parent population based on the elite strategy, and calculate the objective function value of each individual in the new population.

[0095] S8: Determine the termination condition. If the maximum number of iterations is reached, terminate the iteration and generate the Pareto optimal solution set; otherwise, go to step 2.

[0096] Application example:

[0097] Based on a map open platform, a road network structure map of a city's trunk road network was obtained using MATLAB programming. The map contains 44 nodes and 72 road segments. Figure 2 As shown in Table 1.

[0098] Table 1 Main Original Parameter Settings

[0099]

[0100] The main parameters of the NSGA-II algorithm are designed as follows: the population size of the genetic algorithm is 100, the crossover probability and mutation probability are set to 0.9 and 0.1 respectively, and the maximum number of iterations is set to 800.

[0101] To provide the best possible network scheme, we analyzed the network schemes under different numbers of pure bus routes, removed the more extreme objective function values, i.e., the function values ​​where one objective is better than the other, and calculated the traffic Gini coefficient G and the total social travel cost C for the remaining schemes. The results are shown in Table 2.

[0102] Table 2. Average values ​​of the two objective functions for different numbers of pure bus routes.

[0103]

[0104] As shown in Table 2, the total cost C of the pure electric bus network increases with the increase in the number of routes in the pure bus network, while the fairness of the pure electric bus system changes only slightly and fluctuates. Therefore, the number of pure bus routes K is selected as 11.

[0105] Based on this number of routes, the traffic Gini coefficient G and the total social travel cost C were calculated, and the results are shown in Table 3.

[0106] Table 3. Calculation results of the traffic Gini coefficient G and total social travel cost C

[0107]

[0108] When both objective function values ​​are relatively good, the Pareto optimal solution set of the bi-objective nonlinear programming model for the pure electric bus network is obtained, and the results are shown in Table 4.

[0109] Table 4. Zhengzhou City Pure Electric Bus Route Network Planning Scheme Collection

[0110]

[0111]

[0112]

[0113]

[0114] Based on the obtained Pareto optimal solution set, and considering both residents' travel demand and the operating cost of pure electric buses, the best solution is selected. Comparison shows that Solution 1 has better overall social travel cost and public transport system fairness. Therefore, the public transport network planning scheme obtained from Solution 1 is as follows: Figure 3 As shown in Table 5, the departure frequency for each pure electric bus route in this scheme is as follows.

[0115] Table 5. Frequency of each bus route in a city's public transport network planning scheme.

[0116]

[0117] The embodiments described above are merely preferred embodiments of the present invention and are only used to explain the present invention. They are not intended to limit the scope of the present invention. For those skilled in the art, other implementation methods can be easily made by substitution or modification based on the technical content disclosed in this specification. Therefore, all changes and improvements made on the principle of the present invention should be included within the scope of the patent application of the present invention.

Claims

1. A pure electric bus network planning method considering fairness, characterized in that, Includes the following steps: Step 1: Obtain the distribution of stations and the distances between stations in the design area to obtain the road network structure map of the design area; Step 2: Based on passenger travel-related parameters, construct an objective function for a fairness model of the pure electric bus system, aiming to minimize the traffic Gini coefficient. These parameters include passenger walking speed, walking time, waiting time, and time spent on the bus. The objective function for the fairness model of the pure electric bus system is as follows: ， Where: G is the traffic Gini coefficient. This represents the cumulative proportion of the population variable. , , ; This is the cumulative ratio of public transportation travel time to private driving travel time. , ; Step 3: Considering passenger travel time costs and pure electric bus operating costs, construct an objective function for the total cost model of the pure electric bus network with the goal of minimizing the total social travel cost; Step 4: Based on the objective function of the fairness model of the pure electric bus system and the objective function of the total cost model of the pure electric bus network, construct a bi-objective nonlinear programming model for the pure electric bus network; Step 5: Using the NSGA-II genetic algorithm, based on the number of pure electric bus routes, route length, departure frequency, operating mileage, and route non-linearity coefficient, set the constraints of the bi-objective nonlinear programming model of the pure electric bus network, solve the bi-objective nonlinear programming model of the pure electric bus network, and obtain the planned pure electric bus network.

2. The pure electric bus network planning method considering fairness according to claim 1, characterized in that, The passenger travel time cost includes the passenger walking and waiting time cost, and the passenger on-vehicle time cost; the pure electric bus operating cost includes charging cost, charging equipment construction cost, vehicle purchase cost, and vehicle maintenance cost.

3. The pure electric bus network planning method considering fairness according to claim 1 or 2, characterized in that, The objective function of the total cost model for the pure electric bus network is as follows: ， Where: C represents the total social travel cost. The daily travel time cost for passengers. ; Cost of daily passenger walking and waiting time. In the formula The unit cost of passenger walking and waiting time is expressed in yuan / hour. The distance (in km) from the passenger's starting point to the boarding station i is the walking distance. The distance (in km) is the distance a passenger walks from their alighting point (j) to their final destination. Let be the passenger's walking speed, in km / h; E is the set of all pure electric bus routes stopping at stations i and j. The departure frequency of the all-electric bus route from station i to station j is vehicles / hour. The passenger flow from station i to station j is expressed in people / hour. This indicates the conversion factor for passenger flow during peak periods; Cost of daily passenger time on the vehicle In the formula Cost per unit of passenger time in the vehicle, in yuan / hour; To from the site to station The distance of the shortest path s in time, in km; The operating speed of the pure electric bus is in km / h. To from the site to station The total number of paths; The daily operating cost of pure electric buses In the formula The daily charging cost for pure electric buses, , Let X be the charging price, in yuan / (kw·h); X is the set of all pure electric bus routes, and the number of elements in the set is K, that is, K is the number of pure electric bus routes. The energy consumption per kilometer for a pure electric bus is expressed in kWh / km. For the line The departure frequency of pure electric buses, vehicles / hour; For the line Length, km; The construction cost of a single charging device is RMB per unit. The design lifespan of the charging equipment is [number] days. The number of charging facilities built; In the formula The battery capacity of a pure electric bus is expressed in kWh. The charging efficiency of the charging equipment; The charging power of the charging device, in kW; The daily purchase cost and maintenance cost of pure electric buses, In the formula The purchase cost of a pure electric bus is yuan per vehicle. The lifespan of a pure electric bus is [number] days. The price for a single maintenance service for a pure electric bus is [amount in yuan]. The maintenance cycle for pure electric buses is times per year. The number of vehicles required to ensure the normal operation of a pure electric bus network. In the formula This refers to the total travel time of a pure electric bus operating in one direction.

4. The pure electric bus network planning method considering fairness according to claim 1, characterized in that, The bi-objective nonlinear programming model for the pure electric bus network is as follows: ， Where S is the solution set of the bi-objective nonlinear programming model of the pure electric bus network, x is the optimal solution, G is the objective function of the fairness model of the pure electric bus system, and C is the objective function of the total cost model of the pure electric bus network.

5. The pure electric bus network planning method considering fairness according to claim 4, characterized in that, The constraints are as follows: ， in, and The lines are respectively Minimum and maximum length; and These are the minimum and maximum values ​​of the number K of pure electric bus routes, respectively. For the line The straight-line distance between the starting station and the ending station; This represents the maximum value of the non-linear coefficient; For the line The frequency of departures for pure electric buses; For the line The set consisting of all cross-sections; and The lines are respectively upper section Passenger flow in both upward and downward directions; This represents the maximum passenger capacity of a pure electric bus. Energy consumption per kilometer for pure electric buses; The number of runs completed before charging; The charging power of the charging device; This refers to the charging time. The charging efficiency of the charging device.

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