Bus intelligent dynamic scheduling optimization method based on real-time data

Abstract

The invention belongs to the technical field of bus scheduling, and particularly relates to a bus intelligent dynamic scheduling optimization method based on real-time data, and the method optimizes the load factor and the generalized transportation cost at the same time through an improved minimum cost maximum flow model. Weights are given to all targets through collaborative optimization, the optimal weight for improving the bus operation efficiency is selected through a numerical experiment, a model is established based on a multi-target optimization method, solving is conducted through a genetic algorithm, the purposes of dynamically adjusting the departure interval and selecting the bus types are achieved, resources are efficiently configured, and the waiting time of passengers is remarkably shortened.

Description

Technical Field

[0001] The present application belongs to the technical field of bus dispatching, and specifically relates to a bus intelligent dynamic dispatching optimization method based on real-time data. Background Art

[0002] With the rapid growth of the global population and the acceleration of urbanization, urban traffic problems are becoming increasingly serious, especially during peak hours. Traffic congestion has become an important factor affecting the travel efficiency of urban residents, the quality of public transportation services and energy consumption. At the same time, environmental pollution and traffic safety issues are becoming increasingly serious, and the pressure on urban traffic management is increasing. Traditional traffic management models mostly rely on fixed departure schedules and simple traffic flow forecasts. These methods are difficult to cope with complex traffic dynamics, especially in the case of emergencies or unpredictable traffic flow fluctuations, which often lead to waste of traffic resources or failure to meet passenger needs.

[0003] In this context, the intelligent dispatch optimization method of public transportation based on real-time data came into being. By using advanced technologies such as the Internet of Things, big data, and artificial intelligence, the intelligent transportation system can monitor and analyze traffic flow in real time, and dynamically adjust traffic signals and departure schedules to achieve a more efficient, greener, and safer urban transportation system. Therefore, the random optimization model based on real-time data, as a new idea, can more accurately respond to these challenges, improve the overall efficiency and resource utilization of the transportation system, and provide theoretical support and technical guarantee for the further development of the intelligent transportation system. Summary of the invention

[0004] The bus intelligent dynamic scheduling method considered in this invention is mainly based on real-time data. The main research idea is: based on the collected real-time data, the peak and trough periods of passenger flow in a day are divided, and the traffic flow in the road section is obtained through the real-time monitoring data of the road GPS to judge the degree of road congestion, so as to predict the arrival time of the bus. In addition, multi-objective optimization is performed based on passenger flow data to achieve the purpose of improving vehicle operation efficiency and passenger satisfaction by selecting departure models and departure intervals. The specific technical solution is as follows: A method for optimizing bus intelligent dynamic scheduling based on real-time data, comprising the following steps: S1. The total cost of passenger travel includes the waiting time of passengers and the cost of passengers. The objective function of the total cost of passenger travel is constructed as follows: ; ; In the formula, is the total cost of passenger travel; Waiting time for passengers, for The dimensionless function of For monetary cost, for The dimensionless function of is the bus operating cost, Costs to passengers; S2: Taking the maximum vehicle load rate as the objective function, taking into account the vehicle type and departure interval, the specific objective function is as follows: ; In the formula, is the vehicle load factor, is the vehicle capacity corresponding to different models, is the indicator vector, representing the line Whether to select a vehicle model when starting the trip , For Site To site The passenger flow capacity; is the total number of sites; S3: Use genetic algorithm to search for the optimal solution of the objective function in S1 and S2, and find the optimal solution through survival of the fittest; the overall objective function is: ; In the formula, Represent the sub-goal weights respectively, satisfying .

[0005] Preferably, in step S1, at the station Waiting for the train Passenger time cost , expressed as follows: ; On the down route at the station Waiting for the train Passenger time cost , expressed as follows: ; ; In the formula, Waiting time for all passengers, Represents the upward direction, Represents the downward direction, is the arrival rate of passengers waiting for the uplink route, is the arrival rate of passengers waiting for the downlink route, which is a The function of Indicates the number of trips in the upward direction From the site The time of departure, Indicates the number of trips in the down direction From the site The time of departure, represents the set of all upstream trips, represents the set of all downstream trips, represents the set of all upstream sites, Represents the set of all downstream sites.

[0006] Preferably, shipping cost and passenger costs They are: ; ; In the formula, For transportation costs, Costs for passengers, To determine the line Is it a 0-1 variable indicating the minimum bus operating cost? The line is from the station To site When the line with the lowest operating cost is is 1, otherwise it is 0; From site To site Take the route between The transportation costs incurred, especially when season ,when and When there is no direct line between ; For ride routes From the site To site The average cost of passengers It is a site To site The passenger flow capacity of the road sections between them.

[0007] Preferably, the relationship between the vehicle travel time between stations and the time of arrival at the adjacent station satisfies the following equation: ; ; To avoid repeated route selection, the constraints are as follows: ; In the formula, and They are functions of the vehicle's travel time on the road section between each adjacent station in the uplink and downlink directions respectively.

[0008] Preferably, in step S2, a vehicle model selection constraint function is established, and its formula is as follows: ; In the formula, For ride routes Select Model The indicator variable is 1 if selected and 0 if not selected.

[0009] Preferably, in step S2, the passenger flow capacity should satisfy: ; In the formula, From site To site passenger flow, which is a non-negative quantity.

[0010] Preferably, each individual in step S1 is sequentially encoded, and for the uplink direction: ; in, The interval between adjacent trains. , The trip number collection for the upward direction; For the downlink direction: ; in, The interval between adjacent trains. , A collection of trips in the down direction; The departure time plan of the dual-station bus line is a combination of the up-direction and down-direction plans, expressed as: ; Establish an evaluation function to assign probability to each chromosome, the formula is as follows: , ; in, For any chromosome, is a real number, , For population size.

[0011] Preferably, in step S3, a roulette wheel method is used to select and cultivate a new generation of chromosomes, and the steps are as follows: Step 1: Calculate the cumulative probability of each chromosome ,Right now: ; ; In the formula, In addition to chromosomes Any chromosome other than Step 2: Generate a random number ,like , then chromosome is selected, repeat the step times, we get chromosomes.

[0012] Preferably, in step S3, a chromosome is randomly selected Assume that the crossover probability is ,from Randomly generated numbers ,if For the part of the chromosome that belongs to the upward direction, two non-overlapping gene fragments of equal length are randomly selected for exchange. The operation of the chromosome in the downward direction is similar to that to generate a new population.

[0013] Preferably, in step S3, assuming that the mutation probability is ,from Randomly generated number ,if , for the part of the chromosome that is in the ascending direction, the length will be The gene fragment of is replaced with a newly generated gene fragment of the same length; a randomly generated gene fragment of length The gene fragment is in the interval The interval length is: ; They cover The gene fragments are located on the chromosomes at both ends of the gene.

[0014] Compared with the prior art, the present invention has the following beneficial effects: 1. Traditional methods usually use a fixed type of vehicle, and do not consider the flexible selection of vehicle models based on real-time passenger flow or the needs of different road sections. This method lacks flexibility and the ability to cope with changing traffic conditions. During peak periods, fixed vehicle models may be overloaded, and during non-peak periods, there may be empty vehicles running, which affects overall efficiency. This application introduces a strategy of mixed dispatch of multiple models to dynamically select suitable vehicle models based on real-time passenger flow data. Large-capacity vehicles can be selected during peak periods, while small vehicles are used during off-peak periods to minimize unnecessary waste of resources while improving vehicle utilization and operational efficiency. This not only improves service quality, but also optimizes transportation costs.

[0015] 2. Traditional scheduling optimization methods mostly rely on historical data for modeling and optimization. Historical data provides information such as past traffic patterns and passenger flow, and can predict passenger flow in different time periods, but its limitation is that the data cannot reflect the instantly changing traffic environment. For example, factors such as special weather and traffic accidents may cause sudden changes in traffic, and historical data cannot respond to such changes in a timely manner. By introducing real-time data, this patent can monitor variables such as traffic flow and passenger demand in real time, and adjust the scheduling strategy accordingly to ensure the efficiency and flexibility of transportation.

[0016] 3. In previous studies, optimization algorithms are usually solved based on fixed conditions and assumptions, using a global optimization strategy. Algorithms usually perform scheduling optimization within a larger time frame, taking into account the operation of the entire transportation system, but they may not be able to quickly obtain the optimal solution in a short period of time, and often require a large amount of computing resources to process large-scale data. Through dynamic adjustment and real-time feedback mechanisms, the optimization process can be carried out quickly within a smaller time frame and the optimization target can be adjusted in real time. Through this method, the system can significantly improve computing efficiency and adapt to changing traffic conditions while ensuring the quality of optimization. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 For the flow chart, Figure 2 is the genetic algorithm flow chart, Figure 3 This is a schematic diagram of the operation of the bus double station line. Figure 4 This is the optimization result diagram of the departure interval in each time period. DETAILED DESCRIPTION

[0018] The technical solution of the present application is described in detail below through specific embodiments and drawings. It should be understood that the embodiments of the present application and the specific features in the embodiments are detailed descriptions of the technical solution of the present application, rather than limitations on the technical solution of the present application, and the specific technical features may be combined with each other.

[0019] A method for optimizing bus intelligent dynamic scheduling based on real-time data, comprising the following steps: By building a traffic flow model to monitor the traffic volume based on real-time data, the degree of traffic congestion can be determined to facilitate vehicle dispatch.

[0020] Consider a one-way flow of cars on a stretch of road. To simplify the model, assume that the length of the stretch of road is much longer than the distance between vehicles, that each car has the same length, and that the traffic flow is considered a continuous quantity.

[0021] Bundle The axis is built in the direction of traffic on the highway, and cars move along The axis moves in the positive direction. Road section, The change in the total number of vehicles in a time period is equal to the number of vehicles entering this area minus the number of vehicles leaving this area: ; In the formula, is the function of traffic density (number of vehicles per unit road length), For car traffic.

[0022] Divide both sides of the equation by After finishing, we get: ; Taking the limit at both ends simultaneously gives: ; Depend on get: ; Based on the characteristics of traffic flow, the relationship model between density and speed is established as follows: ; In the formula, is a function of density. When the density is as small as 0, the maximum speed limit of the road is reached. Therefore, The maximum speed limit on the road. is the maximum traffic density of the road.

[0023] Based on this, the vehicle speed can be obtained according to the road density monitored in real time, and the vehicle arrival time can be predicted.

[0024] Common bus routes are dual-station bus routes, that is, routes with both upstream and downstream stations. In this case, the waiting time for passengers should be the sum of the waiting time for passengers in the upstream direction and the waiting time for passengers in the downstream direction. Assume that the passenger arrival rate at each station in the upstream and downstream directions is a function of time. The function of and This means that the passenger arrival rate is a continuous function of time, that is, for any given time, the passenger arrival rate of the corresponding station can be obtained. For the up direction, let the number of trains be Arrival site The time is , , , then the time interval between the arrival of two adjacent trains is , therefore, at the site Train No. The waiting time for passengers is: ; The total waiting time for passengers at all stations and all trains in the upward direction is: ; Similarly, the total waiting time for passengers at all stations and all trains in the down direction is: ; S1. The total cost of passenger travel includes the waiting time of passengers and the cost of passengers. The objective function of the total cost of passenger travel is constructed as follows: ; ; The normalization process is as follows: ; ; ; ;

[0025] in, is the minimum waiting time for passengers, the minimum is 0, It is the maximum waiting time for passengers, which is determined based on the actual departure interval data. is the minimum cost, which is the minimum when no vehicle is dispatched, and the minimum is 0. The maximum cost is determined by the actual number of vehicles dispatched.

[0026] On the up route at the station Waiting for the train Passenger time cost , expressed as follows: ; On the down route at the station Waiting for the train Passenger time cost , expressed as follows: ; ; In the formula, Waiting time for all passengers, Represents the upward direction, Represents the downward direction, is the arrival rate of passengers waiting for the uplink route, is the arrival rate of passengers waiting for the downlink route, which is a The function of Indicates the number of trips in the upward direction From the site The time of departure, Indicates the number of trips in the down direction From the site The time of departure, represents the set of all upstream trips, represents the set of all downstream trips, represents the set of all upstream sites, represents the set of all downstream sites, is the total cost of passenger travel; The size of is determined by the waiting time of passengers and the travel expenses of passengers. Waiting time for passengers, For monetary cost, is the bus operating cost, Costs for passengers.

[0027] Shipping costs and passenger costs They are: ; ; In the formula, For transportation costs, Costs for passengers, To determine the line Is it a 0-1 variable indicating the minimum bus operating cost? The line is from the station To site When the line with the lowest operating cost is is 1, otherwise it is 0; From site To site Take the route between The transportation costs incurred, especially when season ,when and When there is no direct line between ; For ride routes From the site To site The average cost of passengers It is a site To site The passenger flow capacity of the road sections between them.

[0028] Generally speaking, during the operation of a route, the remaining passenger capacity of the vehicle will change after passing through the passing stations. On site To site When running between , the current capacity of the bus is There are three possible initial vehicle capacities (e.g., a small vehicle with a passenger capacity of less than 20 people, a medium-sized vehicle with a passenger capacity of 20-50 people, and a large vehicle with a passenger capacity of more than 50 people), recorded as ( ).

[0029] When passing the station, the vehicle capacity is updated as follows: ; In the formula For time interval Internal Site Passengers waiting to board the vehicle Number of people, For time interval Inside the vehicle Passing by site And the number of people getting off.

[0030] S2: Taking the maximum vehicle load rate as the objective function, taking into account the vehicle type and departure interval, the specific objective function is as follows: ; In the formula, is the vehicle load factor, is the vehicle capacity corresponding to different models, is the indicator vector, representing the line Whether to select a vehicle model when starting the trip , For Site To site The passenger flow capacity; is the total number of sites; The relationship between the vehicle travel time between stations and the time of arrival at adjacent stations is as follows: ; ; To avoid repeated route selection, the constraints are as follows: ; In the formula, and They are functions of the vehicle's travel time on the road section between each adjacent station in the uplink and downlink directions respectively.

[0031] Establish the vehicle model selection constraint function, which is as follows: ; In the formula, For ride routes Select Model The indicator variable is 1 if selected and 0 if not selected.

[0032] In step S2, the passenger flow capacity should meet the following requirements: ; In the formula, From site To site passenger flow, which is a non-negative quantity.

[0033] S3: Use genetic algorithm to search for the optimal solution of the objective function in S1 and S2, and find the optimal solution through survival of the fittest; the overall objective function is: ; Represent the sub-goal weights respectively, satisfying .

[0034] Sequentially encode each individual in step S1, for the uplink direction: ; in, The interval between adjacent trains. , The trip number collection for the upward direction; For the downlink direction: ; in, The interval between adjacent trains. , A collection of trips in the down direction; The departure time plan of the dual-station bus line is a combination of the up-direction and down-direction plans, expressed as: ; Establish an evaluation function to assign probability to each chromosome, the formula is as follows: , ; in, is any chromosome, that is, any number in the set of upstream and downstream solutions, is a real number, , For population size.

[0035] In step S3, a roulette wheel method is used to select and cultivate a new generation of chromosomes, and the steps are as follows: Step 1: Calculate the cumulative probability of each chromosome ,Right now: ; ; In the formula, In addition to chromosomes Any chromosome other than

[0036] Step 2: Generate a random number ,like , then chromosome is selected, repeat the step times, we get chromosomes.

[0037] In step S3, a chromosome is randomly selected Assume that the crossover probability is ,from Randomly generated number ,if For the part of the chromosome that belongs to the upward direction, two non-overlapping gene fragments of equal length are randomly selected for exchange. The operation of the chromosome in the downward direction is similar to that to generate a new population.

[0038] In step S3, assume that the mutation probability is ,from Randomly generated number ,if , for the part of the chromosome that is in the ascending direction, the length will be The gene fragment of is replaced with a newly generated gene fragment of the same length; a randomly generated gene fragment of length The gene fragment is in the interval The interval length is: ; They cover The gene fragments are located on the chromosomes at both ends of the gene.

[0039] In step S3 of the present invention, preferably, the following assumptions are made: 1. When the target bus arrives, all passengers will choose to get on the bus, that is, the bus capacity can be greater than 100%; 2. The vehicle stays at the station for a fixed time and does not fluctuate greatly with the number of passengers getting on and off the vehicle; 3. The fixed costs (such as driver wages, vehicle maintenance, etc.) and variable costs (such as fuel consumption) of each trip are simplified to fixed values ​​for each trip; 4. Assume that the load factor is proportional to the number of passengers on each trip; 5. Maximize total revenue (assuming each passenger pays a fixed fare) minus total cost, which is maximum profit.

[0040] Based on the passenger flow data collected by S1, mainly including the number of people waiting and the waiting time in each time period at each station, the genetic algorithm is used to solve the problem. The principle of the genetic algorithm is to simulate the natural evolution process in the biological world and find the optimal solution through the survival of the fittest. Due to the evolutionary characteristics of the algorithm, the genetic algorithm imitates the process of biological evolution in nature, including initializing the population, calculating fitness, chromosome selection, chromosome crossover, and chromosome mutation. The genetic algorithm is robust in finding high-quality non-dominated solutions and running time. When applying the genetic algorithm, an initial population is first generated. The population is composed of chromosomes. Each chromosome is a feasible chromosome generated according to certain rules, which is the initial feasible solution. Then, according to the principle of survival of the fittest, the chromosomes in the initial population are selected, crossed, mutated, and other operations are continuously iterated until a solution close to the optimal is generated. According to the objective function of the problem to be solved, an evaluation function is designed to evaluate each generation of the population, that is, chromosomes with higher fitness are usually selected, thereby generating a new population. The iterative process is a process to ensure that high-quality chromosomes are left behind. Through iteration, the quality of the population is gradually improved. The steps are as follows: Figure 1 shown.

[0041] The present invention can improve the efficiency of public transportation operations: 1. By collecting and processing passenger flow data, analyzing real-time traffic and passenger flow data, accurately arranging vehicle departure intervals and selecting vehicle models according to different time periods (peak period, off-peak period, and valley period), and realizing reasonable vehicle dispatching, it can avoid the problem that fixed timetables cannot adapt to dynamic changes in traffic, thereby reducing resource waste and unnecessary vehicle idling; 2. Choose the appropriate vehicle type according to passenger flow density to avoid congestion caused by too small vehicles and waste of resources caused by too large vehicles, and increase the full load rate.

[0042] The present invention uses multi-objective optimization and genetic algorithms to reasonably arrange departure times and reduce the average waiting time of passengers at stations. By dynamically adjusting routes and intervals, a traffic flow model is established to alleviate vehicle delays caused by congestion and improve passenger travel experience.

[0043] The present invention enhances the flexibility and adaptability of the system. Through real-time data monitoring (such as GPS, card swiping data) and traffic density prediction models, the system can quickly respond to emergencies or unpredictable traffic flow fluctuations to ensure the reliability and stability of the public transportation system.

[0044] The present invention reduces operating costs: 1. Through the minimum cost maximum flow model and full load rate optimization, the vehicle type and departure frequency are reasonably selected to avoid too many empty vehicles running, thereby reducing operating costs such as fuel and maintenance; 2. Guide passengers to choose appropriate routes, optimize passenger flow distribution between routes, and further reduce operating costs.

[0045] The present invention is based on dynamic bus dispatching for multi-objective optimization. By using traffic flow models and real-time data, the system can flexibly respond to emergencies or abnormal traffic flows (such as sudden traffic jams or major events) to ensure the continuity of bus services. Based on the Greenshields speed-density relationship model, the traffic flow and congestion conditions of road sections are predicted to provide an accurate basis for vehicle scheduling.

[0046] This application is based on multi-objective optimization of dynamic bus dispatch, which has good scalability and applicability. The system is based on real-time data collection and existing algorithms, which is easy to expand to bus networks or cities of different sizes. Passenger APP can collect data and provide suggestions to further improve the promotion of the system and citizen participation.

[0047] The present invention is based on multi-objective optimization of dynamic bus dispatching, which can achieve efficient traffic management, reduce resource waste, and provide strong support for building a smart city in practical applications.

[0048] The above is only a preferred implementation of the present application. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the technical principles of the present application. These improvements and modifications should also be regarded as the scope of protection of the present application.

Claims

1. A bus intelligent dynamic scheduling optimization method based on real-time data, characterized in that: The following steps are involved: S1. The total cost of passenger travel includes the waiting time of passengers and the cost of passengers. The objective function of the total cost of passenger travel is constructed as follows: ； ； In the formula, is the total cost of passenger travel; Waiting time for passengers, for The dimensionless function of For monetary cost, for The dimensionless function of is the bus operating cost, Costs to passengers; S2: Taking the maximum vehicle load rate as the objective function, considering the vehicle type and departure interval, the objective function is as follows: ； In the formula, is the vehicle load factor, is the vehicle capacity corresponding to different vehicle models, is the indicator vector, representing the line Whether to select a vehicle model when starting the trip , For Site To site The passenger flow capacity; is the total number of sites; S3: Use genetic algorithm to search for the optimal solution of the objective function in S1 and S2, and find the optimal solution through survival of the fittest; the overall objective function is: ； In the formula, Represent the sub-goal weights respectively, satisfying .

2. The method for optimizing bus intelligent dynamic scheduling based on real-time data according to claim 1 is characterized in that: In step S1, at the station in the up route Waiting for the train Passenger time cost , expressed as follows: ； On the down route at the station Waiting for the train Passenger time cost , expressed as follows: ； ； In the formula, Waiting time for all passengers, Represents the upward direction, Represents the downward direction, is the arrival rate of passengers waiting for the uplink route, is the arrival rate of waiting passengers on the downlink line, Indicates the number of trips in the upward direction From the site The time of departure, Indicates the number of trips in the down direction From the site The time of departure, represents the set of all upstream trips, represents the set of all downstream trips, represents the set of all upstream sites, Represents the set of all downstream sites.

3. The method for optimizing public transportation intelligent dynamic scheduling based on real-time data according to claim 1 is characterized in that: Shipping costs and passenger costs They are: ； ； In the formula, For transportation costs, Costs for passengers, To determine the line Is it a 0-1 variable indicating the minimum bus operating cost? The line is from the station To site When the line with the lowest operating cost is is 1, otherwise it is 0; From site To site Take the route between The transportation cost is season ,when and When there is no direct line between ; For ride routes From the site To site The average cost of passengers It is a site To site The passenger flow capacity of the road sections between them.

4. The method for optimizing bus intelligent dynamic scheduling based on real-time data according to claim 1 is characterized in that: The relationship between the vehicle travel time between stations and the time of arrival at adjacent stations is as follows: ； ； To avoid repeated route selection, the constraints are as follows: ； In the formula, and They are functions of the vehicle's travel time on the road section between each adjacent station in the uplink and downlink directions respectively.

5. The method for optimizing bus intelligent dynamic scheduling based on real-time data according to claim 1 is characterized in that: In step S2, a vehicle model selection constraint function is established, and its formula is as follows: ； In the formula, For ride routes Select Model The indicator variable is 1 if selected and 0 if not selected.

6. The method for optimizing public transportation intelligent dynamic scheduling based on real-time data according to claim 1 is characterized in that: In step S2, the passenger flow capacity should meet the following requirements: ； In the formula, From site To site passenger flow.

7. The method for optimizing bus intelligent dynamic scheduling based on real-time data according to claim 1 is characterized in that: Sequentially encode each individual in step S1, for the uplink direction: ； in, The interval between adjacent trains. , The trip number collection for the upward direction; For the downlink direction: ； in, The interval between adjacent trains. , It is the trip collection for the down direction; The departure time plan of the dual-station bus line is a combination of the up-direction and down-direction plans, expressed as: ； Establish an evaluation function to assign probability to each chromosome, the formula is as follows: , ； in, For any chromosome, is a real number, , For population size.

8. The method for optimizing public transportation intelligent dynamic scheduling based on real-time data according to claim 1 is characterized in that: In step S3, a roulette wheel method is used to select and cultivate a new generation of chromosomes, and the steps are as follows: Step 1: Calculate the cumulative probability of each chromosome ,Right now: ； ； In the formula, In addition to chromosomes Any chromosome other than Step 2: Generate a random number ,like , then chromosome is selected, repeat the step times, we get chromosomes.

9. The method for optimizing public transportation intelligent dynamic scheduling based on real-time data according to claim 1 is characterized in that: In step S3, a chromosome is randomly selected Assume that the crossover probability is ,from Randomly generated numbers ,if For the part of the chromosome that belongs to the upward direction, two non-overlapping gene fragments of equal length are randomly selected for exchange. The operation of the chromosome in the downward direction is similar to that to generate a new population.

10. The method for optimizing public transportation intelligent dynamic scheduling based on real-time data according to claim 1 is characterized in that: In step S3, assume that the mutation probability is ,from Randomly generated numbers ,if , for the part of the chromosome that is in the ascending direction, the length will be The gene fragment of is replaced with a newly generated gene fragment of the same length; a randomly generated gene fragment of length The gene fragment is in the interval The interval length is ; They cover The gene fragments are located on the chromosomes at both ends of the gene.

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