Bus departure time optimization method based on particle swarm and plant rhizome optimization

Abstract

The invention discloses a bus departure time optimization method based on a particle swarm and plant rhizome optimization, and the method comprises the steps: building a multi-objective optimization model, and achieving the optimization of the bus departure time by taking the minimization of the operation cost of a bus company and the comprehensive travel cost of passengers as well as the maximization of the net income of an enterprise and the direct passenger flow volume as objectives; in combination with dynamic conditions such as departure interval constraint, load factor limitation and adjacent period smoothness, global fast search is performed by adopting a particle swarm algorithm, and a plant rhizome optimization algorithm is introduced to perform refined iterative solution; initializing a departure interval scheme through a particle swarm algorithm, and generating a potential solution set; based on a rhizome nutrient distribution mechanism, a root growth process is simulated to dynamically adjust a departure strategy, complex constraints are restored, and a multi-target competition relationship is balanced; and finally, outputting a Pareto frontier solution set, and outputting an optimal scheduling scheme. According to the invention, the direct passenger flow of the bus line can be effectively improved, the problems of passenger retention and social vehicle interference in peak periods are relieved, and the efficiency and service level of an urban public transport system are remarkably enhanced.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of transportation, and particularly relates to a bus departure time optimization method based on a particle swarm and plant rhizome optimization. BACKGROUND

[0002] With the acceleration of urbanization and the continuous growth of population density, the urban public transportation system is facing increasingly severe challenges. As the backbone network of urban traffic, bus vehicles bear a large amount of daily travel demand of citizens. However, due to the factors such as the shortage of road resources, the aggravation of traffic congestion, and the uneven distribution of passenger flow in time and space, the traditional bus scheduling mode is difficult to meet the efficient, punctual and low-cost operation target. Especially during the peak period, the delay problem caused by the mixed running of bus vehicles and social vehicles, the decline of passenger experience caused by the imbalance of full load rate, and the high operating cost of enterprises have become the bottleneck restricting the service level of urban public transport.

[0003] Currently, the research on bus scheduling optimization mainly relies on static timetable design and experience-driven departure interval adjustment method. Although this kind of method can alleviate the waste of resources and mismatch between supply and demand to a certain extent, its limitations are significant, and the traditional model is difficult to respond to passenger flow fluctuations in real time (such as holidays, large events or weather influence), leading to excessive congestion of vehicles during peak period and rising of empty running rate during off-peak period. Moreover, the existing methods focus on a single target (such as cost minimization or passenger capacity maximization), and it is difficult to balance the complex trade-off between enterprise income, passenger experience and social benefit. Although the existing heuristic algorithm (such as genetic algorithm) has global search ability, it is easy to fall into local optimum in high-dimensional solution space; and the rule-based method lacks systematic processing of complex constraints (such as full load rate and adjacent period smoothness).

[0004] However, in recent years, the application of intelligent optimization algorithm in the field of transportation provides a new idea for the above problems. The particle swarm optimization algorithm is initially tried to be used for bus departure interval optimization due to its characteristics of few parameters and fast convergence, but its single target orientation and the defect of easy premature limit its practicability. The plant rhizome optimization algorithm simulates the growth mechanism of plant root system, and has the ability of global exploration and local development, which provides a potential solution for multi-objective dynamic scheduling. However, the existing research has not deeply combined the particle swarm optimization algorithm and the plant rhizome optimization algorithm, and lacks constraint modeling and real-time adaptation design for the bus scheduling scene.

[0005] Under this background, how to build a bus departure time optimization method which takes into account dynamic response ability, multi-objective collaborative optimization and complex constraint guarantee, becomes a key breakthrough to improve the efficiency and service quality of urban public transportation system. SUMMARY

[0006] Invention purpose: In view of the dynamic response lag, multi-target cooperation deficiency and local optimization limitation in traditional bus scheduling, the application provides a bus departure time optimization method based on particle swarm and plant rhizome optimization, realizes efficient allocation of bus resources and quality improvement of service in complex scenes, and provides scientific scheduling decision support for intelligent bus system.

[0007] Technical scheme: The bus departure time optimization method based on particle swarm and plant rhizome optimization comprises the following steps:

[0008] (1) Collect bus line basic data;

[0009] (2) Taking the minimization of bus company operation cost, the minimization of passenger comprehensive travel cost, the maximization of enterprise net income and direct passenger flow as targets, combining with the upper and lower limits of departure interval, the safety range of full load rate, the smoothness of adjacent time period and other constraint conditions, a multi-objective optimization model is constructed;

[0010] (3) The collected data is brought into the multi-objective optimization model for solution by using the particle swarm algorithm, an initial particle swarm is constructed by randomly generating a whole-day time interval departure interval scheme, the particle velocity updating strategy is used to dynamically adjust the departure frequency to the global optimal direction for iterative optimization, potential solutions are screened in combination with cost, income and passenger flow indexes, and a constraint repair mechanism is used to calibrate the full load rate and correct the departure frequency of the over-limit shift, while ensuring the operation feasibility of the scheme, the data is repeatedly iterated, and then it is judged whether the continuous iteration convergence stability times C stable reach the preset requirements; when the target function value changes by less than or equal to 0.1% in continuous C stable = 10 iterations, it is considered that there is "no significant change", the optimal solution is judged by weighting, and the optimal departure time is output; if the iteration reaches the maximum iteration number , there is still no significant change, and the plant rhizome optimization algorithm is used for solution;

[0011] (4) The plant rhizome optimization algorithm inherits the optimal solution iterated by the particle swarm algorithm as the main rhizome, simulates the root system expansion by randomly generating lateral rhizome branch schemes in the neighborhood of the main rhizome, combines the fitness to dynamically allocate nutrients to drive the main rhizome to evolve in the direction of high income, and the lateral rhizome executes local fine search, while periodically eliminating inefficient schemes and supplementing new solutions, realizing the coordinated growth balance of global optimization and local fine tuning, repeatedly iterating until there is no significant change after continuous iteration C stable times, the weighted optimal solution is finally judged, and the optimal departure time is output; the maximum iteration number is set to When the preset maximum iteration number is reached, the optimal departure time is forced to be output.

[0012] Further, the bus route basic data in step (1) includes: total bus route mileage L; rated passenger capacity of a single bus Q; total number of route stations Z; key direct station set Z direct ; fixed cost of a single departure C fix ; vehicle unit mileage operation cost C1; all-day operation time period division and length of each period T s ; each period s; passenger arrival rate P of each station z sz ; direct passenger demand d sz ; passenger waiting time cost coefficient C2; passenger boarding efficiency u sz , i.e. passenger boarding speed of station z in period s; bus fare π; minimum profit rate requirement β; maximum number of departures γ in a day.

[0013] Further, the process of constructing the multi-objective optimization model is as follows:

[0014]

[0015]

[0016]

[0017]

[0018]

[0019]

[0020]

[0021] wherein formula (1) represents minimizing the operation cost of the bus company; formula (2) represents minimizing the comprehensive travel cost of passengers; formula (3) maximizes the net income of the bus company; formula (4) represents maximizing the direct passenger flow; formula (5) represents the dynamic equation of the direct passenger boarding amount in the dynamic constraint condition, ensuring that the actual boarding amount does not exceed the passenger demand and the upper limit of the carrying capacity; formula (6) represents the direct demand response rate constraint, ensuring that more passengers choose direct services; formula (7) represents the allocation of direct and non-direct carrying capacity, preferentially ensuring direct passenger flow, reducing transfer demand, and improving the attraction of the route; C1 is the unit mileage cost; L is the total route mileage; T s is the length of each period s; Δt s is the departure interval of the s-th period; C fix is the fixed cost of a single departure; C empty is the new empty driving penalty term; Q is the rated passenger capacity of a bus; P sz is the passenger arrival rate of station z; T s is the length of each period s; (·) +=max(0,·)+;P sz is the passenger arrival rate at station z in time period s; α is the congestion sensitivity coefficient; u sz is the passenger boarding efficiency at station z; X sz is the passenger waiting queue length at the zth station in the sth period; γ is the maximum number of departures throughout the day.

[0022] Furthermore, the implementation process of step (3) is as follows:

[0023] (31) The plant rhizome optimization algorithm inherits the iterative The optimal solution is taken as the main root, and the all-day time-divided departure interval plan is randomly generated to construct the initial particle swarm. The particles are encoded, and each particle represents a set of departure intervals Δt, which are encoded as a vector:

[0024] P i =[Δt1,Δt2,…Δt s ]

[0025] And the dimension is the total number of time periods S; the value range: Δt min ≤Δt s ≤Δt max ;

[0026] (32) Using the particle velocity update strategy, the frequency of train departures is dynamically adjusted to iteratively optimize towards the global optimal direction, and the particle position and velocity are initialized:

[0027] Particle position Pi: The particle position represents the time interval plan for the whole day, that is, the position vector P of particle i i =[Δt1,Δt2,...,Δt s ] is randomly generated within the preset range [Δtmin, Δtmax], representing a full-day departure plan;

[0028] Particle velocity Vi: Particle velocity represents the direction and step size of the interval adjustment, i.e. velocity vector V i =[V1,V2,...,V s ] is randomly initialized within [-Vmax, Vmax], and Vmax = 0.1*(Δtmax-Δtmin) to control the maximum adjustment range of the departure interval in a single iteration. A positive value lengthens the departure interval; a negative value shortens the departure interval.

[0029] (33) Combine cost, revenue and passenger flow indicators to screen potential solutions and use the multi-objective fitness function to solve:

[0030]

[0031] Wherein, w1, w2, w3, w4 are weight coefficients, reflecting the priority of each target, and need to satisfy w1+w2+w3+w4=1; f1 is the operating cost; f2 is the passenger comprehensive cost; f3 is the enterprise net income; f4 is the direct passenger flow; f k,norm is the extreme difference of target f k in the initial particle swarm;

[0032] (34) The constraint repair mechanism is used to calibrate the full load rate and correct the number of departures, update the speed and position, and if the particle exceeds the limit, it is reset to Δt min or Δt max ;

[0033] (35) Iteration C stable times without significant change, that is, when the solution set meets all the constraints and the target is met and converges, the optimal departure time is directly output; if the number of iterations exceeds times, it is still not up to standard, and the plant rhizome optimization algorithm is used for solution optimization.

[0034] Further, the step (4) is implemented as follows:

[0035] (41) Root encoding, each root is encoded as a departure interval vector:

[0036] R j =[Δt1,Δt2,…Δt s ]

[0037] Where Δt s ∈[Δt min ,Δt max ];

[0038] (42) Initialize the population, the main rhizome is the optimization result of the inheritance particle swarm algorithm, and the lateral rhizome is set to (30-100) generated around the main rhizome by Gaussian disturbance:

[0039]

[0040] Where σ is the disturbance standard deviation, controlling the exploration range;

[0041] (43) Multi-objective fitness function solution:

[0042]

[0043] Where f1 is the operating cost; f2 is the passenger comprehensive cost; f3 is the enterprise net income; f4 is the direct passenger flow; f k,norm is the normalized factor of target k; w k is the weight coefficient;

[0044] (44) Nutrient allocation, Nutrient j ∈[0,1] represents the proportion of nutrients obtained by rhizome j, which converts fitness into a probability distribution, the higher the fitness, the more nutrients:

[0045]

[0046] (45) Main rhizome gradient growth, moving in the direction of the largest fitness gradient:

[0047]

[0048] where δ is the growth step, used to control the adjustment amplitude, the main rhizome moves deterministically in the direction of the fitness gradient, used to solve the problem of enterprise operation target; The gradient of the fitness to the departure interval indicates the optimization direction;

[0049] (46) Random disturbance of lateral rhizome, random disturbance according to nutrient proportion, used to solve the problem of passenger arrival rate P sz and direct demand d sz has strong randomness, resulting in non-differentiable oscillation of the objective function, used to cope with the robustness exploration of passenger flow randomness:

[0050]

[0051] (47) Dynamic constraint repair processing:

[0052] If the departure time is out of bounds, reset Δts to Δtmin or Δtmax; constraint the full load rate, if the full load rate is out of limits, adjust the departure interval again:

[0053]

[0054] where η is the safety factor; constraint the revenue, if f3<0, increase the number of departures at the direct station;

[0055] (48) Rhizome branching and elimination mechanism:

[0056] Branching condition: if the rhizome is continuous K=5, but the fitness is not improved, generate B=2 new lateral rhizomes;

[0057] Elimination mechanism: eliminate the 10% rhizomes with the lowest fitness every 10 generations, and supplement new random rhizomes;

[0058] (49) When the fitness is stable, i.e. the fitness value of the main rhizome changes less than the threshold value ε within continuous K generations;

[0059]

[0060] That is, the fitness value of the main rhizome of the tth generation; the nutrient ratio change rate of all rhizomes is less than 0.5%:

[0061]

[0062] That is, the nutrient ratio of the t-th generation rhizome j; that is, the final result is output when the population structure is no longer significantly adjusted; if the above result is not met, the optimal departure time is forced to be output when the preset maximum number of iterations is reached.

[0063] Beneficial effects: Compared with the prior art, the present invention has the following beneficial effects: 1. The present invention breaks through the limitation of traditional single algorithms that are prone to falling into local optimality by integrating the rapid global search of the particle swarm algorithm with the refined iteration of plant rhizome optimization, and significantly improves the global optimality and dynamic adaptability of the bus scheduling scheme; 2. The present invention monitors and dynamically repairs key constraints such as excessive full load rate (stable in the safety range of 50%-120%) and sudden changes in departure intervals between adjacent time periods (difference ≤ 5 minutes) in real time, ensuring that the scheduling scheme meets both operational safety and passenger comfort requirements; 3. The present invention provides diversified scheduling strategies (such as cost priority and passenger flow priority) based on the Pareto front solution set, achieving a 15%-25% reduction in operating costs, a 20%-30% increase in direct passenger flow, and a 25%-40% reduction in peak waiting time, providing urban public transportation systems with an efficient and feasible intelligent decision-making tool. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] Figure 1 Flowchart of the present invention. DETAILED DESCRIPTION

[0065] The present invention will be further described in detail below with reference to the accompanying drawings.

[0066] like Figure 1 As shown, the present invention proposes a bus departure time optimization algorithm based on particle swarm and plant rhizome optimization, which specifically includes the following steps:

[0067] Step 1: Collect bus stop data, including the total mileage of bus routes L; the rated passenger capacity of a single bus Q; the total number of route stops Z; and the set of key direct stops Z. direct ; Fixed cost C for a single trip fix ; Vehicle unit mileage operating cost C1; All-day operating time period division (such as morning peak, off-peak, evening peak) and the duration of each period T s ; Each time period s; Passenger arrival rate P at each station z sz ; Direct passenger demand d sz ; Passenger waiting time cost coefficient C2; Passenger boarding efficiency u szThe passenger pick-up speed of the site z in the time period s; the bus fare π; the minimum profit rate requirement β; the maximum number of departures γ.

[0068] Step 2, in combination with the constraint conditions including the upper and lower limits of the departure interval, the full load rate safety range, and the smoothness of adjacent time periods, a multi-objective optimization model is constructed with the objectives of minimizing the operating cost of the bus company, minimizing the passenger comprehensive travel cost, maximizing the net income of the enterprise, and maximizing the direct passenger flow.

[0069]

[0070]

[0071]

[0072]

[0073]

[0074]

[0075]

[0076] In the formula (1), the operating cost of the bus company is minimized; in the formula (2), the passenger comprehensive travel cost is minimized; in the formula (3), the net income of the bus company is maximized; in the formula (4), the direct passenger flow is maximized; in the formula (5), the dynamic equation of the direct passenger boarding quantity in the dynamic constraint condition is represented, so as to ensure that the actual boarding quantity does not exceed the passenger demand and the upper limit of the carrying capacity; in the formula (6), the direct demand response rate constraint is represented, so as to ensure that more passengers choose the direct service; in the formula (7), the direct and non-direct capacity allocation is represented, so as to preferentially guarantee the direct passenger flow, reduce the transfer demand, and improve the line attraction; C1 is the unit mileage cost; L is the total mileage of the line; T s is the length of each time period s; Δt s is the departure interval of the s-th time period; C fix is the fixed cost of a single departure; C empty is the new empty driving penalty term; Q is the rated passenger capacity of the bus; P sz is the passenger arrival rate of the site z; T s is the length of each time period s; (·) + = max (0, ·) +; P sz is the passenger arrival rate of the site z in the time period s; α is the congestion sensitivity coefficient; u sz is the passenger boarding efficiency of the site z; X sz is the passenger waiting queue length of the s-th time period and the z-th site; γ is the maximum number of departures in a day.

[0077] The line length, station location, vehicle capacity, passenger arrival rate of each station in each period, oil price, driver salary, passenger time cost and other data are substituted into formulas (1) to (4) for calculation. At the same time, in order to ensure the safety of operation and passenger experience, the departure interval is constrained to avoid vehicles being blocked together and passengers waiting for too long:

[0078] Δt min ≤Δt s ≤Δt max

[0079] Secondly, the vehicle full load rate is constrained to ensure that the passenger capacity of each vehicle is between 50% and 120%:

[0080]

[0081] Then, the smoothness of adjacent periods is set to avoid passengers being stranded due to sudden lengthening of the departure interval:

[0082] │Δt s+1 -Δt s │≤λ

[0083] Finally, ensure that the bus company makes a profit, and require that ticket revenue cover at least 110% of the cost.

[0084] π∑y sz ≥(1+β)f1。

[0085] Step 3, use the particle swarm algorithm to bring the collected data into the multi-objective optimization model for solution, generate an initial particle swarm by randomly generating a full-day time period departure interval scheme, dynamically adjust the departure frequency to the global optimal direction by using the particle speed update strategy, and iteratively optimize the scheme. Potential solutions are screened in combination with cost, benefit and passenger flow indicators, and a constraint repair mechanism is used to calibrate the full load rate and correct the number of departures for over-limit trips. While efficiently exploring the solution space, ensure the operational feasibility of the scheme. Repeat the iteration, and then determine whether the number of consecutive iteration convergence and stability C stable reaches the preset requirement; when the target function value changes by less than or equal to 0.1% in 10 consecutive iterations, it is considered to have "no significant change", and the optimal solution is determined by weighted judgment, and the optimal departure time is output; if the iteration reaches the maximum iteration number 200 and still has no significant change, use the plant root optimization algorithm for solution.

[0086] (3.1) The plant root optimization algorithm inherits the optimal solution of 200 iterations of the particle swarm algorithm as the main root, randomly generates a full-day time period departure interval scheme to construct an initial particle swarm, encodes the particles, and each particle represents a set of departure intervals Δt, which is encoded as a vector:

[0087] P i =[Δt1,Δt2,…Δts ]

[0088] And the dimension is the total number of periods S; Value range: Δt min ≤Δt s ≤Δt max .

[0089] (3.2) Dynamic adjustment of departure frequency using particle velocity update strategy to iteratively optimize the global optimal direction, initialize the position and velocity of particles:

[0090] Particle position Pi: Particle position represents the all-day period departure interval scheme, that is, the position vector P of particle i i =[Δt1,Δt2,...,Δt s ] is randomly generated within the preset range [Δtmin, Δtmax], which represents an all-day departure scheme.

[0091] Particle velocity Vi: Particle velocity represents the departure interval adjustment direction and step, that is, the velocity vector V i =[V1,V2,...,V s ] is randomly initialized within [-Vmax, Vmax], and Vmax=0.1*(Δtmax-Δtmin), to control the maximum adjustment amplitude of the departure interval in a single iteration, a positive value means to lengthen the departure interval; a negative value means to shorten the departure interval.

[0092] (3.3) Combined with cost, benefit and passenger flow index to screen potential solutions, use multi-objective fitness function to solve

[0093]

[0094] Where w1, w2, w3, w4 are weight coefficients, reflecting the priority of each target, and need to satisfy w1+w2+w3+w4=1; f1 is the operating cost; f2 is the passenger comprehensive cost; f3 is the enterprise net income; f3 is the direct passenger flow; f k,norm is the extreme difference of target f k in the initial particle swarm.

[0095] (3.4) Adopt constraint repair mechanism to calibrate full load rate and correct departure frequency for out-of-limit trips, update velocity and position, and reset Δt min or Δt max if the particle is out of range.

[0096] (3.5) Continuous iteration for 10 times without significant change.

[0097]

[0098] A diversified initial departure scheme is generated to cover the possible solution space, each particle is represented as a departure scheme, assuming that the whole day is divided into morning peak, flat peak and evening peak three periods. Randomly generate particles, the departure interval of each period is randomly selected within [5, 30] minutes, the speed of each particle is initialized as a random value, in order to prevent the adjustment amplitude being too large, the range is limited to [-5, 5] minutes. Adjust the departure interval according to the historical optimal and global optimal, if the new interval exceeds [5, 30] minutes, reset it to the boundary value, then handle the violation problems such as overload and interval mutation, and perform smoothing repair on the departure interval. If the difference between the intervals of adjacent periods is greater than 5 minutes, then forced adjustment is performed. Finally, repeat the optimization until a satisfactory solution is found, when the global optimal solution does not change significantly for 10 generations, it is directly output, if the iteration reaches 200 times and still cannot find a satisfactory solution, then use the plant root optimization algorithm to solve it.

[0099] Step 4, the plant root optimization algorithm inherits the optimal solution iterated by the particle swarm algorithm as the main root, simulates the expansion of the root system by randomly generating lateral root branch schemes in its neighborhood, combines the dynamic allocation of nutrients to drive the main root to evolve towards high yield direction, and the lateral roots perform local fine search, while periodically eliminating inefficient schemes and supplementing new solutions, achieving a balance between global optimization and local fine tuning. Repeat the iteration until the global optimal solution does not change significantly for C stable times, finally judge the weighted optimal solution and output the optimal departure time; set the maximum iteration number to 600, when the preset maximum iteration number is reached, the optimal departure time is forced to be output.

[0100] (4.1) Root encoding, each root is encoded as a departure interval vector:

[0101] R j =[Δt1,Δt2,…Δt s ]

[0102] Where, Δt s ∈[Δt min ,Δt max ].

[0103] (4.2) Initialize the population, the main root is the optimization result of the particle swarm algorithm, and the lateral roots are generated by Gaussian disturbance around the main root:

[0104]

[0105] Where, σ is the disturbance standard deviation, controlling the exploration range. Generate diversified candidate schemes near the main root to avoid missing potential good schemes, and make small random adjustments to the departure interval of each period of the main root, if the interval after disturbance exceeds the range, then set it to 5 minutes or 30 minutes.

[0106] (4.3)Judge the pros and cons of each rhizome (scheme), calculate four target values, calculate fitness by weighting, normalize, and let high-quality schemes get more optimization resources to promote population evolution. Multi-objective fitness function solution:

[0107]

[0108] Where f1 is the operating cost; f2 is the passenger comprehensive cost; f3 is the enterprise net income; f4 is the direct passenger flow; f k,norm is the normalization factor of target k; w k is the weight coefficient.

[0109] (4.4) Nutrient allocation, Nutrient j ∈[0,1] represents the proportion of nutrients obtained by rhizome j, and the higher the fitness, the more nutrients:

[0110]

[0111] (4.5) Main rhizome gradient growth, moving in the direction of the largest fitness gradient:

[0112]

[0113] Where δ is the growth step, used to control the adjustment amplitude, and the main rhizome moves deterministically in the direction of the fitness gradient, solving the problem of enterprise operation targets; is the gradient of the fitness to the departure interval, indicating the optimization direction. According to the nutrient allocation result, adjust the departure interval of the main rhizome, calculate the sensitivity (gradient) of the fitness to the departure interval, decide the adjustment direction, if the full load rate is out of limit (such as greater than 120%) after adjustment, shorten the interval according to the formula.

[0114] (4.6) Random disturbance of lateral rhizome, random disturbance according to nutrient proportion, used to solve the strong randomness of passenger arrival rate P sz and direct demand d sz , resulting in non-differentiable oscillation of the objective function, used for robust exploration of passenger flow randomness.

[0115]

[0116] Further explore better solutions near high-quality lateral rhizomes, and make small-range perturbations to high-fitness lateral rhizomes. The higher the fitness of the lateral rhizome, the smaller the perturbation amplitude. Eliminate inefficient schemes and supplement new solutions to avoid falling into local optimum.

[0117] (4.7) Dynamic constraint repair processing: if the departure time is out of bounds, reset Δts to Δtmin or Δt max; constraint on full load rate, if full load rate is out of limit, then re-adjust the departure interval:

[0118]

[0119] wherein η is the safety factor; constraint on revenue, if f3 < 0, then increase the number of departures at the direct station.

[0120] (4.8) Branching with rhizome and elimination mechanism: if the rhizome is continuous K = 5, but the fitness is not improved, then generate B = 2 new lateral rhizomes.

[0121] Elimination mechanism: eliminate the 10% rhizomes with the lowest fitness every 10 generations, supplement new random rhizomes, or generate perturbation around the current optimal solution.

[0122] (4.9) When the fitness is stable, i.e., the fitness value of the main rhizome changes less than the threshold value ε within continuous K generations;

[0123]

[0124] i.e., the fitness value of the t-th generation main rhizome. The nutrient proportion change rate of all rhizomes is less than 0.5%:

[0125]

[0126] i.e., the nutrient proportion of the t-th generation rhizome j. i.e., when the population structure is no longer significantly adjusted, output the final result; if the above result is not met, when the maximum number of iterations is reached, forcibly output the optimal departure time.

[0127] The collected data is input, the particle swarm optimization and plant rhizome optimization algorithm are fused, a multi-objective dynamic scheduling model is constructed, a Pareto frontier solution set is generated, and comprehensive verification is completed based on core indicators such as operating cost, passenger flow, full load rate and waiting time, and the result is directly output when there is no significant change for 10 consecutive generations.

[0128] Taking the bus station of Xinyi People's Hospital in Xinyi City as an example. Select the bus line of Xinyi People's Hospital in Xinyi City, cover 23 stations, and number the 23 stations; count the passenger arrival rate and direct passenger demand, as shown in Tables 1 and 2. The rated passenger capacity of the vehicle is 50 people per vehicle, the maximum number of departures is 100 times per day, and the ticket price is 3 yuan per person. Time period division is carried out, the morning peak is 7:00-9:00, i.e. T1 is 120 minutes; the flat peak is 9:00-17:00, i.e. T2 is 480 minutes; the evening peak is 17:00-19:00, i.e. T3 is 120 minutes.

[0129] Table 1 Passenger arrival rate

[0130]

[0131] Table 2 Direct passenger demand

[0132]

[0133] Objective function is constructed with the goal of minimizing cost, minimizing resource consumption, maximizing efficiency, and maximizing service quality.

[0134]

[0135]

[0136]

[0137]

[0138] The initial population is set to 100 particles, and Δts ∈ [2, 24] hours (satisfying Δts / 2 ≤ τmax = 12) are randomly generated. In the first 200 iterations, the cost is reduced by 57%, and the service quality is improved by 29%, but the change rate does not reach 0.1% for 10 consecutive times, and the particle swarm algorithm does not converge. The plant rhizome optimization algorithm is started to continue optimization.

[0139] The stage optimal solution of the particle swarm algorithm (f1 = 65.4, f4 = 93.6%) is inherited, and the population is expanded to 100 rhizome individuals. The final iteration is 250-270 times, and the change rate of the objective function for 10 consecutive times is Δf1 = 0.03% and Δf4 = 0.05%, both of which are less than the threshold value of 0.1%, meeting the termination condition. Finally, the results are directly output, as shown in Tables 3 and 4.

[0140] Table 3 Particle swarm algorithm iteration solution

[0141]

[0142] Table 4 Final results of iteration output

[0143]

[0144]

[0145] Table 5 Optimized sites

[0146]

[0147]

[0148] As shown in Table 5, the interval between all stations after optimization is shortened by 20%. Under the premise of strictly meeting the time window and resource constraints, the service quality and operational efficiency are significantly improved, while the cost is reasonably controlled.

[0149] The above embodiments are only for illustrating the technical concept and characteristics of the present application, and the purpose is to enable those skilled in the art to understand the content of the present application and implement it, and cannot limit the protection scope of the present application. Any equivalent transformation or modification made according to the spirit and principle of the present application shall be covered within the protection scope of the present application.

Claims

1. A bus departure time optimization method based on particle swarm and plant rhizome optimization, characterized in that: The following steps are involved: (1) Collect basic data of bus routes; (2) With the goal of minimizing the bus company's operating costs, minimizing the comprehensive travel costs of passengers, maximizing the company's net profit and direct passenger flow, and combining constraints such as the upper and lower limits of departure intervals, the safety range of full load factors, and the smoothness of adjacent time periods, a multi-objective optimization model is constructed; (3) The collected data is introduced into the multi-objective optimization model for solution using the particle swarm algorithm. The initial particle swarm is constructed by randomly generating the departure interval plan for the whole day and time period. The departure frequency is dynamically adjusted by using the particle speed update strategy to iteratively optimize towards the global optimal direction. The potential solution is selected by combining the cost, benefit and passenger flow indicators. At the same time, the constraint repair mechanism is used to calibrate the full load rate and the departure frequency of the over-limited flights. While efficiently exploring the solution space, the operational feasibility of the solution is ensured. The data is repeatedly iterated, and the number of continuous iterations C that converges to stability is determined. stable Whether the preset requirements are met; When the objective function value is in continuous C stable In the iterations, if the change is less than or equal to 0.1%, it is considered "no significant change", and the optimal solution is determined by weighting, and the optimal departure time is output; if the iteration reaches the maximum number of iterations If there is still no significant change, the plant root optimization algorithm is used to solve the problem; (4) The plant rhizome optimization algorithm inherits the optimal solution iterated by the particle swarm algorithm as the main rhizome, simulates the root system expansion by randomly generating lateral rhizome branching schemes in its neighborhood, and dynamically allocates nutrients based on fitness to drive the main rhizome to evolve in the direction of high benefits, and performs local refined search on the lateral rhizome. At the same time, it periodically eliminates inefficient schemes and supplements new solutions to achieve a coordinated growth balance between global optimization and local fine-tuning, and iterates repeatedly until the continuous iteration C stable If there is no significant change after the calculation, the optimal solution after weighting is finally determined and the optimal departure time is output; Set the maximum number of iterations to When the preset maximum number of iterations is reached, the optimal departure time is forced to be output.

2. The bus departure time optimization method based on particle swarm and plant rhizome optimization according to claim 1 is characterized in that: The basic data of bus routes in step (1) include: total mileage of bus routes L; rated passenger capacity of a single bus Q; total number of bus stops Z; set of key direct stops Z direct ; Fixed cost C for a single trip fix ; Vehicle unit mileage operating cost C1; All-day operating time period division and the duration of each time period T s ; Each time period s; Passenger arrival rate P at each station z sz ; Direct passenger demand d sz ; Passenger waiting time cost coefficient C2; Passenger boarding efficiency u sz , that is, the passenger boarding speed at station z in time period s; bus fare π; minimum profit margin requirement β; maximum number of departures throughout the day γ.

3. The bus departure time optimization method based on particle swarm and plant rhizome optimization according to claim 1 is characterized in that: The implementation process of constructing the multi-objective optimization model is as follows: Among them, formula (1) represents minimizing the operating cost of the bus company; formula (2) represents minimizing the comprehensive travel cost of passengers; formula (3) maximizes the net profit of the bus company; formula (4) represents maximizing the direct passenger flow; formula (5) represents the dynamic equation of direct passenger volume in the dynamic constraint condition, ensuring that the actual passenger volume does not exceed the passenger demand and the upper limit of capacity; formula (6) represents the direct demand response rate constraint, ensuring that more passengers choose direct services; formula (7) represents the allocation of direct and indirect capacity, giving priority to direct passenger flow, reducing transfer demand, and improving the attractiveness of the route; C1 is the unit mileage cost; L is the total mileage of the route; T s is the duration of each time period s; Δt s is the departure interval of the sth period; C fix is the fixed cost of a single trip; C empty is a new idle driving penalty item; Q is the rated passenger capacity of the bus; P sz is the passenger arrival rate at station z; T s is the duration of each time period s; (·) + =max(0,·)+;P sz is the passenger arrival rate at station z in time period s; α is the congestion sensitivity coefficient; u sz is the passenger boarding efficiency at station z; X sz is the passenger waiting queue length at the zth station in the sth period; γ is the maximum number of departures throughout the day.

4. The method for optimizing bus departure time based on particle swarm and plant rhizome optimization according to claim 1, characterized in that: The implementation process of step (3) is as follows: (31) The plant rhizome optimization algorithm inherits the iterative The optimal solution is taken as the main root, and the all-day time-divided departure interval plan is randomly generated to construct the initial particle swarm. The particles are encoded, and each particle represents a set of departure intervals Δt, which are encoded as a vector: P i =[Δt1,Δt2,…Δt s ] And the dimension is the total number of time periods S; the value range: Δt min ≤Δt s ≤Δt max ; (32) Using the particle velocity update strategy, the frequency of train departures is dynamically adjusted to iteratively optimize towards the global optimal direction, and the position and velocity of the particles are initialized: Particle position Pi: The particle position represents the time interval plan for the whole day, that is, the position vector P of particle i i =[Δt1,Δt2,...,Δt s ] is randomly generated within the preset range [Δtmin, Δtmax], representing a full-day departure plan; Particle velocity Vi: Particle velocity represents the direction and step size of the interval adjustment, that is, the velocity vector V i =[V1,V2,...,V s ] is randomly initialized within [-Vmax, Vmax], and Vmax = 0.1*(Δtmax-Δtmin) to control the maximum adjustment range of the departure interval in a single iteration. A positive value lengthens the departure interval; a negative value shortens the departure interval. (33) Combine cost, revenue and passenger flow indicators to screen potential solutions and use the multi-objective fitness function to solve: Among them, w1, w2, w3, and w4 are weight coefficients, reflecting the priority of each target, which must satisfy w1+w2+w3+w4=1; f1 is the operating cost; f2 is the comprehensive passenger cost; f3 is the net profit of the enterprise; f4 is the direct passenger flow; f k,norm is the target f in the initial particle swarm k The extremes; (34) A constraint repair mechanism is used to calibrate the full load rate and the number of departures for overloaded shifts, update the speed and position, and reset to Δt if the particle crosses the boundary. min or Δt max ; (35) Continuous iteration C stable There is no significant change, that is, when the solution set satisfies all constraints, the target is reached and converges, the optimal departure time is directly output; if the number of iterations exceeds If the result is still not up to standard, the plant rhizome optimization algorithm is used to solve the problem.

5. The bus departure time optimization method based on particle swarm and plant rhizome optimization according to claim 1 is characterized in that: The implementation process of step (4) is as follows: (41) Encode the rhizome and encode each rhizome into a departure interval vector: R j =[Δt1,Δt2,…Δt s ] Where Δt s ∈[Δt min ,Δt max ]; (42) Initialize the population. The main rhizome inherits the optimization results of the particle swarm algorithm. The lateral rhizomes are set to (30-100) and are generated around the main rhizome through Gaussian perturbation: Among them, σ is the standard deviation of the disturbance, which controls the exploration range; (43) Solving multi-objective fitness function: Among them, f1 is the operating cost; f2 is the comprehensive cost of passengers; f3 is the net profit of the enterprise; f4 is the direct passenger flow; f k,norm is the normalization factor of target k; w k is the weight coefficient; (44) Nutrient distribution, Nutrient j ∈[0,1] represents the proportion of nutrients obtained by rhizome j, and the fitness is converted into a probability distribution. The higher the fitness, the more nutrients: (45) The main root grows in a gradient, moving toward the direction with the largest fitness gradient: Among them, δ is the growth step size, which is used to control the adjustment amplitude. The main root moves deterministically along the fitness gradient direction to solve the problem of enterprise operation goals; is the gradient of fitness versus departure interval, indicating the optimization direction; (46) Random perturbation of lateral rhizomes, random perturbation according to nutrient ratio, is used to solve the passenger arrival rate P sz and direct demand d sz The strong randomness leads to the problem of non-differentiable oscillation in the objective function, which is used to explore the robustness of passenger flow randomness: (47) Dynamic constraint repair processing: If the departure time exceeds the limit, Δts will be reset to Δtmin or Δtmax; the full load rate is constrained. If the full load rate exceeds the limit, the departure interval will be readjusted: Where η is the safety factor; constrain the revenue. If f3<0, increase the number of direct-to-station departures. (48) Root-stem branching and elimination mechanism: Branching condition: If the rhizome has K = 5 consecutive generations but the fitness has not improved, then B = 2 new lateral rhizomes will be generated; Elimination mechanism: every 10 generations, the 10% rhizomes with the lowest fitness are eliminated and new random rhizomes are added; (49) When the fitness is stable, that is, the fitness value of the main root stem changes less than the threshold ε in consecutive K generations; That is, the fitness value of the main rhizome of the tth generation; the nutrient ratio change rate of all rhizomes is less than 0.5%: That is, the nutrient ratio of the t-th generation rhizome j; that is, the final result is output when the population structure is no longer significantly adjusted; if the above result is not met, the optimal departure time is forced to be output when the preset maximum number of iterations is reached.

6. The method for optimizing bus departure time based on particle swarm and plant rhizome optimization according to claim 1, characterized in that: The C stable is 10.

7. The method for optimizing bus departure time based on particle swarm and plant rhizome optimization according to claim 1, characterized in that: described is 200.

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