Subway timetable optimization method based on dual archiving and multi-strategy adaptive differential evolution

Abstract

The invention relates to a metro timetable optimization method based on dual archiving and multi-strategy adaptive differential evolution, which comprises the following steps: an input layer models metro lines, interval lengths, stations and passenger flow input into an ordered metro timetable optimization model, and sets constraint conditions and objective functions; the input layer converts the subway timetable optimization model into a QUBO form, and generates a structured QUBO file; the optimization layer optimizes a structured QUBO file through generation of a candidate timetable, a hierarchical archiving mechanism, crossover operation, selection and update and a population scale adaptive strategy; and the output layer generates a global optimal timetable, generates a performance report and graphically displays a running diagram, an interval diagram and an energy consumption curve. Based on an advanced differential evolution optimization framework, a hierarchical memory structure and a parameter adaptive strategy are combined, and a traditional timetable generation process is systematically improved, so that high-precision and fast-convergence running chart optimization meeting multiple constraint conditions is realized.

Description

Technical Field

[0001] This invention belongs to the field of urban rail transit operation organization and intelligent scheduling technology, and specifically relates to a subway timetable optimization method based on dual archiving and multi-strategy adaptive differential evolution. Background Technology

[0002] As a crucial component of modern urban public transportation systems, the efficiency and safety of subway operations directly impact urban travel quality and traffic capacity. In the design and operation of subway lines, train timetable optimization is a core aspect of system scheduling. Timetable design requires achieving coordinated and optimal train arrangement across multiple constraints, including section travel time, stopping time, safety intervals, intersection restrictions, and passenger demand. Traditional subway timetable design often relies on manual experience or fixed heuristic algorithms for adjustments, making it difficult to address the global optimization needs under large-scale, complex constraints.

[0003] With the expansion of urban rail transit networks and dramatic changes in passenger flow, timetable development must simultaneously meet the following objectives:

[0004] Safety constraints: Ensure that the time interval between any two trains is not less than the minimum safe interval;

[0005] Operational efficiency: Minimize passenger waiting and transfer times and improve train utilization;

[0006] Minimize energy consumption: Reduce traction energy consumption by rationally controlling the running time and acceleration / deceleration phases within the interval;

[0007] Robustness: Maintains a viable operating state even in the presence of disturbances (such as delays or equipment fluctuations).

[0008] The complexity of this multi-objective and multi-constraint problem makes the Timetable Optimization Problem (TTOP) theoretically an NP-hard problem.

[0009] It is difficult to obtain the globally optimal solution within an acceptable time using either exhaustive search or traditional programming methods. Summary of the Invention

[0010] This invention provides a method and system for optimizing subway timetables based on dual archiving and multi-strategy adaptive differential evolution, aiming to solve at least one of the technical problems existing in the prior art.

[0011] The technical solution of this invention relates to a subway timetable optimization method based on dual archiving and multi-strategy adaptive differential evolution. This method is applied to a subway timetable optimization system based on dual archiving and multi-strategy adaptive differential evolution. The system comprises an input layer, an optimization layer, and an output layer connected sequentially. The optimization method includes the following steps:

[0012] S100. The input layer models the subway line, section length, station and passenger flow input into an ordered subway timetable optimization model, and sets constraints and objective function F.

[0013] S200, The input layer converts the subway timetable optimization model into QUBO (Quadratic Unconstrained Binary Optimization) form, generating a structured QUBO file;

[0014] S300, The optimization layer optimizes the structured QUBO file by generating candidate timetables, hierarchical archiving mechanism, crossover operation, selection and update and population size adaptive strategy;

[0015] S400, the output layer generates a globally optimal timetable, generates a performance report, and graphically displays the running graph, interval graph, and energy consumption curve.

[0016] Furthermore, in step S100, the subway timetable optimization model includes the following variables:

[0017] Let the set of stations along the line be S = {s1,s2,...,s...} n The set of trains T = {T1,T2,...,T} m}, each train T i At each site j The departure time is t dep i,j Arrival time is t arr i,j .

[0018] Furthermore, in step S100,

[0019] The constraints include safety interval constraints, running time constraints, passenger flow matching constraints, and platform capacity constraints.

[0020] The safety interval constraint is used to prevent train collisions and section congestion. The interval between any two trains in the same section must meet the following requirements:

[0021] ,

[0022] Where, t dep i,j For departure time, The minimum interval time;

[0023] The runtime constraint requires that the runtime for each interval be within a reasonable range.

[0024] ,

[0025] Where, t arr i,j For the arrival time, The minimum running time in the interval. This represents the maximum running time within the interval.

[0026] Furthermore, the passenger flow matching constraint is used to adjust the train departure frequency at different times, so that the departure frequency matches the peak passenger flow distribution, thus ensuring a balance between transportation supply and demand.

[0027] To avoid scheduling conflicts, the platform capacity constraint stipulates that only one train is allowed to stop at any station at a time.

[0028] Furthermore, in step S100,

[0029] The objective function is:

[0030] ,

[0031] Where F is the objective function, C delay For average train delay, C conflict As a penalty for starting the car conflict, C energy For energy consumption costs, C deviation To avoid deviations from the planned timetable, , , and These are the weighting coefficients used to balance multi-objective optimization.

[0032] Furthermore, in step S200, the QUBO (Quadratic Unconstrained Binary Optimization) form is as follows:

[0033] E(x) = x T Qx + c,

[0034] Where E(x) represents the energy function, x is a binary decision variable indicating whether the train departs at each time, and Q is a symmetric penalty matrix, where each element Q is a binary variable representing the train's departure time.ij The energy coupling strength between corresponding variables is determined by the combined coding constraints and target weights, where c is a constant term.

[0035] Furthermore, step S300 includes:

[0036] The optimization layer is initialized by randomly generating NP candidate timetable schemes to construct an initial population. Each individual in the initial population is encoded as a set of train timetable sequences.

[0037] Based on a two-layer evolutionary strategy of shallow diversity preservation and deep strong convergence, a multi-layer archive structure A1, A2, ..., A is adopted in the hierarchical archiving mechanism. k Individuals in the initial population are stored hierarchically according to fitness and evolutionary depth.

[0038] For each individual X in the population i Perform differential mutation (Mutation) operations on samples selected from different layers:

[0039] ,

[0040] Where g is the iteration algebra, F is the scaling factor, F is used to control the perturbation amplitude, and r1, r2, r3 take values ​​[1, NP], which are different from each other and different from i.

[0041] Furthermore, step S300 also includes:

[0042] Perform a crossover operation, randomly selecting a subset of dimensions from V based on the crossover rate Cr. i Replace the original individuals in the population to generate the test vector U. i The crossover rate Cr is dynamically adjusted and adaptively updated using a normal distribution.

[0043] Cr g+1 = 0.9 · Cr g +0.1 · N(µ Cr ,σ 2 ),

[0044] Perform selection and update operations, Cr g Let Cr represent the crossover rate used in the g-th generation population. g+1 This represents the crossover probability used for the next generation, i.e., the (g+1)th generation, after being updated through an adaptive mechanism, N(µ). Cr ,σ 2 ) represents the normal distribution function, µ Cr It is the mean memory term of the crossover rate, σ 2 It is variance;

[0045] Compare the objective function values; if the experimental individuals U produced by the mutation crossover... i The score was higher than that of the original individual X. i Better, i.e., f(U) i )< f(X i ), where f(·) represents the fitness function or objective function value,

[0046] Then the experimental individuals U generated by the mutation crossover i Replace the original individual X i Update the multi-layered archive structure to maintain distribution balance;

[0047] The population size is adaptive, and the NP is dynamically reduced according to the convergence rate to reduce redundant computation and improve search efficiency.

[0048] When the number of iterations reaches the preset upper limit or the energy function converges, the globally optimal timetable scheme is output.

[0049] Furthermore, a subway timetable optimization system based on dual archiving and multi-strategy adaptive differential evolution is provided to implement the aforementioned subway timetable optimization method based on dual archiving and multi-strategy adaptive differential evolution. The subway timetable optimization system based on dual archiving and multi-strategy adaptive differential evolution includes:

[0050] The input layer is used to parse the input data of lines, sections, stations and passenger flow, and generate a structured pickle / json format QUBO file;

[0051] An optimization layer optimizes the structured QUBO file by generating candidate timetables, hierarchical archiving mechanisms, crossover operations, selection and update, and population size adaptive strategies.

[0052] The output layer generates a globally optimal timetable, a performance report, and graphical displays of the running graph, interval graph, and energy consumption curve.

[0053] Furthermore, the present invention also proposes a computer-readable storage medium storing program instructions thereon, which, when executed by a processor, implement the aforementioned subway timetable optimization method based on dual archiving and multi-strategy adaptive differential evolution.

[0054] Compared with existing technologies, the present invention has the following characteristics:

[0055] The proposed subway timetable optimization method based on dual archiving and multi-strategy adaptive differential evolution is based on an advanced differential evolution optimization framework. It combines a hierarchical memory structure and parameter adaptive strategy to systematically improve the traditional timetable generation process, thereby achieving high-precision, fast-convergence, and multi-constraint-compliant timetable optimization. Attached Figure Description

[0056] Figure 1 This is a flowchart of a subway timetable optimization method based on dual archiving and multi-strategy adaptive differential evolution.

[0057] Figure 2 The Mermaid architecture diagram is shown for a subway timetable optimization method based on dual archiving and multi-strategy adaptive differential evolution.

[0058] Figure 3 The Mermaid flowchart illustrates the metro timetable optimization method based on dual archiving and multi-strategy adaptive differential evolution. Detailed Implementation

[0059] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0060] The following will provide a clear and complete description of the concept, specific structure, and technical effects of the present invention in conjunction with the embodiments and accompanying drawings, so as to fully understand the purpose, solution, and effects of the present invention.

[0061] It should be noted that, unless otherwise specified, when a feature is referred to as "fixed" or "connected" to another feature, it can be directly fixed or connected to the other feature, or indirectly fixed or connected to the other feature. The singular forms "a," "described," and "the" used herein are also intended to include the plural forms, unless the context clearly indicates otherwise. Furthermore, unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art. The terminology used in this specification is for the purpose of describing particular embodiments only and not for limiting the invention. The term "and / or" as used herein includes any combination of one or more of the associated listed items.

[0062] It should be understood that although the terms first, second, third, etc., may be used in this disclosure to describe various elements, these elements should not be limited to these terms. These terms are only used to distinguish elements of the same type from each other. For example, a first element may also be referred to as a second element without departing from the scope of this disclosure, and similarly, a second element may also be referred to as a first element. Any and all instances or exemplary language (“e.g.,” “such as,” etc.) used herein are intended only to better illustrate embodiments of the invention and, unless otherwise required, do not impose a limitation on the scope of the invention. Furthermore, the industry term “pose” as used herein refers to the position and orientation of an element relative to a spatial coordinate system.

[0063] Reference Figure 1 and Figure 3 This invention provides a subway timetable optimization method and system based on dual archiving and multi-strategy adaptive differential evolution. The subway timetable optimization method based on dual archiving and multi-strategy adaptive differential evolution is applied to a subway timetable optimization system based on dual archiving and multi-strategy adaptive differential evolution. The subway timetable optimization system based on dual archiving and multi-strategy adaptive differential evolution includes an input layer, an optimization layer, and an output layer connected sequentially. The subway timetable optimization method based on dual archiving and multi-strategy adaptive differential evolution includes the following steps:

[0064] S100. The input layer models the subway line, section length, station and passenger flow input into an ordered subway timetable optimization model, and sets constraints and objective function F.

[0065] S200, The input layer converts the subway timetable optimization model into QUBO (Quadratic Unconstrained Binary Optimization) form, generating a structured QUBO file;

[0066] S300, The optimization layer optimizes the structured QUBO file by generating candidate timetables, hierarchical archiving mechanism, crossover operation, selection and update and population size adaptive strategy;

[0067] S400, the output layer generates a globally optimal timetable, generates a performance report, and graphically displays the running graph, interval graph, and energy consumption curve.

[0068] Compared with existing technologies, the present invention has the following characteristics:

[0069] The proposed subway timetable optimization method based on dual archiving and multi-strategy adaptive differential evolution is based on an advanced differential evolution optimization framework. It combines a hierarchical memory structure and parameter adaptive strategy to systematically improve the traditional timetable generation process, thereby achieving high-precision, fast-convergence, and multi-constraint-compliant timetable optimization.

[0070] This invention employs an intelligent subway timetable optimization method based on hierarchical archive differential evolution. This method transforms the timetable scheduling problem into a global optimization problem by establishing a QUBO (Quadratic Unconstrained Binary Optimization) model, and then uses a hierarchical archive differential evolution algorithm to solve it, achieving coordinated optimization of train departure times, interval travel times, arrival times, and train intervals. This method, while considering both line safety constraints and passenger demand, can achieve multi-objective global optimization, including: minimizing train conflicts and delays; minimizing energy consumption and train idling; maximizing line capacity; and ensuring the feasibility and robustness of the timetable.

[0071] Specifically, the present invention has the following characteristics:

[0072] (1) Improve optimization accuracy and global convergence: By introducing a multi-level individual storage and historical solution reuse mechanism, the global search capability is enhanced, premature convergence is avoided, and high-precision global optimization of the timing relationship between trains is achieved.

[0073] (2) Strengthen constraint modeling and feasibility correction mechanism: Establish a multi-layer constraint model covering train interval, turnaround coordination, section conflict and energy consumption balance, and design constraint repair operators to automatically adjust candidate schemes that do not meet the constraints, so that the optimization results can be executed in both mathematical and engineering sense.

[0074] (3) Construct a scalable multi-section optimization framework: Through modular modeling and multi-threaded computing structure, multiple sections and multiple train sets can be optimized simultaneously, thereby improving the solution speed and applicability of the algorithm in large-scale subway networks.

[0075] (4) Real-time optimization and dynamic update: The method of the present invention supports rapid response to operational disturbances, sudden delays and section blockades, and can regenerate feasible operation diagrams that meet constraints in a short time, thereby improving the emergency response and real-time adjustment capabilities of the scheduling system.

[0076] The terms involved in this invention are explained as follows:

[0077] • QUBO (Quadratic Unconstrained Binary Optimization) refers to a quadratic unconstrained binary optimization model. In this experiment, the subway scheduling problem is discretized and mapped into QUBO form, which is generated by the file_QUBO() function and saved as a .pkl or .json file.

[0078] • The Ising Model is an equivalent form of QUBO, used for solving quantum annealing and classical simulated annealing problems. It is obtained through the conversion using utilities.qubo_to_ising().

[0079] • The LP benchmark file (LP Output / ground state) uses the optimal benchmark solution obtained by the linear programming solver (CPLEX). The file is named LP_solutions / ....json and is used to compare with HA-DE and SA results.

[0080] • HADE (Hierarchical Archive-based Differential Evolution): This research proposes an improved differential evolution algorithm that enhances global search performance through "hierarchical archiving + dynamic parameter adaptation + multi-level sampling". Execution entry point: solve_qubo_hardde(q_pars, qubo_file, out_json).

[0081] • ppair / psum are hyperparameters used in experiments to control the pairing probability between individuals and the size of the parameter summation, respectively defining the search strength and the global perturbation amplitude.

[0082] • dmax represents the maximum allowable delay time for subway train operation. It is a key constraint in timetable optimization and is also written into a file name (e.g., ..._dmax6_....json).

[0083] • Hist (Histogram File) stores feasible and infeasible energy distributions, experimental analysis data through time statistics, etc., and usually has the suffix .pkl or .json, generated by analyze_qubo_Dwave().

[0084] • Energy Histogram / Objective Histogram: The energy or objective function distribution plots output by the experiment are used to demonstrate the search characteristics and convergence trend of the algorithm.

[0085] • Passing Time Histogram: A histogram showing the distribution of train passage times between two stations, generated by _plot_hardde_passing_times_pdf(), with a filename such as ..._HADE_A_B.pdf.

[0086] • Feasible / not feasible energies represent the sets of energy samples that satisfy all scheduling constraints and the sets of samples that do not satisfy the constraints, respectively. The former reflects the distribution of effective solutions, while the latter is used for feasibility analysis.

[0087] • The ground state offset (q_offset / q_offset) records the baseline offset of the QUBO energy, used for energy alignment. During plotting, the histogram is shifted using the offset to make it reference zero.

[0088] The train timetable optimization problem is complex due to its multi-objective and multi-constraint nature, making the Metro Timetable Optimization Problem (TTOP) theoretically an NP-hard problem. Exhaustive search or traditional planning methods are unlikely to yield a globally optimal solution within an acceptable timeframe.

[0089] Optimizing subway train timetables is a core technical issue in the planning and scheduling of urban rail transit systems. The degree of optimization directly affects train operating efficiency, line capacity utilization, and passenger travel experience. Traditional subway scheduling schemes mostly adopt static optimization methods based on rules or heuristic algorithms, which are difficult to consider multiple dimensions such as train intervals, passenger flow, line constraints, and energy consumption.

[0090] The main drawbacks of existing technologies are as follows:

[0091] (1) The timetable optimization accuracy is insufficient, making it difficult to balance safety and efficiency. Most existing subway timetable optimization methods use heuristic or mixed integer programming to solve the problem. Heuristic algorithms (such as genetic algorithms and particle swarm optimization) have certain search capabilities, but they are prone to getting trapped in local optima under complex constraints. While mathematical programming methods can theoretically find the global optimum, the computation time increases sharply when the number of operating sections, train sets, and constraints increases, making it impossible to meet the needs of real-time scheduling. Therefore, existing methods are unable to obtain a high-precision, feasible optimization solution that balances operational efficiency and safety constraints within a limited time.

[0092] (2) Insufficient constraint modeling and lack of characterization of actual operating scenarios. Traditional models mostly only consider basic constraints such as minimum train departure interval, running time, and turnaround time. However, in scenarios such as multi-line intersections, co-operation, section conflicts, and transfer coordination, they often fail to establish complete logical constraint relationships. The lack of constraints leads to frequent conflicts, delay propagation, or transfer failures in the generated timetables during the simulation stage, resulting in a lack of engineering feasibility.

[0093] (3) Fixed parameter settings result in insufficient algorithm adaptability. Existing intelligent optimization algorithms mostly use fixed control parameters, such as difference factors, crossover probabilities, and population size. In the subway scheduling problem, due to the complexity of the objective function and the dynamic changes in constraints, different search stages require different exploration intensity and local convergence speed from the algorithm. Fixed parameter configuration often leads to low search efficiency in the early stages and easy trapping in local optima in the later stages, affecting the stability of the final solution.

[0094] (4) Lack of utilization of historical information and cross-interval collaborative optimization mechanism. Existing algorithms only utilize the individual information of the current generation in each run, ignoring the high-quality solutions generated during the historical evolution process. In the subway scheduling problem, the inter-station structure and train operation patterns have strong similarities. If historical optimization results can be reused, the search efficiency and global stability can be greatly improved. However, existing technologies lack mechanisms for storing, hierarchically utilizing, and transferring historical solutions, resulting in repetitive calculations and low efficiency in the optimization process.

[0095] (5) Insufficient real-time performance, making it difficult to cope with dynamic operational adjustments. During peak hours or in the event of emergencies (such as delays or turnarounds), the existing optimization system takes tens of minutes or even hours to generate a new timetable, which cannot meet the actual needs of the subway dispatching system for "minute-level adjustments". High computational complexity and lack of dynamic scalability are key issues restricting real-time optimization capabilities.

[0096] The advantages and effects of this invention are as follows:

[0097] (1) Compared with traditional continuous space evolution algorithms such as L-SHADE and JADE, this invention significantly improves global search capability through hierarchical archives and adaptive control.

[0098] (2) This invention transforms the multi-constraint subway time optimization problem into a QUBO energy model, which can be run directly on a quantum annealer or a parallel classical computer and is compatible with multiple platforms for solving.

[0099] (3) The model can achieve coordinated optimization of train safety interval, passenger flow peak matching and energy consumption trade-off. The resulting timetable is significantly better than the existing scheduling algorithm in terms of delay rate, energy consumption and conflict rate.

[0100] (4) The algorithm has a high degree of modularity and strong computational stability, and supports automatic adaptation to different line lengths and departure densities, which significantly improves the intelligence and engineering feasibility of subway scheduling design.

[0101] Furthermore, in step S100, the subway timetable optimization model includes the following variables:

[0102] Let the set of stations along the line be S = {s1,s2,...,s...} n The set of trains T = {T1,T2,...,T} m}, each train T i At each site j The departure time is t dep i,j Arrival time is t arr i,j .

[0103] Furthermore, in step S100,

[0104] The constraints include safety interval constraints, running time constraints, passenger flow matching constraints, and platform capacity constraints.

[0105] The safety interval constraint is used to prevent train collisions and section congestion. The interval between any two trains in the same section must meet the following requirements:

[0106] ,

[0107] Where, t dep i,j For departure time, The minimum interval time;

[0108] The runtime constraint requires that the runtime for each interval be within a reasonable range.

[0109] ,

[0110] Where, t arr i,j For the arrival time, The minimum running time in the interval. This represents the maximum running time within the interval.

[0111] Furthermore, the passenger flow matching constraint is used to adjust the train departure frequency at different times, so that the departure frequency matches the peak passenger flow distribution, thus ensuring a balance between transportation supply and demand.

[0112] To avoid scheduling conflicts, the platform capacity constraint stipulates that only one train is allowed to stop at any station at a time.

[0113] Furthermore, in step S100,

[0114] The objective function is:

[0115] ,

[0116] Where F is the objective function, C delay For average train delay, C conflict As a penalty for starting the car conflict, C energy For energy consumption costs, C deviation To avoid deviations from the planned timetable, , , and These are the weighting coefficients used to balance multi-objective optimization.

[0117] Specifically, the parameters mentioned above are not based on universally accepted formulas; their values ​​are defined according to the specific optimization direction. The core principle is to optimize the objective based on weights and parameters. Different objective functions will affect the subsequent search process, and optimization is performed based on the input parameters and weights.

[0118] Furthermore, in step S200, the QUBO (Quadratic Unconstrained Binary Optimization) form is as follows:

[0119] E(x) = x T Qx + c,

[0120] Where E(x) represents the energy function, x is a binary decision variable indicating whether the train departs at each time, and Q is a symmetric penalty matrix, where each element Q of the penalty matrix Q is a binary variable representing whether the train departs at each time. ij The energy coupling strength between corresponding variables is determined by the combined coding constraints and target weights, where c is a constant term.

[0121] Regarding E(x), in the QUBO (Quadratic Unconstrained Binary Optimization) model, E(x) represents the energy function. It transforms the originally complex "constrained optimization problem" into a problem of "finding the minimum energy point." Physically, it originates from the Ising model in statistical physics. In optimization problems, it should be understood as a comprehensive cost score. The lower the value of E(x), the better the timetable scheme.

[0122] Specifically, the input layer includes a QUBO building module. The system first parses the route, section, station, and passenger flow input data to generate a structured QUBO file (pickle / json format). Each element Q of the matrix Q... ijThe energy coupling strength between corresponding variables. Large-scale QUBO matrices employ a sparse storage structure to improve computational efficiency.

[0123] Furthermore, step S300 includes:

[0124] The optimization layer is initialized by randomly generating NP candidate timetable schemes to construct an initial population. Each individual in the initial population is encoded as a set of train timetable sequences.

[0125] Based on a two-layer evolutionary strategy of shallow diversity preservation and deep strong convergence, a multi-layer archive structure A1, A2, ..., A is adopted in the hierarchical archiving mechanism. k Individuals in the initial population are stored hierarchically according to fitness and evolutionary depth.

[0126] For each individual X in the population i Perform differential mutation (Mutation) operations on samples selected from different layers:

[0127] ,

[0128] Where g is the iteration algebra, F is the scaling factor, F is used to control the perturbation amplitude, and r1, r2, r3 take values ​​[1, NP], which are different from each other and different from i.

[0129] Furthermore, step S300 also includes:

[0130] Perform a crossover operation, randomly selecting a subset of dimensions from V based on the crossover rate Cr. i Replace the original individuals in the population to generate the test vector U. i The crossover rate Cr is dynamically adjusted and adaptively updated using a normal distribution.

[0131] Cr g+1 = 0.9 · Cr g +0.1 · N(µ Cr ,σ 2 ),

[0132] Perform selection and update operations, Cr g Let Cr represent the crossover rate used in the g-th generation population. g+1 This represents the crossover probability used for the next generation, i.e., the (g+1)th generation, after being updated through an adaptive mechanism, N(µ). Cr ,σ 2 ) represents the normal distribution function, µ Cr It is the mean memory term of the crossover rate, σ 2 It is variance;

[0133] Compare the objective function values; if the experimental individuals U produced by the mutation crossover... i The score was higher than that of the original individual X. i Better, i.e., f(U) i )< f(X i ), where f(·) represents the fitness function or objective function value,

[0134] Then the experimental individuals U generated by the mutation crossover i Replace the original individual X i Update the multi-layered archive structure to maintain distribution balance;

[0135] The population size is adaptive, and the NP is dynamically reduced according to the convergence rate to reduce redundant computation and improve search efficiency.

[0136] When the number of iterations reaches the preset upper limit or the energy function converges, the globally optimal timetable scheme is output.

[0137] Specifically, g represents the generation / Iteration index of the algorithm; Cr g Represents the crossover rate used in the g-th generation population; Cr g+1 This represents the crossover probability used for the next generation (g+1 generation) evolution after being updated through an adaptive mechanism.

[0138] N(µ Cr ,σ 2 ) is a normal distribution function, µ Cr It is the mean memory term of the crossover rate, σ 2 It is variance. It represents the crossover rate from a historical success rate of µ. Cr The random sampling from the centered distribution demonstrates the algorithm's adaptive search capability.

[0139] In the formula f(Ui) < f(Xi), f(·) refers to the fitness function or objective function value. In this invention, f(·) corresponds to the comprehensive objective function F defined by S100 or the QUBO energy value E(x) defined by S200.

[0140] In comparing the objective function values, the comparison logic is "selecting the best," that is, if the score (cost / energy) of the experimental individual Ui generated by the mutation crossover is lower (better) than that of the original individual Xi, then it is replaced.

[0141] Here, Xi represents the i-th individual in the current population, and each individual Xi corresponds to a specific subway timetable sequence.

[0142] When performing the selection and update operation, the objective function value is compared. If f(Ui) < f(Xi), then Xi is replaced with Ui, and the multi-level file structure is updated to maintain distribution balance.

[0143] When performing the steps of adaptive population size, dynamically reducing NP based on the convergence rate, reducing redundant computation and improving search efficiency, the optimization layer is initialized, randomly generating NP candidate timetable schemes to construct an initial population. Each individual in the initial population is encoded as a set of train timetable sequences. Each individual is encoded as a set of train timetable sequences, and the individual with the worst function value is removed each time the population is reduced.

[0144] Furthermore, a subway timetable optimization system based on dual archiving and multi-strategy adaptive differential evolution is provided to implement the aforementioned subway timetable optimization method based on dual archiving and multi-strategy adaptive differential evolution. The subway timetable optimization system based on dual archiving and multi-strategy adaptive differential evolution includes:

[0145] The input layer is used to parse the input data of lines, sections, stations and passenger flow, and generate a structured pickle / json format QUBO file;

[0146] An optimization layer optimizes the structured QUBO file by generating candidate timetables, hierarchical archiving mechanisms, crossover operations, selection and update, and population size adaptive strategies.

[0147] The output layer generates a globally optimal timetable, a performance report, and graphical displays of the running graph, interval graph, and energy consumption curve.

[0148] In one specific embodiment, refer to Figure 2 The present invention includes the following mermaid architecture diagram:

[0149] flowchart TD

[0150] A[Input Layer] Input Layer:::input --> B[Optimization Layer] OptimizationLayer]:::process

[0151] B --> C [Output Layer] Output Layer:::output

[0152] %% Input Layer Module

[0153] subgraph A1 [Input layer: runtime data and constraint information]

[0154] A11 [Circuit Structure] [Section length, station location]

[0155] A12 [Running Constraints] [Safety intervals, turnaround times, and transfer requirements]

[0156] A13 [Energy Consumption and Speed ​​Limiting] Traction characteristics, gradient, speed limits]

[0157] end

[0158] %% Optimization layer module

[0159] subgraph B1 [Optimization Layer: Intelligent Optimization Solution Module]

[0160] B11 [Population Initialization and Encoding] Encoding & Initialization

[0161] B12 [Objective Function Calculation] [Delays, energy consumption, and conflict costs]

[0162] B13 [Evolution Operation] Mutation, Crossover, Selection

[0163] B14 [Constraint Repair Module] Constraint Repair

[0164] B15 [Parameter Adaptation and Hierarchical Archiving] Adaptive & Hierarchical Memory]

[0165] end

[0166] %% Output layer module

[0167] subgraph C1 [Output Layer: Result Generation and Evaluation]

[0168] C11 [Output optimal timetable] Train Timetable Generation

[0169] C12 [Generate Performance Report] [Delay indicators, energy consumption statistics]

[0170] C13 [Graphical Display] [Operation Chart / Interval Chart / Energy Consumption Curve]

[0171] end

[0172] %% Data Flow

[0173] A1 --> B1

[0174] B1 --> C1

[0175] %% Style Definition

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[0177] classDef process fill:#e8f5e9,stroke:#43a047,stroke-width:2px,color:#1b5e20,font-weight:bold;

[0178] classDef output fill:#fff3e0,stroke:#fb8c00,stroke-width:2px,color:#e65100,font-weight:bold;

[0179] In one specific embodiment, refer to Figure 3 The present invention includes the following mermaid flowchart:

[0180] %%{init: {"theme": "base", "themeVariables": {

[0181] "fontSize": "35px",

[0182] "fontFamily": "Microsoft YaHei, SimSun, Arial",

[0183] "primaryColor": "#1f77b4",

[0184] "tertiaryColor": "#e8f2fb",

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[0186] }}}%%

[0187] flowchart LR

[0188] A([System Overall Flow]):::start --> B[Read Input Parameters]:::proc

[0189] B --> C[Build QUBO file]:::proc

[0190] C --> D{Whether to execute the computation branch}:::dec

[0191] D -->|Yes| E[Solve ILP baseline]:::proc

[0192] E --> F [Run SA simulated annealing]:::proc

[0193] F --> G[Execute optimization algorithm to solve]:::proc

[0194] G --> H{Whether to execute the analysis branch}:::dec

[0195] D -->|No| H

[0196] H -->|Yes| I[Unified Analysis and Plotting]:::proc

[0197] I --> J [Draw histogram and display results]:::proc

[0198] H -->|No| K([Output Result and Product Path]):::finish

[0199] J --> K

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[0204] classDef dec fill:#fff2cc,stroke:#d4aa00,stroke-width:1px,color:#111;

[0205] Furthermore, the present invention also proposes a computer-readable storage medium storing program instructions thereon, which, when executed by a processor, implement the aforementioned subway timetable optimization method based on dual archiving and multi-strategy adaptive differential evolution.

[0206] The main variables and symbols involved in this invention are described below:

[0207]

[0208] The key points and areas to be protected in this invention are:

[0209] a. An algorithm system based on metro train operation optimization: This system includes core technical components such as multi-station modeling of metro lines, constraint modeling, QUBO optimization model construction, hierarchical archiving mechanism, adaptive differential evolution, and dynamic population control. By transforming the complex multi-train timetable optimization problem into a QUBO (Quadratic Unconstrained Binary Optimization) form, intelligent and quantifiable energy function optimization solutions are achieved.

[0210] b. Algorithm improvement for subway scheduling optimization problem: This invention introduces a multi-layer file structure, parameter adaptive mechanism and dynamic shrinkage strategy into the traditional DE evolution framework, which not only maintains population diversity but also enhances convergence, significantly improving the solution speed and global optimal stability.

[0211] c. Constraint fusion and energy modeling innovation: By embedding safety interval constraints, interval running time constraints, passenger flow matching constraints and platform capacity constraints into energy terms, the "constraint-objective" integrated QUBO modeling is realized, enabling train operation schemes to be directly optimized on quantum annealing or classical high-performance computing platforms.

[0212] d. Scalable modular implementation framework: A scalable computing framework based on Python + Qtrains modules is proposed, which supports timetable optimization and simulation across multiple lines, time periods, and sections, and is suitable for various urban rail transit scenarios.

[0213] It should be understood that the method steps in the embodiments of the present invention can be implemented or carried out by computer hardware, a combination of hardware and software, or by computer instructions stored in a non-transitory computer-readable storage medium. The method can use standard programming techniques. Each program can be implemented in a high-level procedural or object-oriented programming language to communicate with the computer system. However, if necessary, the program can be implemented in assembly or machine language. In any case, the language can be a compiled or interpreted language. Furthermore, for this purpose, the program can run on a programmed application-specific integrated circuit (ASIC).

[0214] Furthermore, the procedures described herein may be performed in any suitable order unless otherwise indicated herein or otherwise clearly contradicted by the context. The procedures described herein (or variations and / or combinations thereof) may be executed under the control of one or more computer systems configured with executable instructions, and may be implemented by hardware or a combination thereof as code (e.g., executable instructions, one or more computer programs, or one or more applications) that commonly executes on one or more processors. The computer program comprises a plurality of instructions executable by one or more processors.

[0215] Furthermore, the method can be implemented operatively connected to any suitable type of computing platform, including but not limited to personal computers, minicomputers, mainframes, workstations, networked or distributed computing environments, standalone or integrated computer platforms, or communicating with charged particle tools or other imaging systems, etc. Aspects of the invention can be implemented as machine-readable code stored on a non-transitory storage medium or device, whether removable or integrated into a computing platform, such as a hard disk, optical read and / or write storage medium, RAM, ROM, etc., such that it is readable by a programmable computer, and when the storage medium or device is read by the computer, it can be used to configure and operate the computer to perform the processes described herein. Furthermore, the machine-readable code, or portions thereof, can be transmitted via wired or wireless networks. The invention described herein includes these and other different types of non-transitory computer-readable storage media when such media comprises instructions or programs that implement the steps described above in conjunction with a microprocessor or other data processor. When programmed according to the methods and techniques described in the invention, the invention may also include the computer itself.

[0216] A computer program can be applied to input data to perform the functions described herein, thereby transforming the input data to generate output data stored in non-volatile memory. The output information can also be applied to one or more output devices, such as a display. In a preferred embodiment of the invention, the transformed data represents physical and tangible objects, including specific visual depictions of physical and tangible objects generated on the display.

[0217] The above description is merely a preferred embodiment of the present invention. The present invention is not limited to the above-described embodiments. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention, as long as they achieve the technical effects of the present invention by the same means, should be included within the scope of protection of the present invention. Within the scope of protection of the present invention, the technical solutions and / or implementation methods can have various modifications and variations.

Claims

1. A subway timetable optimization method based on dual archiving and multi-strategy adaptive differential evolution, characterized in that, The aforementioned subway timetable optimization method based on dual archiving and multi-strategy adaptive differential evolution is applied to a subway timetable optimization system based on dual archiving and multi-strategy adaptive differential evolution. The subway timetable optimization system based on dual archiving and multi-strategy adaptive differential evolution includes an input layer, an optimization layer, and an output layer connected sequentially. The subway timetable optimization method based on dual archiving and multi-strategy adaptive differential evolution includes the following steps: S100. The input layer models the subway line, section length, station and passenger flow input into an ordered subway timetable optimization model, and sets constraints and objective function F. S200, the input layer converts the subway timetable optimization model into QUBO format, generating a structured QUBO file; in step S200, the QUBO format is: E(x) = x T Qx + c, Where E(x) represents the energy function, x is a binary decision variable representing whether the train departs at each time, and Q is a symmetric penalty matrix, where each element Q is a binary variable representing the train's departure time. i,j The energy coupling strength between corresponding variables is determined by the combined coding constraints and target weights, where c is a constant term. S300, The optimization layer optimizes the structured QUBO file by generating candidate timetables, hierarchical archiving mechanism, crossover operation, selection and update and population size adaptive strategy; S400: The output layer generates a globally optimal timetable, generates a performance report, and graphically displays the running graph, interval graph, and energy consumption curve.

2. The subway timetable optimization method based on dual archiving and multi-strategy adaptive differential evolution as described in claim 1, characterized in that, In step S100, the subway timetable optimization model includes the following variables: Let the set of stations along the line be S = {s1,s2,...,s...} n The set of trains T = {T1,T2,...,T} m }, each train T i At each site j The departure time is t dep i,j Arrival time is t arr i,j .

3. The subway timetable optimization method based on dual archiving and multi-strategy adaptive differential evolution according to claim 2, characterized in that, In step S100, The constraints include safety interval constraints, running time constraints, passenger flow matching constraints, and platform capacity constraints. The safety interval constraint is used to prevent train collisions and section congestion. The interval between any two trains in the same section must meet the following requirements: ， Where, t dep i,j For departure time, The minimum interval time; The runtime constraint requires that the runtime for each interval be within a reasonable range. ， Where, t arr i,j For the arrival time, The minimum running time in the interval. This represents the maximum running time within the interval.

4. The subway timetable optimization method based on dual archiving and multi-strategy adaptive differential evolution according to claim 3, characterized in that, The passenger flow matching constraint is used to adjust the train departure frequency at different times, so that the departure frequency matches the peak passenger flow distribution and ensures the balance between transportation supply and demand. To avoid scheduling conflicts, the platform capacity constraint stipulates that only one train is allowed to stop at any station at a time.

5. The subway timetable optimization method based on dual archiving and multi-strategy adaptive differential evolution according to claim 1, characterized in that, In step S100, The objective function is: ， Where F is the objective function, C delay For average train delay, C conflict As a penalty for starting the car conflict, C energy For energy consumption costs, C deviation To avoid deviations from the planned timetable, , , and These are the weighting coefficients used to balance multi-objective optimization.

6. The subway timetable optimization method based on dual archiving and multi-strategy adaptive differential evolution according to claim 1, characterized in that, Step S300 includes: The optimization layer is initialized by randomly generating NP candidate timetable schemes to construct an initial population. Each individual in the initial population is encoded as a set of train timetable sequences. Based on a two-layer evolutionary strategy of shallow diversity preservation and deep strong convergence, a multi-layer archive structure A1, A2, ..., A is adopted in the hierarchical archiving mechanism. k Individuals in the initial population are stored hierarchically according to fitness and evolutionary depth. For each individual X in the population i Differential mutation operation is performed on samples selected from different layers: ， Where g is the iteration algebra, F is the scaling factor, F is used to control the perturbation amplitude, and r1, r2, r3 take values ​​[1, NP], which are different from each other and different from i.

7. The subway timetable optimization method based on dual archiving and multi-strategy adaptive differential evolution according to claim 5, characterized in that, Step S300 also includes: Perform a crossover operation, and randomly select a subset of dimensions from V based on the crossover rate Cr. i Replace the original individuals in the population to generate the test vector U. i The crossover rate Cr is dynamically adjusted and adaptively updated using a normal distribution. Cr g+1 = 0.9 · Cr g +0.1 · N(µ Cr ,σ 2 ), Perform selection and update operations, Cr g Cr represents the crossover probability used in the g-th generation of the population. g+1 This represents the crossover probability used for the next generation, i.e., the (g+1)th generation, after being updated through an adaptive mechanism, N(µ). Cr ,σ 2 ) represents the normal distribution function, µ Cr It is the mean memory term of the crossover rate, σ 2 It is variance; Compare the objective function values; if the experimental individuals U produced by the mutation crossover... i The score was higher than that of the original individual X. i Better, i.e., f(U) i ) < f(X i ), where f(·) represents the fitness function or objective function value, then the experimental individuals U generated by mutation crossover are... i Replace the original individual X i Update the multi-layered archive structure to maintain distribution balance; The population size is adaptive, and the NP is dynamically reduced based on the convergence rate. When the number of iterations reaches the preset upper limit or the energy function converges, the globally optimal timetable scheme is output.

8. A subway timetable optimization system based on dual archiving and multi-strategy adaptive differential evolution, used to implement the subway timetable optimization method based on dual archiving and multi-strategy adaptive differential evolution as described in any one of claims 1 to 7, characterized in that, The metro timetable optimization system based on dual archiving and multi-strategy adaptive differential evolution includes: The input layer is used to parse the input data of lines, sections, stations and passenger flow, and generate a structured pickle / json format QUBO file; An optimization layer optimizes the structured QUBO file by generating candidate timetables, hierarchical archiving mechanisms, crossover operations, selection and update, and population size adaptive strategies. The output layer generates a globally optimal timetable, a performance report, and graphical displays of the running graph, interval graph, and energy consumption curve.

9. A computer-readable storage medium, characterized in that, It stores program instructions, which, when executed by a processor, implement the metro timetable optimization method based on dual archiving and multi-strategy adaptive differential evolution as described in any one of claims 1 to 7.

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