Determining a timetable for rail vehicles in case of disruptions

Abstract

Provided is a method for determining a modified timetable (13) for several rail vehicles when at least one disruption to an original timetable (4) is present, wherein a timetable for each rail vehicle contains a time-distance definition (T1.1, T2.1,...), the method comprising: Based on the original timetable (4), cyclically (18) performing a heuristic optimization (5) to generate a first timetable (6); storing time-distance definitions (7, 9) for one or more rail vehicles generated during the cyclically performed heuristic optimization (5); formulating (10) a QUBO task based on the stored time-distance definitions (9); solving (16) the QUBO task to generate a second timetable (11); comparing the first timetable (6) and the second timetable (11) to select the modified timetable (13).

Description

AREA OF INVENTION

[0001] The present invention relates to a method and a corresponding device for determining a modified timetable for several rail vehicles when at least one disruption to the original timetable occurs. The present invention further relates to a rail vehicle control center comprising the method. STATE OF THE ART

[0002] In a modern railway system, there is a current timetable that precisely defines how train traffic is organized. This includes, for example, the train sequence on each line and the exact intervals between trains. However, the current timetable cannot always be adhered to because various disruptions can occur, leading to unexpected delays. This creates conflicts in train traffic and the timetable, where, for example, one train has to wait for another because the latter is blocking a section of track ahead.

[0003] To resolve these conflicts in rail traffic as effectively as possible, methods and algorithms have been developed in recent years to determine an optimized timetable that resolves existing conflicts within the current schedule. Traditionally, an optimized timetable was calculated to support dispatching, in which conflicts are resolved as effectively as possible for all routes. However, a common problem is that subsequent conflicts cause the number of possible alternatives to grow exponentially. Conventionally applied global search optimization methods require a significant amount of time for this, sometimes too long for real-time applications.

[0004] It has been observed that a replacement timetable determined by conventional optimization of an original timetable does not represent the best possible timetable in all situations or under all circumstances.

[0005] It is therefore an object of the present invention to provide a method and a corresponding device for determining a modified timetable for several rail vehicles in the event of at least one disruption to an original timetable, wherein, on the one hand, the time required to determine the modified timetable remains within acceptable limits in order to be suitable, for example, for real-time applications, and wherein, furthermore, the modified timetable determined is with greater certainty or probability an actually improved or optimized timetable compared to conventional timetables. SUMMARY OF THE INVENTION

[0006] The problem is solved by the subject matter of the independent claims, which relate on the one hand to a method and on the other hand to a device for determining a changed timetable for several rail vehicles. The dependent claims specify certain embodiments of the present invention.

[0007] According to one embodiment of the present invention, a method for determining a modified timetable for several rail vehicles in the event of at least one disruption to an original timetable is provided, wherein a timetable for each rail vehicle contains a time-distance definition, and the method comprises: cyclically performing a heuristic optimization based on the original timetable to generate a first timetable; storing / collecting / maintaining time-distance definitions for one or more rail vehicles generated during the cyclically performed heuristic optimization; formulating a QUBO task based on the stored time-distance definitions; solving the QUBO task to generate a second timetable; and comparing and / or analyzing the first and second timetables to select the modified timetable.

[0008] The procedure can be implemented, for example, in hardware and / or software, in particular using a specially designed chip, and carried out, for example, by a railway vehicle control center, monitoring center, or control station.

[0009] The rail vehicles in question could be, for example, long-distance trains, regional trains, commuter trains, trams, subways, or similar. Support could be provided for between 50 and 500 rail vehicles, or even a higher number.

[0010] The disruption could be a collision, an accident, a partial closure of a track section, damage to or destruction of a track section, a power outage, a communication failure, or similar. The disruption could, for example, result in an extended dwell time due to increased passenger volume and / or a points failure and / or a door malfunction and / or a delay of a feeder train.

[0011] The disruption may result in at least one planned journey of at least one rail vehicle not being carried out in part or in full according to the timetable.

[0012] Both the original timetable and the revised timetable define a time-distance definition (also referred to as a "trip") for each rail vehicle, which specifies, for example, that the respective rail vehicle should be at a specific location at a specific time according to the schedule. The time-distance definition can be represented, for example, as a list of locations and times.

[0013] For optimization, for example, an input argument can be found for a given objective function such that the function assumes a minimum or maximum value. A heuristic can, for example, consist of performing or determining a trial-and-error modification of one or more time-distance definitions. Modifications to time-distance definitions can also be made based on previously acquired experience. Various heuristic optimization methods are known in the prior art.

[0014] Heuristic optimization is performed cyclically in the sense that it is carried out repeatedly or iteratively, whereby previously obtained results can be used for the next cycle. Heuristic optimization can be performed cyclically, for example, between five and one hundred times or between five and one thousand times. The number of cycles can depend on when the revised timetable, and thus also the initial timetable, actually needs to be available.

[0015] During the heuristic optimization process, one or more modified time-distance definitions are generated, which, together with the unchanged time-distance definitions, each form a cycle-associated schedule. Thus, schedules are generated repeatedly and iteratively, each assigned to a specific cycle number. The first schedule can be considered the one generated by the last cycle.

[0016] All potentially modified time-distance definitions generated in all cycles (of the heuristic optimization) are collected and, in particular, stored in a database. These stored time-distance definitions are not used directly for the heuristic optimization but are dynamically used to formulate a QUBO (Quadratic Unconstrained Binary Optimization) task. The set of stored time-distance definitions may contain one or more time-distance definitions for a specific rail vehicle. The QUBO task theoretically examines all combinations of all stored time-distance definitions. For example, the QUBO task can evaluate one or more combinations of time-distance definitions that were not considered or analyzed during the heuristic optimization.The QUBO problem can be solved using conventionally available means, in particular a specially designed chip, either in hardware and / or software.

[0017] The second timetable may be potentially more optimal (with respect to an evaluation function) than the first, due to the possibly larger number of combinations or the consideration of a greater number of combinations of time-distance definitions. While the first timetable can be fundamentally conflict-free (i.e., there are no collisions between two rail vehicles), the second timetable could theoretically contain conflicts. However, potential conflicts in the second timetable (and possibly also in the first timetable) can be identified and eliminated in a later evaluation or selection step.

[0018] Comparing and analyzing the first and second timetables can be done automatically or, in some cases, by human intelligence. For example, the first and second timetables can be displayed clearly, or differences between them can be highlighted. This allows a revised timetable to be analyzed more quickly and potentially achieve a higher quality or better rating compared to conventionally revised timetables.

[0019] According to one embodiment of the present invention, during the heuristic search or optimization, only the best and multi-conflict-free routes (e.g., distance-time definitions) are constructed, since the heuristic method incrementally improves the conflict-free timetable. All these routes are stored, and the QUBO task is formulated based on them. Due to the improved selection of routes (e.g., distance-time definitions that were cumulatively collected and stored during the heuristic optimization), the solution to the QUBO task can contain a more optimal timetable.

[0020] According to one embodiment of the present invention, formulating the QUBO task involves: specifying a numerical evaluation scheme that evaluates time-distance definitions and / or pairs of time-distance definitions;Computation of a two-dimensional input data structure, in particular a square matrix, from the provided time-distance definitions and the evaluation scheme, wherein the input data structure represents an evaluation of an individual or joint presence of the provided time-distance definitions according to the evaluation scheme; definition / construction of an objective function to be optimized based on the two-dimensional input data structure, wherein in particular each (doubly) indexed element of the input data structure represents an evaluation of the presence / occurrence of a time-distance definition assigned to the (doubly) index and / or an evaluation of the presence / occurrence of a pair of time-distance definitions assigned to the (doubly) index.

[0021] The evaluation scheme can be used to define the objective function. For example, the evaluation scheme can favor situations where no collisions occur, and / or that a single time-distance definition is included in the timetable for each rail vehicle.

[0022] The two-dimensional input data structure can be doubly indexed, meaning it can contain elements accessible or identifiable by two independent indices. Non-diagonal elements of the two-dimensional input data structure can evaluate the co-occurrence of two time-distance definitions, which are, for example, assigned to the row index and the column index. Diagonal elements of the input data structure can evaluate the presence of a single time-distance definition, which is, for example, indexed by the row index (= column index). The objective function to be optimized can be defined, for example, by applying the two-dimensional input data structure to a binary vector that has the dimension of the number of rows or the number of columns of the input data structure. This allows for the formulation of a quadratic unconstrained binary optimization problem (QUBO problem), thus enabling easy implementation.

[0023] According to one embodiment of the present invention, the evaluation scheme takes into account at least one of the following: a collision of two time-distance definitions occurring; the presence of exactly one time-distance definition of a rail vehicle.

[0024] If a route (e.g., distance-time definition) exists in the timetable, its quality (or rating / weighting) (weighted punctuality and track accuracy) can be included in the matrix diagonal (objective function). In the other (non-diagonal) positions of the matrix, the penalties (or their numerical values) for two simultaneously selected routes can be stored: e.g., a) for a missed connection (e.g., small penalty) and b) for a collision between these two routes (e.g., large penalty).

[0025] The rating scheme can be adapted to the required use cases by, for example, defining operator-specific weights for delays, misplaced tracks and / or missed connections.

[0026] This allows the method to be adapted to various use cases. For example, the evaluation scheme can also be derived from experience or modified.

[0027] According to one embodiment of the present invention, solving the QUBO problem comprises: inputting the two-dimensional input data structure into a hardware and / or software-based computing machine; performing a quadratic unconstrained binary optimization in the computing machine, in particular to optimize the objective function for an argument to be determined; outputting a one-dimensional output data structure (associated with the optimized objective function), in particular a binary result vector, wherein each component is associated with a time-path definition (of the provided time-path definitions).

[0028] The binary result vector can indicate which of the entered or provided time-distance definitions are included in the result schedule and which are not, by setting the respective result vector component to 1 or 0, respectively.

[0029] The binary result vector could also contain non-implementable solutions: if a) none or more than one of several alternative routes was selected, or b) selected routes overlap. In this case, the DA solution (e.g., the solution to the QUBO problem) can be discarded, and the best solution calculated so far using the heuristic method can be employed (see, e.g., Block 6 in [reference]). Fig. 1, which is described in more detail below).

[0030] The binary result vector might, for example, contain more ones than the number of rail vehicles. In this case, the result vector for a rail vehicle would contain, for instance, more than one time-distance definition. In such a case, the binary result vector can be further processed or modified to select one of the time-distance definitions for a rail vehicle.

[0031] The binary result vector could, for example, also contain a 1 for two time-distance definitions that lead to a collision. This problem could also be detected and resolved in a subsequent evaluation or analysis step. Quadratic unconstrained binary optimization is based on a square matrix applied to a binary vector to define the objective function. The square matrix is ​​also referred to as the Q-matrix. It corresponds to the previously mentioned two-dimensional input data structure. The Q-matrix can contain real matrix elements, making it a triangular matrix. Thus, the QUBO problem can be solved easily, for example, using methods known in the prior art.

[0032] According to embodiments of the present invention, the computing machine comprises at least one of the following: a QUBO chip; a quantum computer; a graphics processing unit. This allows the method to be partially hardware-supported in order to increase the computing speed.

[0033] According to one embodiment of the present invention, the cyclical execution of the heuristic optimization comprises a repeated, in particular iterative, execution of the heuristic optimization using at least one previously determined result, wherein the time-distance definitions generated in each cycle of repeated execution are stored cumulatively with the time-distance definitions generated and previously stored in previous cycles, in order to increase the number of stored time-distance definitions in each cycle, in particular to be higher than the number of rail vehicles.

[0034] This allows conventionally available algorithms to be used for implementation.

[0035] According to one embodiment of the present invention, the heuristic optimization in each cycle step comprises: modifying at least one time-distance definition of at least one rail vehicle associated with a previously created timetable candidate or the original timetable; creating a timetable candidate based on previous time-distance definitions of one or more rail vehicles and the at least one modified time-distance definition; evaluating the timetable candidate and comparing it with previously created candidates, if any; and outputting the first timetable associated with the cycle step, wherein, in particular, between 10 and 1000 cycles are executed.

[0036] The modification of the time-path definition can be random or goal-oriented. Depending on the heuristic used, the modification of the time-path definition can be random (e.g., genetic algorithms, simulated annealing) or deterministic (e.g., tabu search, greedy methods). The goal of these modifications is to improve the objective function.

[0037] The evaluation of the timetable candidate can be carried out, for example, using a heuristic optimization objective function. This allows for an assessment of the candidate and a comparison of this assessment with previously determined assessments of other timetable candidates. If the assessment of the current timetable candidate is better or more favorable than the previous assessments, the respective current candidate can be selected as the first timetable. Thus, conventionally available methods are applicable to parts of the method according to the invention.

[0038] According to one embodiment of the present invention, changing a time-distance definition comprises at least one of the following: changing at least one location point of the time-distance definition; changing at least one point in time of the time-distance definition; waiting longer or shorter at one or more locations of the time-distance definition; driving faster or slower between two or more locations of the time-distance definition.

[0039] According to one embodiment of the present invention, the evaluation of the timetable candidate and comparison with previously created candidates is carried out based on an evaluation function. The evaluation function can be adapted to the current requirements of the application.

[0040] The evaluation or objective function of the heuristic optimization can be designed similarly or identically to the function defined in the QUBO task.

[0041] The evaluation / objective function(s) of the heuristic optimization may partially overlap with or differ from the evaluation / objective function(s) of the QUBO task.

[0042] A rating / objective function of heuristic optimization can, for example, include ratings or penalties for delays and / or for track changes and / or for missed connections.

[0043] The QUBO evaluation / objective function can, for example, include an evaluation / objective function for heuristic optimization and / or additionally include evaluations or penalties for collisions and / or multiple route alternatives and / or for no route alternative.

[0044] According to one embodiment of the present invention, the heuristic optimization uses at least one of the following methods: Branch and Bound; Greedy; TabuSearch; genetic algorithm; Simulated annealing.

[0045] According to one embodiment of the present invention, the method is executed in real time, wherein the heuristic optimization is aborted before a first time point at which the modified timetable is required, and the last available timetable candidate is taken as the first timetable, wherein the formulation and solving of the QUBO task is carried out based on the time-distance definitions stored before the first time point in order to generate the second timetable.

[0046] The process can be initiated, for example, as soon as a disruption occurs that prevents the execution of the original timetable. The point at which train services must resume according to a revised timetable can be determined, for example, by a monitoring or control center. All timetables generated up to that point—that is, the first and second timetables—can then be used to determine the revised timetable before the point at which train services are to be, or will be, resumed.

[0047] According to one embodiment of the present invention, the method further comprises at least one of the following: displaying the first and second timetables to a user separately or in combination, in particular superimposing them; displaying differences between the first and second timetables to a user; enabling a user to select the first or the second timetable in order to determine the modified timetable.

[0048] Displaying both the first and second timetables to the user allows for a faster selection process. Potential drawbacks or problems of the first and / or second timetable can be highlighted to the user. The final selection of the first or second timetable can be automated and / or made through human intelligence and user input.

[0049] According to one embodiment of the present invention, the method further comprises at least one of the following: instructing the rail vehicles and / or a rail vehicle control center and / or a rail vehicle control system and / or a rail vehicle monitoring system in accordance with the amended timetable. This allows relevant bodies to be informed of the amended timetable in order to implement it reliably and smoothly.

[0050] According to one embodiment of the present invention, the time-distance definition assigned to a rail vehicle specifies at what time the rail vehicle should be at a particular location. The time-distance definition can, for example, be implemented as a list of pairs of times and locations. The time-distance definition can also be defined graphically or displayed.

[0051] According to one embodiment of the present invention, a device for determining a modified timetable for several rail vehicles in the event of at least one disruption to an original timetable is provided, wherein a timetable for each rail vehicle contains a time-distance definition, the device comprising: a computing machine with memory configured to: perform a cyclic heuristic optimization based on the original timetable in order to generate a first timetable; store time-distance definitions for one or more rail vehicles generated during the cyclically performed heuristic optimization; solve a QUBO problem formulated based on the stored time-distance definitions in order to generate a second timetable;a display and / or analysis device designed to display and / or analyze the first and second timetables in order to enable selection of the modified timetable.

[0052] It should be understood that features, individually or in any combination, mentioned, described or applied in connection with a method of determining a modified timetable for several rail vehicles are likewise applicable or may be applied to a device for determining a modified timetable for several rail vehicles according to embodiments of the present invention, and vice versa.

[0053] According to one embodiment of the present invention, a railway vehicle control center is provided, comprising: a device according to the preceding embodiment; a communication system configured to transmit the changed timetable at least to the railway vehicles.

[0054] Embodiments of the present invention will now be explained with reference to the accompanying drawings. The invention is not limited to the illustrated or described embodiments. BRIEF DESCRIPTION OF THE DRAWINGS Fig. Figure 1 schematically illustrates a device for determining a changed timetable for several rail vehicles according to an embodiment of the present invention, which is configured to carry out a method of determining a changed timetable according to an embodiment of the present invention; Fig. Figure 2 illustrates by way of example the generation of a second timetable based on a database of time-distance definitions according to an embodiment of the present invention; Fig. Figure 3 illustrates by way of example various time-distance definitions for rail vehicles as they are considered or generated according to embodiments of the present invention; and Fig. Figure 4 schematically illustrates a device or method for determining a changed timetable according to an embodiment of the present invention. DETAILED DESCRIPTION OF EXECUTION FORMS

[0055] The in Fig. A schematically illustrated device 1 for determining a modified timetable for several rail vehicles in the event of at least one disruption to an original timetable comprises a computing machine 2 with a memory 3. The computing machine 2 is configured to cyclically perform a heuristic optimization using module 5, based on an original timetable 4 which exhibits a disruption, in order to generate a first timetable 6 (e.g., containing 100 trips).

[0056] The computing machine 2 is further configured to store time or distance definitions 7 for one or more rail vehicles, which were generated during the cyclically performed heuristic optimization 5, in particular to store them in a database 8 which is contained in the memory 3. The computing machine 2 is further configured to solve a QUBO problem 10 formulated on the basis of the stored time-distance definitions 9 (which are contained in the database 8, e.g. containing 7000 trips) in order to generate a second timetable 11.

[0057] The device 1 further comprises a display and / or analysis device 12, which is configured to display and / or analyze the first timetable 6 and the second timetable 11 in order to enable the selection of the modified timetable 13. The modified timetable 13 is thus obtained by selection from the first timetable 6 and the second timetable 11.

[0058] Module 10 for formulating a QUBO task comprises a calculation module 14, in which a two-dimensional input data structure (hereinafter also referred to as the Q-matrix) is calculated from the provided time-distance definitions 9 and an evaluation scheme (not illustrated in detail). The calculated matrix is ​​shown in module 15. In formulation step 10, an objective function to be optimized is also established or defined, based on the Q-matrix and, in particular, an evaluation scheme.

[0059] The objective function to be optimized can, for example, have the following form: Sum (Q[i, j]*x[i]*x[j])→min for ri=0..N, j=0..N N denotes the number of alternative routes (e.g., distance-time definitions)

[0060] The elements Q are ijthe elements of the Q-matrix and the vector xi represents the binary result vector (for which the objective function is optimized and, in particular, minimized), where each component of the vector xi corresponds to a time-distance definition.

[0061] In the Fig. In the illustrated device 1, the computing machine 2 comprises a QUBO solution module 16 in the form of a QUBO chip, which receives the Q-matrix 15 and calculates the second timetable 11 as an optimized timetable. In other embodiments, the computing machine can, for example, comprise a quantum computer or a graphics processing unit with many parallel processors as the QUBO solution module 16.

[0062] The two-dimensional input data structure, i.e., the Q-matrix, is fed into the QUBO chip 16, which performs a quadratic unconstrained binary optimization. The output of the QUBO chip 16 is the second timetable 11, which can be viewed as a binary result vector of the QUBO processing. Those time-distance definitions to which a 1 is assigned in the result vector are indeed time-distance definitions in the first timetable 11.

[0063] The cyclic optimization, or cyclic optimization module 5 of the computer 2, contains a modification module 17, which is called cyclically (indicated by arrow 18) after passing through an evaluation module 19 (also contained in the heuristic optimization module 5). In the modification module 17, at least one time-distance definition of at least one rail vehicle, assigned to a previously created candidate 18 of a timetable or to the original timetable 4 (e.g., containing 100 trips), is modified. In the first step, at least one time-distance definition of the input original timetable 4 is changed. In subsequent cycles, at least one time-distance definition of a candidate 18 (e.g., containing 100 trips) of a first timetable 6, generated within module 5, is modified.The one or more modified time-distance definitions 20 and the unchanged time-distance definitions 21 are associated in evaluation module 19 and form candidate 18 of a first timetable. In evaluation module 19, candidate 18 is further evaluated and, in particular, compared with previously created candidates. The evaluation performed in module 19 ultimately outputs the first timetable 6.

[0064] In module 17, decision parameters are modified, for example, by introducing an additional stop, changing track priorities, modifying routes, eliminating a stop, or canceling a connection, etc. These decision parameters (22) are used in an operational simulation (18) to construct a conflict-free timetable. The physical behavior of the trains and signal boxes is modeled to calculate precise and conflict-free routes (e.g., distance-time definitions). The newly constructed timetable is evaluated against the objective function, and the calculated value is communicated to modification module 17. The timetable itself is also sent to database 8 and stored there to create a pool of alternatives for QUBO.

[0065] The evaluation in Module 19 can be based, for example, on an objective function or on an evaluation function. Within Optimization Module 5, particularly in Modification Module 17, various algorithms can be applied, such as branch and bound, greedy, tabu search, genetic algorithms, or other heuristic methods.

[0066] The display and / or analysis device 12 also allows a user to view the first timetable 6 and / or the second timetable 11 separately or in combination to facilitate selection. For example, differences between the first timetable 6 and the second timetable 11 can also be displayed to the user using module 12.

[0067] Fig. Figure 2 shows an example of the contents of a database 8 when, for instance, a timetable for two rail vehicles T1 and T2 is to be created. The database contains the time-distance definitions T1.0 and T1.1 for the first rail vehicle and the time-distance definitions T2.0, T2.1, and T2.2 for the second rail vehicle, which were generated cumulatively by the cyclic application of heuristic optimization 5. Solving the QUBO problem results in the second timetable 11, which can be represented, for example, as a one-dimensional vector 11a with the components 0, 1, 0, 0, 1. Thus, the second timetable 11 comprises the time-distance definitions T1.1 and T2.2.

[0068] An example of the aforementioned time-distance definitions is in Fig. Figure 3 is shown in a coordinate system with abscissa 23, representing position x, and ordinate 24, representing time t. The time-distance definitions T1.0 and T2.0, shown with solid lines, illustrate time-distance definitions within the original but perturbed timetable 4. The time-distance definitions shown with dashed lines represent those generated during the heuristic optimization.

[0069] The original timetable exhibits a conflict or collision between time-distance definitions T1.0 and T2.0 at their intersection point. The generated time-distance definition T1.1 has no waiting time or a relatively short waiting time at coordinates x1 and t1, but still conflicts with time-distance definition T2.0. However, it does not conflict with the generated time-distance definition T2.1, which has a waiting time at location X2. Time-distance definition T2.2 has a waiting time of t3-t0 at location X2 and can therefore avoid the collisions with time-distance definition T1.1.

[0070] Fig. Figure 4 schematically illustrates a further device 101 for determining a changed timetable 113 in the event of at least one disruption to an original timetable 104. Similar or identical elements or functions in Fig. 1 and Fig. Four figures are labeled with reference symbols that differ by only 100. The description of an element not described in detail in one figure can be derived from the description of that corresponding element in relation to the other figure.

[0071] The heuristic optimization method (e.g., genetic algorithms, tabu search, etc.) implemented by module 105 is applied to the disrupted timetable 104 to generate alternatives or investigated timetables. The investigated timetables 107, which are generated cyclically, are collected in database 108 as a set of time-distance definitions 109. From these time-distance definitions (also called alternatives) 109, a QUBO optimization problem is formulated and solved by the QUBO solution module 116. The QUBO solution module can, for example, be implemented as a digital annealer. The digital annealer 116 solves the optimization problems by selecting the best combination from pre-qualified alternatives.

[0072] The methods of heuristic optimization and solving the QUBO problem are combined according to embodiments of the present invention. Heuristic optimization is conventionally limited by CPU performance and may not achieve the global optimum using the conventional method. By rapidly combining the searched alternatives, a better solution can be constructed than previously achieved according to embodiments of the invention. The Digital Annealer (DA) requires the best and most complete alternatives possible in order to construct a good solution simply by combining them.

[0073] During the heuristic optimization (e.g., in modules 5 and 105 in Fig. 1 and Fig. 4) Only valid (especially conflict-free or collision-free) and qualitatively better solution alternatives (i.e., candidate roadmaps) are constructed, which corresponds to the Digital Annealer (e.g., Module 16 or 116 in the Fig. 1 or Fig. 4) makes it possible to actually construct an optimum. If the Digital Annealer does not find a good, conflict-free solution (it is still NP-Hard), the result of the heuristic optimization (for example, the first timetable 6 or 106 in Fig. 1 and Fig. 4) used.

[0074] In device 101, a disrupted timetable 104 is fed to module 105, which performs heuristic optimization (e.g., 16 CPU cores, 1 minute). The analyzed timetables 107 are accumulated in database 108. The sum of the time-distance definitions or alternatives 109 stored in database 8 are fed to the QUBO solution module 116, which generates the Digital Annealer-optimized timetable 111 (also referred to as the second timetable).

[0075] The heuristic optimization module 105 outputs the first timetable 106, or the optimized timetable 106. The optimized timetable (also referred to as the first timetable) 106 and the DA-optimized timetable 111 (also referred to as the second timetable) are sent to the evaluation module 112 for evaluation, comparison, or display. The final timetable (also referred to as the revised timetable) 113 is output as a result of the evaluation in 112.

[0076] Besides the Digital Annealer, GPUs (Graphics Processing Units) could also be used to solve the QUBO.

Claims

[1] Method of determining a modified timetable (13) for a plurality of rail vehicles in the presence of at least one disruption of an original timetable (4), wherein a timetable for each rail vehicle contains a time-distance definition (T1.1, T2.1,...), the method comprising: Based on the original schedule (4), cyclically (18) performing a heuristic optimization (5) to generate a first schedule (6); Maintaining time-distance definitions (7, 9) for one or more rail vehicles generated during the cyclically performed heuristic optimization (5); Formulating (10) a QUBO task based on the stored time-distance definitions (9); Solving (16) the QUBO task to generate a second schedule (11); Comparing the first timetable (6) and the second timetable (11) to select the modified timetable (13). [2] Method according to the preceding claim, wherein formulating the QUBO task comprises: Specifying a numerical evaluation scheme that evaluates time-distance definitions and / or pairs of time-distance definitions; Calculating a two-dimensional input data structure (15, Q), in particular a square matrix, from the provided time-distance definitions and the evaluation scheme, wherein the input data structure (15, Q) represents an evaluation of an individual or joint presence of the provided time-distance definitions according to the evaluation scheme, Setting up an objective function (f(x)) to be optimized based on the two-dimensional input data structure (15, Q), wherein in particular each indexed element of the input data structure represents an evaluation of the presence / occurrence of a time-path definition assigned to the index and / or an evaluation of the presence / occurrence of a pair of time-path definitions assigned to the index. [3] Method according to the preceding claim, wherein the evaluation scheme takes into account at least one of the following: an occurring collision of two time-distance definitions; the existence of exactly one time-distance definition of a rail vehicle; [4] Method according to the preceding claim, wherein solving the QUBO task comprises: Inputting the two-dimensional input data structure (15, Q) into a hardware and / or software-based computing machine (2, 16); Performing a quadratic unconstrained binary optimization in the computing engine, in particular to optimize the objective function for an argument to be determined; Outputting a one-dimensional output data structure (x), in particular a binary result vector, wherein each component of the binary result vector is assigned to a time-path definition. [5] Method according to the preceding claim, wherein the computing machine comprises at least one of the following: a QUBO chip (16); a quantum computer; a graphics processing unit (GPU). [6] Method according to one of the preceding claims, wherein the cyclical execution of the heuristic optimization (5) comprises a repeated, in particular iterative, execution of the heuristic optimization using at least one previously determined result, wherein the time-distance definitions (7) generated in each cycle of the repeated execution are stored accumulatively with the time-distance definitions generated and previously stored in previous cycles, so as to increase the number of stored time-distance definitions (9) with each cycle, in particular to be higher than the number of rail vehicles. [7] Method according to one of the preceding claims, wherein the heuristic optimization in each cycle step comprises: Changing (17) at least one time-distance definition of at least one rail vehicle assigned to a previously created candidate (18, 22) of a timetable or to the original timetable (4); Creating a candidate (22) of a timetable based on previous time-distance definitions of one or more rail vehicles and the at least one changed time-distance definition; Evaluating (19) the candidate of the schedule and comparing it with previously created candidates, if any; Outputting the first schedule (6) assigned to the cycle steps, wherein in particular between 10 and 1000 cycles are executed. [8] Method according to the preceding claim, wherein changing a time-distance definition comprises at least one of the following: Changing at least one location point (x1,x2) of the time-distance definition (T1.0, T2.0); Changing at least one point in time (t1,t2) of the time-distance definition; Longer or shorter waiting at one or more locations of the time-distance definition; Driving faster or slower between two or more locations of the time-distance definition. [9] Method according to one of the two preceding claims, wherein the evaluation of the candidate (22) of the timetable and comparison with previously created candidates is carried out based on an evaluation function. [10] Method according to one of the preceding claims, wherein the heuristic optimization (5) applies at least one of the following methods: Branch and Bound; Greedy; TabuSearch; genetic algorithm. [11] Method according to one of the preceding claims, wherein the method is carried out in real time, wherein the heuristic optimization (5) is aborted before a first time point at which the modified timetable is required, and the last available candidate timetable is taken as the first timetable, wherein the formulation and solution of the QUBO task is based on the time-distance definitions stored before the first time point in order to generate the second schedule (11). [12] Method according to one of the preceding claims, further comprising at least one of the following: displaying the first timetable (6) and the second timetable (11) to a user separately or in combination, in particular overlaying; showing a user differences between the first and second timetable; allow a user to select the first or second timetable to determine the modified timetable. [13] Method according to one of the preceding claims, further comprising instructing the rail vehicles and / or a rail vehicle control center and / or a rail vehicle control and / or a rail vehicle monitoring system according to the changed timetable. [14] Method according to one of the preceding claims, wherein the time-distance definition (T1.0, T1.1,...) assigned to a rail vehicle determines at which time (t) the rail vehicle should be located at which location (x) according to plan. [15] Device (1, 101) for determining a modified timetable (13) for a plurality of rail vehicles in the presence of at least one disruption of an original timetable (4), wherein a timetable for each rail vehicle contains a time-distance definition (T1.0, T2.0, ...), wherein the device comprises: a computing machine (2) with memory (3), which is designed: based on the original schedule (4), cyclically perform a heuristic optimization (5) to generate a first schedule (6); to store time-distance definitions (7, 9) for one or more rail vehicles generated during the cyclically performed heuristic optimization; to solve a QUBO task formulated based on the stored time-distance definitions (9) in order to generate a second timetable (11); a display and / or analysis device (12) which is designed to display and / or analyze the first timetable (6) and the second timetable (11) in order to select the changed timetable (13) therefrom. [16] Rail vehicle control centre, comprising: a device according to the preceding claim; a communication system designed to transmit the changed timetable at least to the rail vehicles.

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