An interactive multi-objective optimization method for train operation plan adjustment

Abstract

An interactive multi-objective optimization method for adjusting train operation plan includes two stages: in the first stage, the target space of the multi-objective optimization problem of operation adjustment is segmented to obtain the area of ​​interest to the dispatcher; in the second stage, the dispatcher specifies a reference point, searches for some non-dominated solutions near the reference point, and obtains the corresponding preferred train operation adjustment plan, including: determining the number of Pareto front segmentation areas, calculating the non-dominated solutions of the area boundary; according to the non-dominated solutions of the Pareto front segmentation area boundary, the dispatcher sets the reference point and sets the number of preferred solutions; according to the reference point P ref The direction is calculated corresponding to the preferred non-dominated solution.

Description

Technical Field

[0001] The invention relates to the field of high-speed train dispatching and control technology, and in particular to an interactive multi-objective optimization method for adjusting a train operation plan. Background Art

[0002] High-speed railway traffic dispatching and command is the core of daily operation and management of high-speed railway. According to the information of various links such as train operation status, equipment control, emergency disposal, maintenance and repair, the train operation plan is formulated and adjusted, and sent to the train control system for execution. In terms of train operation adjustment, when some emergencies occur, the scheduled operation plan cannot be implemented smoothly, and the train operation needs to be adjusted quickly in real time to recover from the interference state. The intelligence level of the existing train dispatching system is still at a low level in terms of cognition and decision-making, and the dispatcher's intervention is required in the process of completing complex dispatching tasks. Secondly, the quality of the adjustment plan can be evaluated by multiple optimization objectives, such as reducing train delays, improving passenger satisfaction, increasing the number of passengers transported, reducing recovery time, and reducing the number of canceled trains. Generally speaking, the several objectives that need to be optimized in multi-objective optimization problems are conflicting with each other. If one objective is improved, one or more other objectives will deteriorate. According to the timing of decision makers participating in the solution process, multi-objective optimization problems can be divided into a priori methods, interactive methods, and a posteriori methods. Most of the existing studies consider the case of a single optimization objective, and lack research on multi-objective optimization problems, especially interactive multi-objective optimization problems involving dispatchers and decision systems. Designing an effective interactive multi-objective optimization method for train operation plan adjustment has become a key issue that must be solved to achieve intelligent train scheduling.

[0003] Among the existing multi-objective optimization methods for adjusting train operation plans, the priori method considers that the decision maker has provided global preference information, and searches for a Pareto optimal solution under this preference on this basis. For example, considering the optimization objectives such as minimizing the delay cost and the number of severely affected trains, a single optimization objective is obtained by weighting under the given decision maker's preference, and then solved by a solver or optimization method. However, the disadvantage of this technology is that it requires the decision maker's global preference information, which is actually difficult to accurately describe.

[0004] Among the existing multi-objective optimization methods for adjusting train operation plans, the a posteriori method first searches the entire Pareto frontier and then selects the most preferred solution in the frontier. Unlike the a priori method, this method does not require the decision maker's preference information and can approximate the entire Pareto frontier. However, the disadvantage of this technology is that the computational cost required to approximate the entire Pareto frontier is too high, and it is difficult to achieve satisfactory results in some situations that require fast solutions, especially in the case of dynamic real-time train scheduling. Summary of the invention

[0005] The purpose of the present invention is to provide an interactive multi-objective optimization method for adjusting train operation plans, which can effectively target the preference information of train dispatchers, adjust the dispatching plan by integrating multiple optimization objectives, realize human-machine collaboration in train dispatching, and improve the intelligent level of dispatching command.

[0006] An interactive multi-objective optimization method for train operation plan adjustment includes two stages: in the first stage, the target space of the multi-objective optimization problem of operation adjustment is segmented to obtain the area of ​​interest to the dispatcher; in the second stage, the dispatcher specifies a reference point, searches for some non-dominated solutions near the reference point, and obtains the train operation adjustment plan corresponding to the preference, which is characterized by comprising the following steps:

[0007] Step 1: Determine the number of Pareto front segmentation regions and calculate the non-dominated solutions at the region boundaries;

[0008] Step 2: Based on the non-dominated solutions of the Pareto frontier segmentation area boundary, the dispatcher sets the reference point and the number of preferred solutions;

[0009] Step 3: Follow the Reference Points P ref The direction is calculated corresponding to the preferred non-dominated solution.

[0010] The present invention also discloses a non-volatile storage medium, characterized in that the non-volatile storage medium includes a stored program, wherein when the program is running, the device where the non-volatile storage medium is located is controlled to execute the above method.

[0011] The present invention also discloses an electronic device, characterized in that it comprises a processor and a memory; the memory stores computer-readable instructions, and the processor is used to execute the computer-readable instructions, wherein the computer-readable instructions execute the above method when they are executed. Beneficial Effects

[0012] By allowing the dispatching decision makers to participate in the solution process and interactively provide preference information, it is not necessary to calculate all non-dominated solutions, thus improving the search efficiency on the Pareto frontier. This method can effectively integrate the dispatcher's preferences for different optimization indicators of the adjustment plan into the interactive multi-objective optimization process, efficiently obtain the train operation adjustment plan, realize human-machine collaboration in train dispatching, and improve the level of intelligent dispatching command. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 The present invention is a flowchart of an interactive multi-objective optimization method for adjusting train operation plan.

[0014] Figure 2 This is a schematic diagram of the first region segmentation after obtaining the non-dominated solution of the region boundary.

[0015] Figure 3 This is a schematic diagram of the Pareto front after completing the regional segmentation.

[0016] Figure 4 This is a schematic diagram of the preferred non-dominated solution obtained after setting the reference point.

[0017] Figure 5 It is a schematic diagram of the preferred non-dominated solution obtained by using the interactive multi-objective optimization method in a specific delay scenario. DETAILED DESCRIPTION

[0018] An interactive multi-objective optimization method for train operation plan adjustment is mainly divided into two stages. In the first stage, the target space of the multi-objective optimization problem of operation adjustment is segmented to obtain the area of ​​interest to the dispatcher. In the second stage, the dispatcher specifies a reference point and searches for some non-dominated solutions near the reference point to obtain the train operation adjustment plan under the corresponding preference.

[0019] An interactive multi-objective optimization method for train operation plan adjustment, such as Figure 1 As shown, the following steps are included:

[0020] Step 1: Determine the number of Pareto front segmentation regions and calculate the non-dominated solutions at the region boundaries.

[0021] Step 1.1: The Pareto front segmentation region is obtained by calculating the boundary non-dominated solution and other uniformly distributed non-dominated solutions. For the dual-objective optimization problem in the train operation plan adjustment problem, the following two optimization objectives are considered. The first optimization objective is to minimize the total delay time of train arrival and departure, as shown in formula (1), and the second optimization objective is to minimize the frequency of train operation plan adjustment, which is obtained by calculating the total number of adjustments, as shown in formula (2).

[0022] (1)

[0023] (2)

[0024] In the formula, For trains i Actual arrival station j Time (a means arrival), For trains i Actual departure from the station j Time (d means leaving), Scheduled train diagram i Arrival at the station j Time (a means arrival), Trains for the planned operation diagram i Leaving the station j Time (d means leaving), T and Jare the set of trains and the set of stations respectively, and sgn(·) is the sign function. is the decision vector, For decision-making space.

[0025] Step 1.2: Set the upper limit of the number of divisions in the Pareto front region N 1. Solve under driving constraints. First, calculate the boundary non-dominated solution. , , weight parameter ,in, and See equations (1) and (2), the boundary non-dominated solution and Different and The weighted non-dominated solution. and The corresponding normalized target value is used to initialize the set of line segments composed of the non-dominated solution Among them, the line segment , the normalized objective function .

[0026] Step 1.3: Select the set of line segments that the current non-dominated solution consists of L The longest line segment L ab With ideal point The corresponding area is recorded as S max , the ideal points are minimized by calculating and We get: i is the objective function index, and the non-dominated solutions of the region boundaries are: and .

[0027] Step 1.4: Use the augmented weighted Chebyshev method to obtain the non-dominated solution .

[0028] The optimization objectives of the augmented weighted Chebyshev method are as follows:

[0029] (3)

[0030] In the formula, is the optimization target, i is the weight and the objective function index. Based on the non-dominated solution and , determine the weight , , augmented parameter .

[0031] Since equation (3) contains the nonlinear function max, the model needs to be linearized. Define temporary variables , then formula (3) is:

[0032] (4)

[0033] (5)

[0034] According to equations (4)-(5), we can obtain the non-dominated solution: .

[0035] Step 1.5: Through non-dominated solutions , the original area S max Split into regions S a and Region S b .like Figure 2 shown.

[0036] If the non-dominated solution If it is repeated with the non-dominated solution obtained in the previous calculation process, it means that there is no non-dominated solution in this area and it cannot be further segmented.

[0037] If there is no repetition, then the ideal point and and The original area S max Split into S a , ideal point and and The original area S max Split into S b . Update the set of line segments composed of non-dominated solutions L .gather L Increase L ax* , L x*b , L ax* for and The line segment formed by the normalized target value , L x*b for and The line segment formed by the normalized target value .

[0038] Step 1.7: Delete the line segment set LThe longest line segment in L ab .

[0039] Step 1.8: Determine whether the number of divisions in the current Pareto front region meets the upper limit N 1. If the upper limit is reached, proceed to step 1.9. If the upper limit is not reached, proceed to step 1.3 and continue region segmentation.

[0040] Step 1.9: Complete the first stage of calculation, and get at most N 1+2 non-dominated solutions, dividing the Pareto front into N 1+1 areas. Figure 3 The middle is the case where the number of divisions is 3.

[0041] Step 2: Based on the non-dominated solutions of the Pareto front segmentation region boundary, the dispatcher sets the reference point and the number of preferred solutions.

[0042] Step 2.1: Target N 1 area, the dispatcher selects an area according to personal preference S p The boundary non-dominated solutions corresponding to this region are and .

[0043] Step 2.2: Dispatcher in the area S p Setting the reference point , must meet , .

[0044] Step 2.3: Set the preferred number of solutions N 2. It represents the number of non-dominated solutions that the dispatcher hopes to obtain near the reference point.

[0045] Step 3: Follow the Reference Points P ref The direction is calculated corresponding to the preferred non-dominated solution.

[0046] Step 3.1: Based on the reference point P ref , determine the weight , According to equations (4)-(5), we get the non-dominated solution .

[0047] Step 3.2: Establish the corresponding optimization models M1 (Equations (6)-(7)) and M2 (Equations (8)-(9)) of the improved augmented ε constraint method.

[0048] (6)

[0049] (7)

[0050] (8)

[0051] (9)

[0052] In the formula, the coefficient , is a non-negative auxiliary variable, and To constrain the right-hand side parameters, respectively control the optimization objectives and Set , , auxiliary variable flag = 0.

[0053] Step 3.3: If , solve model M1 and obtain the non-dominated solution of the problem .set up Otherwise, proceed to step 3.4.

[0054] Step 3.4: Determine whether the non-dominated solutions of the current solution model M1 and M2 satisfy N 2-1 Quantity requirement, if met, proceed to step 3.8. Otherwise, proceed to step 3.5.

[0055] Step 3.5: If And flag = 0, solve M2 and get the non-dominated solution of the problem .set up Otherwise, proceed to step 3.7.

[0056] Step 3.6: If , then flag = 1.

[0057] Step 3.7: Determine whether the non-dominated solutions of the current solution model M1 and M2 satisfy N 2-1 Quantity requirement, if met, proceed to step 3.8. Otherwise, proceed to step 3.3.

[0058] Step 3.8: Complete the second stage calculation. N 2 preferred non-dominated solutions. Figure 4 As shown in the figure. N 2= ​​3. “★” is the reference point P ref , “*” is the preferred non-dominated solution obtained.

[0059] Examples of embodiments of the present invention are as follows:

[0060] This example uses some stations on the main line of a passenger-dedicated platform and some trains on the down line as model parameters. The daily scheduled time is the time (in minutes) that the train originally planned to enter and leave the station before adjustment. Considering that some trains have late arrivals and departures, the upper limit of the number of Pareto frontier area splits is set. N 1= 3, the number of preferred solutions N 2=5, the dispatcher manually sets the preferred area and reference point. Under the model parameters of this application scenario, CPLEX can be used to solve the problem. The running results are as follows: Figure 5 As shown in the figure, we can see that a non-dominated solution that satisfies the dispatcher's preference is obtained.

[0061] The interactive multi-objective optimization method for adjusting the train operation plan of the present invention is aimed at the multi-objective optimization model for adjusting the train operation plan. By allowing the dispatching decision maker to participate in the solution process, the preference information is interactively provided, and all non-dominated solutions do not need to be calculated, thereby improving the search efficiency on the Pareto front. The method can effectively integrate the dispatcher's preferences for different optimization indicators of the adjustment plan into the interactive multi-objective optimization process, efficiently obtain the train operation adjustment plan, realize the human-machine collaboration of train dispatching, and improve the intelligent level of dispatching command.

[0062] The above shows and describes the basic principles, main features and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The above embodiments and descriptions only describe the principles of the present invention. The present invention may be subject to various changes and improvements without departing from the spirit and scope of the present invention. These changes and improvements fall within the scope of the present invention. The scope of protection claimed by the present invention is defined by the attached claims and their equivalents.

Claims

1. An interactive multi-objective optimization method for train operation plan adjustment includes two stages: in the first stage, the target space of the multi-objective optimization problem of operation adjustment is segmented to obtain the area of ​​interest to the dispatcher; In the second stage, the dispatcher specifies a reference point, searches for some non-dominated solutions near the reference point, and obtains the train operation adjustment plan corresponding to the preference, which is characterized by including the following steps: Step 1: Determine the number of Pareto front segmentation regions and calculate the non-dominated solutions at the region boundaries; Step 2: Based on the non-dominated solutions of the Pareto frontier segmentation area boundary, the dispatcher sets the reference point and the number of preferred solutions; Step 2.1: Target N 1 area, the dispatcher selects an area according to personal preference S p The boundary non-dominated solutions corresponding to this region are and ; Step 2.2: Dispatcher in the area S p Setting the reference point , must meet , ;in: is the total delay time of train arrival and departure, Adjust frequency for train operation schedule; Step 2.3: Set the preferred number of solutions N 2; represents the number of non-dominated solutions that the dispatcher hopes to obtain near the reference point; Step 3: Follow the Reference Points P ref The direction is calculated corresponding to the preferred non-dominated solution.

2. The interactive multi-objective optimization method for adjusting train operation plan according to claim 1 is characterized by: Determining the number of Pareto front segmentation regions and calculating the non-dominated solutions of the region boundaries include the following: Step 1.1: The Pareto front segmentation region is obtained by calculating the boundary non-dominated solution and other uniformly distributed non-dominated solutions. For the dual-objective optimization problem in the train operation plan adjustment problem, the following two optimization objectives are considered. The first optimization objective is to minimize the total delay time of train arrival and departure, as shown in formula (1). The second optimization objective is to minimize the frequency of train operation plan adjustment, which is obtained by calculating the total number of adjustments, as shown in formula (2): （1） （2） In the formula, For trains i Actual arrival station j time, a means arrival, For trains i Actual departure from the station j time, d means leaving, Scheduled train diagram i Arrival at the station j time, a means arrival, Trains for the planned operation diagram i Leaving the station j time, d means leaving, T and J are the set of trains and the set of stations respectively, sgn(·) is the sign function; is the decision vector, for decision-making space; Step 1.2: Set the upper limit of the number of divisions in the Pareto front region N 1. Solve the problem under driving constraints. First, calculate the boundary non-dominated solution. , , weight parameter ,in, and See equations (1) and (2), the boundary non-dominated solution and Different and Weighted non-dominated solutions; boundary non-dominated solutions and The corresponding normalized target value is used to initialize the set of line segments composed of the non-dominated solution , where the line segment , the normalized objective function ; Step 1.3: Select the set of line segments that the current non-dominated solution consists of L The longest line segment L ab With ideal point The corresponding area is recorded as S max , the ideal points are minimized by calculating and We get: i is the objective function index, and the non-dominated solutions of the region boundaries are: and ; Step 1.4: Use the augmented weighted Chebyshev method to obtain the non-dominated solution ; The optimization objectives of the augmented weighted Chebyshev method are as follows: （3） In the formula, is the optimization target, i is the weight and objective function index; based on the non-dominated solution and , determine the weight , , augmented parameter ; Since equation (3) contains the nonlinear function max, the model needs to be linearized. Define the temporary variable , then formula (3) is: （4） （5） According to equations (4)-(5), we can obtain the non-dominated solution: ; Step 1.5: Through non-dominated solutions , the original area S max Split into regions S a and Region S b ; If the non-dominated solution If it is repeated with the non-dominated solution obtained in the previous calculation process, it means that there is no non-dominated solution in the area and it cannot be further segmented; If there is no repetition, the ideal point and and The original area S max Split into regions S a , ideal point and and The original area S max Split into regions S b ; Update the set of line segments composed of non-dominated solutions L ;gather L Increase L ax* , L x*b , L ax* for and The line segment formed by the normalized target value , L x*b for and The line segment formed by the normalized target value ; Step 1.6: Delete the line segment set L The longest line segment in L ab ; Step 1.7: Determine whether the number of divisions in the current Pareto front region meets the upper limit N 1. If the upper limit is reached, proceed to step 1.8; if the upper limit is not reached, proceed to step 1.3 and continue region segmentation; Step 1.8: Complete the first stage of calculation and get at most N 1+2 non-dominated solutions, dividing the Pareto front into N 1+1 areas.

3. The interactive multi-objective optimization method for adjusting train operation plan according to claim 2 is characterized by: According to the reference point P ref The preferred non-dominated solutions corresponding to the direction calculation include the following: Step 3.1: Based on the reference point P ref , determine the weight , According to equations (4)-(5), we get the non-dominated solution ; Step 3.2: Establish the optimization model M1 corresponding to the improved augmented ε constraint method, i.e., equations (6)-(7), and model M2, i.e., equations (8)-(9); （6） （7） （8） （9） In the formula, the coefficient , is a non-negative auxiliary variable, and To constrain the parameters on the right, respectively control the optimization objectives and The upper limit of set up , , auxiliary variable flag = 0; Step 3.3: If , solve model M1 and obtain the non-dominated solution of the problem ; set up , otherwise, proceed to step 3.4; Step 3.4: Determine whether the non-dominated solutions of the current solution model M1 and M2 satisfy N 2-1 Quantity requirements, if met, proceed to step 3.8; otherwise, proceed to step 3.5; Step 3.5: If And flag = 0, solve M2 and get the non-dominated solution of the problem ;set up ; Otherwise, proceed to step 3.7; Step 3.6: If , then flag = 1; Step 3.7: Determine whether the non-dominated solutions of the current solution model M1 and M2 satisfy N 2-1 Quantity requirements, if met, proceed to step 3.8; otherwise, proceed to step 3.3; Step 3.8: Complete the second stage calculation; get N 2 preferred non-dominated solutions.

4. A non-volatile storage medium, characterized in that: The non-volatile storage medium includes a stored program, wherein the program controls the device where the non-volatile storage medium is located to execute the method according to any one of claims 1 to 3 when the program is executed.

5. An electronic device, characterized in that: It comprises a processor and a memory; the memory stores computer-readable instructions, and the processor is used to execute the computer-readable instructions, wherein the computer-readable instructions execute the method described in any one of claims 1 to 3 when executed.

Images