A method for scheduling machine failures based on the combination of layout transfer A-star algorithm and heuristic rules

Abstract

A method for planning and scheduling a reversing machine that combines the A-star algorithm for layout transfer and heuristic rules belongs to the field of shipborne weapon equipment support technology. First, the reversing machine problem is decoupled into two sub-problems: layout transfer path search and scheduling, and a mathematical programming model is established; second, a station transfer map and a dispatch trajectory library are established; third, a node expansion method and a blocking detection mechanism are set, and a heuristic function is set to form the A-star algorithm for layout transfer, so as to realize layout transfer path search; fourth, a heterogeneous entity collaborative dispatching method based on a delayed dispatching strategy is established based on the dispatch trajectory library, and corresponding equipment allocation heuristic scheduling rules are set to realize the scheduling and scheduling of transfer tasks extracted from the layout transfer path, that is, setting a delayed dispatching strategy and heuristic rules to realize scheduling. The present invention is applicable to a delayed collision avoidance strategy for collaborative collision avoidance of multiple types of dispatching entities, and realizes the planning of a reversing machine scheduling scheme that simultaneously considers limited resource allocation and collaborative dispatch of multiple types of dispatching entities.

Description

Technical Field

[0001] The invention belongs to the technical field of shipborne weapon equipment support, and relates to a reverse aircraft scheduling planning method combining a layout transfer A-star algorithm with heuristic rules. Background Art

[0002] Aircraft carriers are often tightly packed within a hangar. If a transfer aircraft is blocked by multiple aircraft, the blocked aircraft must be moved in a specific order to achieve the desired transfer. This presents three major challenges. First, aircraft transfers within the hangar must be accomplished with the aid of tractors, requiring coordinated movement between two heterogeneous transfer entities: the tractors and the traction system. Second, when aircraft are too densely packed within the hangar, consideration must be given to temporarily moving some aircraft to the deck to provide adequate space. Third, when transferring between the hangar and the flight deck, coordinated scheduling of two types of support equipment, the tractors and elevators, is necessary. Existing aircraft scheduling planning methods for ship-based environments often overlook the need for coordinated collision avoidance among various transfer entities or ignore other aircraft that could be blocking the movement of the target aircraft. For example, the prior art [Chinese Invention Patent CN202411075892.1: A Method for Scheduling Aircraft Operations on Offshore Platforms] fails to consider the coordinated collision avoidance between aircraft and entities such as tractors during the transfer process. The existing technology [a method and device for collaborative scheduling of aircraft maintenance service support and outbound transfer in Chinese invention patent CN202411109844.X] can only realize inter-station transfer task planning when the target aircraft is not blocked by other aircraft.

[0003] Therefore, developing an algorithm to solve the inverted machine problem is of great significance to improving the efficiency of ship-based equipment transfer. Summary of the Invention

[0004] To solve the above technical problems, the present invention proposes a machine switching scheduling planning method that combines the layout transfer A-star algorithm with heuristic rules, which can realize the planning of machine switching scheduling schemes that simultaneously considers limited resource allocation and coordinated transportation of multiple types of entities.

[0005] In order to achieve the above object, the technical solution adopted by the present invention is:

[0006] A method for scheduling and planning a reverse machine by combining a layout transfer A-star algorithm with heuristic rules comprises the following steps:

[0007] Step 1: Decouple the downtime problem into two sub-problems: routing and scheduling, and establish a corresponding mathematical programming model.

[0008] Step 2: Set the station connectivity relationship based on the ship-based environment station information, and establish a station transfer map and transportation trajectory library;

[0009] Step 3: Set the node expansion method and congestion detection mechanism, set the heuristic function, form the layout transfer A-star algorithm, and realize the layout transfer path search;

[0010] Step 4: Relying on the transportation trajectory library, establish a heterogeneous entity collaborative transportation method based on the delayed transportation strategy, set the corresponding equipment allocation heuristic scheduling rules, and realize the scheduling of transfer tasks extracted from the layout transfer path.

[0011] The beneficial effects of the present invention are:

[0012] The present invention decouples the aircraft transfer problem into two stages for the first time: layout transfer route search and scheduling, and establishes corresponding mathematical programming models for each sub-problem. Facing the ship-based environment, the present invention provides a station transfer map and a trajectory library and a blocking list, thereby converting the aircraft transfer sequence planning problem into a layout transfer path search problem, and improves the A-star algorithm to provide a corresponding problem-solving method. Subsequently, the present invention extracts key processing procedures and processing machines based on the characteristics of the transfer tasks during the aircraft transfer process, converts the scheduling problem into a flexible job shop scheduling problem, extracts the transfer task priority based on the layout transfer path, sets heuristic rules and develops a delayed collision avoidance strategy suitable for collaborative collision avoidance of multiple types of transport entities, and finally realizes the planning of aircraft transfer scheduling solutions that simultaneously considers limited resource allocation and collaborative transportation of multiple types of transport entities. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 Flowchart of the present invention.

[0014] Figure 2 This is a reference hangar location diagram for the present invention.

[0015] Figure 3 This is the reference deck station diagram for the present invention.

[0016] Figure 4 Schematic diagram of the reversing task in the embodiment.

[0017] Figure 5 This is the trajectory library of the hangar traction system in the embodiment.

[0018] Figure 6 This is the trajectory library of the deck traction system in the embodiment.

[0019] Figure 7 This is the hangar tractor track library in the embodiment.

[0020] Figure 8 This is the deck tractor trajectory library in the embodiment.

[0021] Figure 9 It is the starting arrangement in the arrangement transfer route in the embodiment.

[0022] Figure 10 This is the arrangement after the first conversion in the arrangement transfer route in the embodiment.

[0023] Figure 11 This is the arrangement after the second conversion in the arrangement transfer route in the embodiment.

[0024] Figure 12 This is the arrangement after the third conversion in the arrangement transfer route in the embodiment.

[0025] Figure 13 This is the arrangement after the fourth conversion in the arrangement transfer route in the embodiment.

[0026] Figure 14 This is the arrangement after the fifth conversion in the arrangement transfer route in the embodiment.

[0027] Figure 15 This is the arrangement after the 6th conversion in the arrangement transfer route in the embodiment.

[0028] Figure 16 This is the arrangement after the 7th conversion in the arrangement transfer route in the embodiment.

[0029] Figure 17 This is the arrangement after the 8th conversion in the arrangement transfer route in the embodiment.

[0030] Figure 18 This is a Gantt chart for scheduling downtime tasks planned in the embodiment. DETAILED DESCRIPTION

[0031] The present invention will be further described below with reference to specific embodiments.

[0032] A method for scheduling and planning a reverse machine by combining a layout transfer A-star algorithm with heuristic rules comprises the following steps:

[0033] Step 1: Decouple the downtime problem into two sub-problems: routing and scheduling, and establish the corresponding mathematical programming model. Specifically:

[0034] Step 1-1: Decouple the downtime problem into the layout transfer route search problem and the scheduling problem;

[0035] In the layout transfer route search phase, this embodiment uses a vector consisting of all occupied station numbers to represent a layout, and the position of each element in the vector corresponds to the aircraft number at its station. Figure 2 Hangar positions shown and Figure 3 The ship-based environment of the deck station shown is Figure 5The aircraft relocation task is scheduled and planned as shown in the figure. At this time, the relocation task can be expressed as the layout [137 138 143 144 149 152 158 159 160 161 162 163 165 166 167 169 171172 173 175 176] is converted to the layout [17731 143 144 149 152 158 159 160 161 162 163 165166 167 169 171 172 173 175 176]. At this time, the layout conversion is achieved by transferring one aircraft at a time, and the aircraft relocation task is achieved through multiple intermediate layouts. The layout transfer process is called the layout transfer path.

[0036] After obtaining the layout transfer path, a series of aircraft transfer tasks are extracted and scheduled based on the layout transition sequence. This method considers each aircraft transfer task as a job, and resource constraints such as tractors and elevators as processing machines. The scheduling problem is formulated as a flexible job shop scheduling problem. Based on the characteristics of the transfer tasks, the following five key processing steps are extracted: ① Deck tractor transfer to the front of the carrier aircraft; ② Deck carrier aircraft transfer to the target station; ③ Elevator hangar-deck transfer; ④ Hanger tractor transfer to the front of the carrier aircraft; ⑤ Hanger carrier aircraft transfer to the target station. Each aircraft transfer task can be viewed as a series of several steps: hangar aircraft transfer tasks are ③→①→②; deck aircraft transfer tasks are ③→④→⑤; hangar-to-deck aircraft transfer tasks are ③→①→②→③→④→⑤; and deck-to-hangar aircraft transfer tasks are ③→④→⑤→③→①→②.

[0037] Step 1-2: Establish a mathematical programming model for the layout transfer path search problem;

[0038] For any aircraft reversal task, the number of aircraft in the task is recorded as , , No. The aircraft number is recorded as , the set of all aircraft is recorded as The initial and target layouts of the machine reversal task are 、 , the starting and ending layouts of the reversing process are 、 , the boundary constraints of the layout transfer path search are shown in formula (1):

[0039] (1)

[0040] During the transition between two adjacent arrays, no aircraft can be transferred to an occupied station. The corresponding constraints are shown in formula (2):

[0041] (2)

[0042] in, Indicates aircraft In the Station number after secondary array transfer; Indicates the Arrangement after secondary arrangement transfer ;

[0043] During the transition between two adjacent arrangements, the transfer aircraft cannot be blocked. The corresponding constraints are shown in formula (3):

[0044] (3)

[0045] in, Indicates position Is the time blocked? If so, ,otherwise ;

[0046] During the transition between any two adjacent layouts, if the elevator station is occupied, the aircraft cannot enter the elevator station on the other level. The corresponding constraints are shown in formula (4):

[0047] (4)

[0048] in, Indicates elevator station; express On the other floor, corresponding stations, in this case, stations 53, 54, and 55 are for the deck elevators, and stations 177, 178, and 179 are for the hangar elevators. and Indicates aircraft and In the The station number after the second array transfer, Indicates the Arrangement after secondary arrangement transfer ;

[0049] For the array transfer task, we hope that the total transfer time is as short as possible, the number of aircraft transfers is as small as possible, and the cross-level transfer of aircraft is minimized. The objective function is recorded as , which is shown in formula (5):

[0050] (5)

[0051] in, represents the transit time penalty coefficient; represents the penalty coefficient for the number of transshipments; represents the penalty coefficient for cross-layer transfer; Indicates the number of layout conversions; Indicates the number of aircraft currently deployed; Indicates aircraft from Transport to trajectory running time; Indicates position and Are they at the same level? If yes, ,otherwise .

[0052] Finally, the mathematical model of the layout transfer problem is obtained as shown in formula (6):

[0053] (6)

[0054] in, represents the objective function in the process of searching for the layout transfer path;

[0055] Step 1-3: Establish a mathematical programming model for the scheduling problem;

[0056] Step 1-3-1: Define scheduling parameters;

[0057] use Indicates the The first The processing type is ; Indicates that all types are A collection of processing steps, ; Represents the set of all processing steps, The number of available machines in the scheduling process is recorded as , ; The number of available hangar stations is recorded as , ; The number of available deck stations is recorded as , .

[0058] Step 1-3-2: Establish process processing constraints;

[0059] Process Need to After execution, the corresponding constraints are shown in formula (7):

[0060] (7)

[0061] in, Indicates the process In the machine The processing start time on the Indicates the process In the machine The processing end time;

[0062] Process The completion time must be greater than the sum of its start time and the required processing time. The corresponding constraint is shown in formula (8):

[0063] (8)

[0064] in, Indicates the process In the machine The processing start time on the Indicates the process In the machine The processing end time on the Indicates the process In the machine Required processing time; is a positive number; Indicates the process Is it on the machine If ,otherwise ;

[0065] Step 1-3-3: Establish machine usage constraints;

[0066] Any process is assigned to only one machine, and the corresponding constraints are shown in formula (9):

[0067] (9)

[0068] in, Indicates the process Is it on the machine If ,otherwise ;

[0069] When a tractor is selected in the tractor transfer process, the corresponding carrier-based aircraft needs to be transported to the target station using the tractor. The corresponding constraints are shown in formula (10):

[0070] (10)

[0071] in, Indicates the process Is it on the machine If ,otherwise ; Indicates the process Is it on the machine If ,otherwise ;

[0072] Two operations using the same tractor must be transported to the target station before the second operation can use the tractor. The corresponding constraints are shown in formula (11):

[0073] (11)

[0074] in, Indicates the process In the machine The processing start time on the Indicates the process In the machine The processing end time on the is a positive number; Indicates the process Is it in process Using the machine After using the machine ,if , otherwise ;

[0075] Step 1-3-4: Establish station occupancy constraints;

[0076] Any process It is only assigned to one target station, and the corresponding constraints are shown in formula (12):

[0077] (12)

[0078] in, express Whether it is by position Transport to ,if , otherwise ;

[0079] If the homework and Serving the same aircraft and aircraft transfer process The starting point and The end points are the same, then The start time should be after The end time of , the corresponding constraints are shown in formula (13):

[0080] (13)

[0081] in, Indicates the process In the machine The processing start time on the Indicates the process In the machine The processing end time on the Indicates the process Whether it is by position Transport to ,if ,otherwise ; Indicates the process Whether it is by position Transport to ,if , otherwise ; Indicates homework and Are they serving the same aircraft? If so, ,otherwise ; is a symbolic function, when hour ,when hour when hour ; 、 、 、 Number any station;

[0082] When the current station of another aircraft is selected as the target station, it is necessary to ensure that the subsequent aircraft can enter the station only after the previous aircraft leaves. In particular, if the target station is the elevator station or passes the elevator station, it is necessary to wait until the elevator returns to the corresponding station before it can be transferred, as shown in formula (14):

[0083] (14)

[0084] in, Indicates the process In the machine The processing start time on the Indicates the process In the machine The processing end time on the is a sufficiently large positive number; express Is it Use station Use the station later ,if , otherwise ; is the elevator transfer time, ;

[0085] The aircraft and the tractor are collectively referred to as transfer entities. During the transfer process, the transfer trajectories of any two transfer entities must ensure coordinated collision avoidance, as shown in formula (15):

[0086] (15)

[0087] in, 、 Represents the process and The selected transport trajectory; 、 Respectively in any Always on track 、 Location information; , represents the safe distance between two transport entities, 、 Transport Entity 、 The circumcircle radius of For safety margin; when transporting entities For tractor , is the radius of the circumcircle of the tractor, ; When transporting entities For traction system ,in is the radius of the circumscribed circle of the traction system, .

[0088] During the transportation process, we hope that the overall transit time will be minimized. The objective function is recorded as , which is shown in formula (16):

[0089] (16)

[0090] Step 1-3-5: Establish a mathematical programming model for scheduling;

[0091] Finally, the combined optimization model constructed for scheduling is shown in formula (17):

[0092] (17)

[0093] in, It is the objective function in the scheduling task.

[0094] Step 2: Set the station connectivity relationship based on the ship-based environment station information, and establish a station transfer map and transportation trajectory library; specifically:

[0095] Step 2-1: Build a station transfer map;

[0096] The stations on the ship-based platform can be divided into three categories: hangar, deck, and elevator. Connectivity is set according to the characteristics of these stations to construct a station transfer map.

[0097] Hangar: Aircraft transfers are mainly carried out in the hangar, and each station is connected to all other hangar stations.

[0098] Deck: The deck environment is relatively open, and each station is only connected to the elevator station on the deck.

[0099] Elevator: In addition to being connected to the stations on the corresponding levels, the corresponding stations of the elevators between two levels must be connected.

[0100] For two stations that are far apart and can be transferred through the middle station, the present invention performs pruning operations on the hangar connectivity to reduce the search space. The specific pruning principle is set according to the station orientation and the distance between stations. hangar stations and In a ship-based environment with multiple deck stations, the station transfer map includes elements, denoted as , ,in For the position Connect all station numbers.

[0101] Step 2-2: Build a transportation track library;

[0102] Step 2-2-1: Establish rail depots for each transport entity;

[0103] According to the processing procedures extracted in step 1-1, procedures ① and ④ require traction system transfer tracks, and procedures ② and ⑤ require tractor transfer tracks. For the traction system, the carrier-based aircraft between any two stations adopt different transfer paths. Therefore, multiple transfer tracks are provided for the two stations that can be connected on the station transfer map. The track library is recorded as , its composition is shown in formula (18):

[0104] (18)

[0105] in, For standing position and Intermediate Priority track; For standing position and The number of trajectories between 、 Indicates the position transfer to any position on the map; Indicates the number of hangar stations, ; Indicates the number of deck stations, ; Indicates the station transfer map Center and Position Connect all station numbers. The hangar traction system trajectory and deck traction system trajectory in the corresponding traction system trajectory library are as follows: Figure 5 and Figure 6 shown.

[0106] For the tractor, it is necessary to ensure that it can transfer between any two stations. The corresponding trajectory library contains the transfer trajectory between any two stations, which is recorded as , and with The hangar tractor track and deck tractor track in the corresponding constructed tractor track library are as follows: Figure 7 and Figure 8 shown.

[0107] Step 2-2-2: Create a blocking list for each transport entity;

[0108] In order to determine whether the transfer between two stations is feasible, a blocking list must be established. The blocking list contains all the station numbers of the blocked transfer trajectory. In order to distinguish between a transfer trajectory that is not blocked by any station and a transfer trajectory that does not exist, the present invention adds an element "0" to the blocking list of the available trajectory. Its composition is shown in formula (19):

[0109] (19)

[0110] in, To record all blocked stations and A vector consisting of the station numbers for inter-transfer.

[0111] Since the tractor can pass under the wings, the triangle area formed by the aircraft wheels is considered an obstacle in the tractor trajectory planning. Therefore, the tractor will not be blocked when transferring between any stations. However, the tractor can also choose different transportation trajectories under different arrangements. The corresponding blocking list is constructed and recorded as ,and Have the same structure.

[0112] Step 3: Set the node expansion method and blocking detection mechanism, set the heuristic function, form the layout transfer A-star algorithm, and implement layout transfer path search; specifically:

[0113] Step 3-1: Set up node expansion mode and congestion detection mechanism;

[0114] The aircraft reversal problem uses the layout as the path node to search, and the expansion method is set to move one aircraft according to the station transfer map to form a new layout and complete one expansion. , as the aircraft cannot be transferred to Middle position, for this reason it will be excluded first before each expansion and Overlapping stations, the number of expansions per layout will be ,in Represents a vector The number of elements in .

[0115] According to different deployment forms, the aircraft adopts different transportation trajectories to achieve the transfer between stations. No. Expand to form a column record , any aircraft The corresponding station is recorded as ,airplane From the station Transfer to station When the present invention is based on and When there is a transport track and there is no overlapping station between the blocking list and the currently occupied station, it is determined to be passable, that is, for , , and ,but .

[0116] Step 3-2: Set the objective function;

[0117] In the layout transfer A-star algorithm, it is necessary to set the objective function to guide the path search direction. The objective function is shown in formula (20):

[0118] (20)

[0119] in, Indicates expansion to Post-objective function value; Indicates expansion to the required expenditure; Indicates the layout Estimated cost to achieve target layout;

[0120] Set to the time required to switch to the current layout, and add a penalty for the number of transfers and a penalty for cross-layer transfers. The calculation formula is shown in (21):

[0121] (twenty one)

[0122] in, To expand to Britain Time required, represents the transit time penalty coefficient; represents the penalty coefficient for the number of transshipments; represents the penalty coefficient for cross-layer transfer; Indicates the number of aircraft currently deployed; Indicates aircraft from Transport to Transportation track running time; Indicates position and Are they at the same level? If yes, ,otherwise .

[0123] Set to the estimated cost of transporting all aircraft in the current array to the target station. When there is a transport track between the current station and the target station, the estimated cost is the transport time of the transport track. Due to the pruning of connectivity, some aircraft stations do not have a transport track to the target station. In such cases, the cost is estimated based on the distance between stations and the operating speed. The calculation formula is shown in (22):

[0124] (twenty two)

[0125] in, Indicates the number of aircraft currently deployed; Indicates position and Is the time blocked? If so, ,otherwise ; For aircraft On target Target position in Indicates aircraft from Transport to Transportation track running time; is the penalty coefficient for the non-existence of the transportation trajectory, ; is the maximum operating speed of the traction system, ;

[0126] Step 3-3: Arrange transfer route search;

[0127] After determining the objective function, an unexplored path node pool is established, containing all unexpanded path nodes. Initially, the initial layout is added to the unexplored path node pool, and the layout with the lowest objective function value is selected as the expanded path node. A reachable layout is obtained based on the layout transfer map to form a reachable path node. Unexplored path nodes from the obtained reachable path nodes are then placed back into the unexplored path node pool. The current path node is removed from the unexplored path node pool, and the path node with the lowest objective function value is selected from the unexplored path node pool for further expansion. This process is repeated until the target layout is reached.

[0128] Step 4: Set the delayed transportation strategy and heuristic rules to implement scheduling;

[0129] Step 4-1: Establish a delayed transportation strategy under conditions of station blocking and multiple optional trajectories;

[0130] In order to achieve collaborative collision avoidance, the present invention has developed a collaborative dispatching method for multiple dispatching entities based on a delayed collision avoidance strategy. The collaborative dispatching method for multiple dispatching entities first retrieves the time and space position information of the selected trajectory and the arranged trajectory from the trajectory library, and then determines whether there is a potential collision within the time interval when the current trajectory overlaps with other trajectories. If there is a potential collision, the dispatching time of the current dispatching entity is delayed. The above judgment is repeated every few seconds until there is no potential collision between the transfer time intervals of the current transfer entity and other transfer entities.

[0131] The principle of selecting the trajectory in the trajectory library for any process should be: ,but ,in Although the priority of the transfer task has been determined by the layout transfer path, low-priority tasks can be executed in advance to improve the efficiency of the transfer. At this time, the low-priority transfer task may block the high-priority transfer task. Priority over process , and the track has been assigned and , by whether it satisfies To detect whether a blockage occurs. If a blockage occurs, the present invention will further determine whether If so, then Postponed until , and continue to achieve coordinated transportation through delayed transportation strategies.

[0132] Step 4-2: Heuristic rule setting;

[0133] Step 4-2-1: Setting the rules for selecting a tractor;

[0134] The transfer path has determined the priority of each task, so in steps 1-3, formulas (8)-(14) 、 and These are all known quantities, and only the scheduling rules for the machines used in each process and the task start timing need to be set.

[0135] If multiple tractors can arrive at the corresponding parking space before the aircraft transfer begins, the tractor with the shortest required time is selected. Specifically, first record the set of all available tractor numbers as ,for ,if Make , then the set of tractors that meet this condition is represented as , selected tractor It should be as shown in formula (23):

[0136] (twenty three)

[0137] in, Indicates the process In the machine Required processing time;

[0138] The start time of the corresponding process should be as shown in formula (24):

[0139] (twenty four)

[0140] in, Indicates the process In the machine The processing start time on the Indicates the process In the machine The processing start time on the Indicates the process In the machine Required processing time; It is a safe interval. ;

[0141] If no tractor meets the above conditions, select the tractor from the collection of all tractors. The tractor that can reach the corresponding station earliest is selected. The selection rule is shown in formula (25):

[0142] (25)

[0143] in, Indicates the process In the machine The processing end time on the

[0144] Step 4-2-2: Setting the elevator selection rules;

[0145] When the target station is at the elevator or the transport track passes through the elevator, the elevator is needed. The elevator is determined based on the target station and the blocking list. If , then the position and The elevator is needed for transportation between stations. Since the elevator is bound to the station, there is no need to choose the elevator. If the elevator It is possible to arrive at the corresponding station before the aircraft transfer begins. The start time of the elevator transfer process is shown in formula (26):

[0146] (26)

[0147] in, Indicates the process In the machine The processing start time on the Indicates the process In the machine The processing start time on the Indicates the process In the machine Required processing time; It is a safe interval. ;

[0148] Otherwise, the start time will be the time when the elevator is responsible for processing the previous process. The end time is as shown in formula (27):

[0149] (27)

[0150] in, Indicates that the machine Any processing operation performed on End time;

[0151] Step 4-2-3: Set the aircraft transfer start time;

[0152] When an aircraft needs to be dispatched multiple times, the low-priority tasks must be completed before the high-priority tasks can be started. With a ratio Higher priority and satisfied , hour, The start time is shown in formula (28):

[0153] (28)

[0154] in, Indicates the process In the machine The processing start time on the Indicates the process In the machine The processing end time on the It is a safe interval. ;

[0155] For transfers between different aircraft, low-priority tasks can be started earlier to improve transfer efficiency. Therefore, their transfer start time is determined solely by the delayed transfer strategy. Furthermore, elevators and tugs can be scheduled earlier to improve efficiency. However, due to equipment occupancy, the equipment may not arrive at the designated location before the aircraft transfer begins. In this case, the start time of subsequent processes will be further delayed based on the arrival time of the transferred equipment.

[0156] Step 4-3: Scheduling based on heuristic rules;

[0157] The solution process first loads the trajectory library and blocking list, and initializes a list containing information about each machine's occupancy time and a dispatch list. Then, it extracts dispatch tasks and selects tractor and traction system dispatch trajectories based on predefined heuristics. A delayed collision avoidance method is applied for coordinated dispatch. Dispatching is performed based on task type and process sequence, and all dispatch information is updated to complete the task scheduling.

[0158] The final layout transfer path is as follows Figures 8-17 As shown in the figure, the number before the “-” on the aircraft represents the aircraft number, and the number after the “-” represents the station number where the aircraft is located. The obtained layout transfer process satisfies all constraints, and there is no station conflict during the transfer of each aircraft. The Gantt chart for scheduling each carrier-based aircraft is shown in the figure. Figure 18 As shown in the figure, the horizontal axis represents dispatch time, and the vertical axis represents the aircraft number being transferred. The numbers before the "-" in the first row of each bar chart indicate the type of transfer entity: "T" represents a tractor, "A" represents a carrier-based aircraft, and "E" represents an elevator. The numbers after the "-" represent the transfer entity number. The numbers before the "-" in the second row indicate the starting station of the transfer task, and the numbers after the "-" in the second row indicate the ending station of the transfer task. The final planned scheduling solution meets all scheduling constraints, and all transfer entities meet the requirements for coordinated collision avoidance during the transfer process.

[0159] The above-described embodiments merely express the implementation methods of the present invention, but should not be understood as limiting the scope of the patent of the present invention. It should be pointed out that for those skilled in the art, several variations and improvements can be made without departing from the concept of the present invention, and these all fall within the scope of protection of the present invention.

Claims

1. A method for scheduling and planning a machine downtime by combining the layout transfer A-star algorithm with heuristic rules, characterized in that: The downtime scheduling planning method comprises the following steps: Step 1: Decouple the downtime problem into two sub-problems: routing and scheduling, and establish a corresponding mathematical programming model. Step 2: Set the station connectivity relationship based on the ship-based environment station information, and establish a station transfer map and transportation trajectory library; Step 3: Set the node expansion method and congestion detection mechanism, set the heuristic function, form the layout transfer A-star algorithm, and realize the layout transfer path search; Step 4: Relying on the transport trajectory library, establish a heterogeneous entity collaborative transport method based on the delayed transport strategy, set the corresponding equipment allocation heuristic scheduling rules, and implement the scheduling of transfer tasks extracted from the layout transfer path; Step 1-3: Establish a mathematical programming model for the scheduling problem; Step 1-3-1: Define scheduling parameters; use Indicates the The first The processing type is ; Indicates that all types are A collection of processing steps, ; Represents the set of all processing steps, ; The number of available machines in the scheduling process is recorded as ; The number of available hangar stations is recorded as ; The number of available deck stations is recorded as ; Step 1-3-2: Establish process processing constraints; Process Need to After execution, the corresponding constraints are shown in formula (7): （7）； in Indicates the process In the machine The processing start time on the Indicates the process In the machine The processing end time on the Process The completion time must be greater than the sum of its start time and the required processing time. The corresponding constraint is shown in formula (8): （8）； in, Indicates the process In the machine The processing start time on the Indicates the process In the machine The processing end time on the Indicates the process In the machine Required processing time; is a positive number; Indicates the process Is it on the machine If ,otherwise ; Step 1-3-3: Establish machine usage constraints; Any process is assigned to only one machine, and the corresponding constraints are shown in formula (9): （9）； in Indicates the process Is it on the machine If ,otherwise ; When a tractor is selected in the tractor transfer process, the corresponding carrier-based aircraft needs to be transported to the target station using the tractor. The corresponding constraints are shown in formula (10): （10）； in Indicates the process Is it on the machine If ,otherwise ; Indicates the process Is it on the machine If ,otherwise ; Two operations using the same tractor must be transported to the target station before the second operation can use the tractor. The corresponding constraints are shown in formula (11): （11）； in Indicates the process In the machine The processing start time on the Indicates the process In the machine The processing end time on the is a sufficiently large positive number; Indicates the process Is it in process Using the machine After using the machine ,if , otherwise ; Step 1-3-4: Establish station occupancy constraints; Any process It is only assigned to one target station, and the corresponding constraints are shown in formula (12): （12）； in express Whether it is by position Transport to ,if , otherwise ; If the homework and Serving the same aircraft and aircraft transfer process The starting point and The end points are the same, then The start time should be after The end time of , the corresponding constraints are shown in formula (13): （13）； in, Indicates the process In the machine The processing start time on the Indicates the process In the machine The processing end time on the Indicates the process Whether it is by position Transport to ,if ,otherwise ; Indicates the process Whether it is by position Transport to ,if , otherwise ; Indicates homework and Are they serving the same aircraft? If so, ,otherwise ; is a symbolic function, when hour ,when hour when hour ; 、 、 、 Number any station; When the current position of another aircraft is selected as the target position, it is necessary to ensure that the subsequent aircraft can enter the position only after the previous aircraft leaves, as shown in formula (14): （14）； in Indicates the process In the machine The processing start time on the Indicates the process In the machine The processing end time on the is a sufficiently large positive number; express Is it Use station Use the station later ,if , otherwise ; The elevator transfer time; To describe the cooperative collision avoidance constraint, the aircraft and the tractor are collectively referred to as transfer entities. During the transfer process, the transfer trajectories of any two transfer entities must ensure cooperative collision avoidance, as shown in formula (15): （15）； in, 、 Represents the process and The selected transport trajectory; 、 Respectively in any Always on track 、 Location information; , represents the safe distance between two transport entities, 、 Transport Entity 、 The circumcircle radius of For safety margin; when transporting entities For tractor ,in is the radius of the circumscribed circle of the tractor. For traction system ,in is the radius of the circumscribed circle of the traction system; During the transportation process, we hope that the overall transit time will be minimized. The objective function is recorded as , which is shown in formula (16): （16）； Step 1-3-5: Establish a mathematical programming model for scheduling; Finally, the combined optimization model constructed for scheduling is shown in formula (17): （17）； in, It is the objective function in the scheduling task.

2. The method for scheduling and planning a machine downtime by combining the layout transfer A-star algorithm and heuristic rules according to claim 1, characterized in that: The step 1 is specific as follows: Step 1-1: Decouple the downtime problem into the layout transfer route search problem and the scheduling problem; During the layout transfer route search phase, a layout is represented by a vector consisting of all occupied station numbers, with each element in the vector corresponding to the aircraft number at that station. Layout transitions are achieved by transferring one aircraft at a time, and aircraft reversal tasks are achieved through multiple intermediate layouts. This layout transfer process is called a layout transfer path. After obtaining the layout transfer path, a series of aircraft transfer tasks are extracted and scheduled according to the layout conversion sequence. Each aircraft transfer task is considered a job, and the constraints of the tractor and elevator are considered as processing machines. The scheduling problem is described as a flexible job shop scheduling problem, and five key processing steps are extracted based on the characteristics of the transfer tasks. Step 1-2: Establish a mathematical programming model for the layout transfer path search problem; For any aircraft reversal task, the number of aircraft in the task is recorded as , No. The aircraft number is recorded as , the set of all aircraft is recorded as ; The initial and target layouts of the machine reversal task are 、 , the starting and ending layouts of the reversing process are 、 , the boundary constraints of the layout transfer path search are shown in formula (1): （1）； During the transition between two adjacent arrays, no aircraft can be transferred to an occupied station. The corresponding constraints are shown in formula (2): （2）； in, Indicates aircraft In the Station number after secondary array transfer; Indicates the Arrangement after secondary arrangement transfer ; During the transition between two adjacent arrangements, the transfer aircraft cannot be blocked. The corresponding constraints are shown in formula (3): （3）； in, Indicates position and Is the time blocked? If so, ,otherwise ; During the transition between any two adjacent layouts, if the elevator station is occupied, the aircraft cannot enter the elevator station on the other level. The corresponding constraints are shown in formula (4): （4）； in, Indicates elevator station; express Corresponding station on another level; and Indicates aircraft and In the The station number after the second array transfer, Indicates the Arrangement after secondary arrangement transfer ; For the layout transfer task, the objective function is recorded as , which is shown in formula (5): （5）； in, represents the transit time penalty coefficient; represents the penalty coefficient for the number of transshipments; represents the penalty coefficient for cross-layer transfer; Indicates the number of layout conversions; Indicates the number of aircraft currently deployed; Indicates aircraft from Transport to trajectory running time; Indicates position and Are they at the same level? If yes, ,otherwise ; Finally, the mathematical model of the layout transfer problem is obtained as shown in formula (6): （6）； in, Represents the objective function in the process of searching for the layout transfer path.

3. The method for scheduling and planning a downtime machine by combining the layout transfer A-star algorithm and heuristic rules according to claim 2, characterized in that: In step 1-1, the five key processing steps are: ① Deck tractor transports to the front of the carrier aircraft; ② Transports the deck carrier aircraft to the target location; ③ Elevator hangar-deck transfer; ④ Deploys the hangar tractor to the front of the carrier aircraft; ⑤ Transports the hangar carrier aircraft to the target location. At this time, the transportation task of each aircraft can be regarded as a series of some of the steps: hangar aircraft transportation task is ③→①→②; deck aircraft transportation task is ③→④→⑤; hangar-to-deck aircraft transportation task is ③→①→②→③→④→⑤; deck-to-hangar aircraft transportation task is ③→④→⑤→③→①→②.

4. The method for scheduling and planning a downtime machine by combining the layout transfer A-star algorithm and heuristic rules according to claim 3, characterized in that: The step 2 is specific as follows: Step 2-1: Build a station transfer map; The stations on the ship-based platform can be divided into three categories: hangar, deck, and elevator. According to the characteristics of these stations, the connection relationship is set up to build a station transfer map; Step 2-2: Build a transportation track library; Step 2-2-1: Establish rail depots for each transport entity; According to the processing procedures extracted in step 1-1, procedures ① and ④ require traction system transfer tracks, and procedures ② and ⑤ require tractor transfer tracks. For the traction system, different transfer paths are adopted for carrier-based aircraft between any two stations. Therefore, multiple transfer tracks are provided for two stations that can be connected on the station transfer map. The track library is recorded as , its composition is shown in formula (18): （18）； in, For standing position and Intermediate Priority track; For standing position and The number of trajectories between 、 Indicates the position transfer to any position on the map; Indicates the number of hangar stations; Indicates the number of deck stations; Indicates the station transfer map Center and Position Connect all station numbers; For the tractor, it is necessary to ensure that it can transfer between any two stations. The corresponding trajectory library contains the transfer trajectory between any two stations, which is recorded as , and with have the same structure; Step 2-2-2: Create a blocking list for each transport entity To determine whether the transfer between two stations is feasible, a blocking list is established, which contains all the station numbers of the blocked transfer trajectory; add element "0" to the blocking list of the available trajectory; the blocking list uses Its composition is shown in formula (19): （19）； in, To record all blocked stations and A vector consisting of the station numbers for inter-transfer; The triangle area formed by the aircraft wheels is regarded as an obstacle in the tractor trajectory planning. The tractor will not be blocked when transferring between any stations. However, the tractor can also choose different transportation trajectories under different arrangements. Construct the corresponding blocking list and record it as ,and Have the same structure.

5. The method for scheduling and planning a downtime machine by combining the layout transfer A-star algorithm and heuristic rules according to claim 4, characterized in that: The step 2-1 is: Hangar: Aircraft transfers are mainly carried out in the hangar, and each station is connected to all other hangar stations; Deck: The deck environment is relatively open, and each station is only connected to the elevator station on the deck; Elevator: In addition to being connected to the corresponding level stations, the corresponding elevator stations between two levels must be connected; For two stations that are far apart, transfer is achieved through the middle station, and the hangar connectivity relationship is pruned; at this time, if there is hangar stations and In a ship-based environment with multiple deck stations, the station transfer map includes elements, denoted as , ,in For the position Connect all station numbers, Number any station.

6. The method for scheduling and planning a machine downtime by combining the layout transfer A-star algorithm and heuristic rules according to claim 5, characterized in that: The step 3 is specific as follows: Step 3-1: Set up node expansion mode and congestion detection mechanism; The aircraft reversal problem uses the layout as the path node for searching, and the expansion method is set to move one aircraft according to the station transfer map to form a new layout and complete one expansion; for any layout , as the aircraft cannot be transferred to Middle position, for this reason it will be excluded first before each expansion and Overlapping stations, the number of expansions per layout will be ,in Represents a vector the number of elements in ; According to different deployment forms, the aircraft adopts different transportation trajectories to achieve the transfer between stations; for any deployment No. Expand to form a column record , any aircraft The corresponding station is recorded as ,airplane From the station Transfer to station When the present invention is based on and When there is a transfer track and there is no overlapping station between the blocking list and the currently occupied station, it is determined to be passable, that is, for , , and ,but ; Step 3-2: Set the objective function; In the layout transfer A-star algorithm, it is necessary to set the objective function to guide the path search direction. The objective function is shown in formula (20): （20）； in, Indicates expansion to Post-objective function value; Indicates expansion to the required expenditure; Indicates the layout Estimated cost to achieve target layout; Set to the time required to switch to the current layout, and add a penalty for the number of transfers and a penalty for cross-layer transfers. The calculation formula is shown in (21): （21）； in, To expand to Britain Time required, represents the transit time penalty coefficient; represents the penalty coefficient for the number of transshipments; represents the penalty coefficient for cross-layer transfer; Indicates the number of aircraft currently deployed; Indicates aircraft from Transport to Transportation track running time; Indicates position and Are they at the same level? If yes, ,otherwise ; Set to the estimated cost of transporting all aircraft in the current array to the target station; the cost is estimated based on the distance between stations and the operating speed. The calculation formula is shown in (22): （22）； in, Indicates the number of aircraft currently deployed; Indicates position and Is the time blocked? If so, ,otherwise ; For aircraft On target Target position in Indicates aircraft from Transport to Transportation track running time; is the penalty coefficient for the non-existence of the transportation trajectory; is the maximum operating speed of the traction system; Step 3-3: Arrange transfer route search; After determining the objective function, an unexplored path node pool is established, which contains all path nodes that have not been expanded. Before the path search begins, the initial layout is added to the unexplored path node pool, and the layout with the minimum objective function value is selected as the expanded path node. The reachable layout is obtained according to the layout transfer map to form the reachable path node; then the unexplored path nodes in the obtained reachable path nodes are placed in the unexplored path node pool, and the current path node is removed from the unexplored path node pool. The path node with the lowest objective function value is selected from the unexplored path node pool again for expansion, and this process is repeated until the target layout is expanded.

7. The method for scheduling and planning a machine downtime by combining the layout transfer A-star algorithm and heuristic rules according to claim 6, characterized in that: The step 4 is specific as follows: Step 4-1: Establish a delayed transportation strategy under station congestion conditions; A collaborative transportation method for multiple transport entities based on a delayed collision avoidance strategy is proposed. First, the selected trajectory and the corresponding time and space position information of the scheduled trajectory are retrieved from the trajectory library. Then, it is determined whether there is a potential collision within the time interval when the current trajectory overlaps with other trajectories. If there is a potential collision, the transportation time of the current transport entity is delayed. Seconds, repeat the above judgment until there is no potential collision between the transfer time intervals of the current transfer entity and other transfer entities; Step 4-2: Heuristic rule setting; Step 4-2-1: Setting the rules for selecting a tractor; The transfer path has been arranged to determine the priority of each task, and the scheduling rules for the machines used in each process and the start time of the task have been set; If multiple tractors can arrive at the corresponding parking space before the aircraft transfer begins, the tractor with the shortest required time is selected; first, the set of all available tractor numbers is recorded as ,for ,if Make , then the set of tractors that meet this condition is represented as , selected tractor It should be as shown in formula (23): （23）； in, Indicates the process In the machine Required processing time; The start time of the corresponding process should be as shown in formula (24): （24）； in, Indicates the process In the machine The processing start time on the Indicates the process In the machine The processing start time on the Indicates the process In the machine Required processing time; It is a safe interval; If no tractor meets the above conditions, select the tractor from the collection of all tractors. The tractor that can reach the corresponding station earliest is selected. The selection rule is shown in formula (25): （25）； in, Indicates the process In the machine The processing end time on the Step 4-2-2: Setting the elevator selection rules; When the target station is at the elevator or the transport track passes through the elevator, the elevator is needed. The elevator is determined based on the target station and the blocking list. If , then the position and The transportation between the two rooms needs to use the elevator; there is no need to choose the elevator; at this time, If the elevator Arrive at the corresponding station before the aircraft transfer begins. The start time of the elevator transfer process is shown in formula (26): （26）； in, Indicates the process In the machine The processing start time on the Indicates the process In the machine The processing start time on the Indicates the process In the machine Required processing time; It is a safe interval; Otherwise, the start time will be the time when the elevator is responsible for processing the previous process. The end time is as shown in formula (27): （27）； in, Indicates that the machine Any processing operation performed on End time; Step 4-2-3: Set the aircraft transfer start time; When an aircraft needs to be transported multiple times, the low-priority tasks must be completed before the high-priority tasks can be started; specifically, for With a ratio Higher priority and satisfied , hour, The start time is shown in formula (28): （28）； in, Indicates the process In the machine The processing start time on the Indicates the process In the machine The processing end time on the It is a safe interval; For transfer tasks between different aircraft, the transfer start time is only determined by the delayed transfer strategy; Step 4-3: Scheduling based on heuristic rules; During the solution process, the trajectory library and blocking list are first loaded, and the list containing the occupancy time information of each machine and the scheduling list are initialized; then, the transportation tasks are extracted and the transportation trajectories of the tractor and traction system are selected according to the set heuristic rules. The delayed collision avoidance method is applied for coordinated transportation. The scheduling is carried out according to the task type and the process sequence, and all transportation information is updated to complete the task scheduling.

8. The method for scheduling and planning a machine downtime by combining the layout transfer A-star algorithm and heuristic rules according to claim 7, characterized in that: In step 4-1, the principle of selecting the trajectory in the trajectory library for any process should be: ,but ,in ; Low priority transport tasks will block high priority transport tasks; if the process Priority over process , and the track has been assigned and , by whether it satisfies To detect whether blocking occurs; If blocking occurs, it will be further determined whether If so, then Postponed until , and continue to achieve coordinated transportation through delayed transportation strategies.

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