A parking space planning method based on dynamic programming and bin packing algorithm

Abstract

This invention proposes a parking space planning method based on dynamic programming and bin packing algorithm, comprising: Step 1, constructing an abstract layout of the apron, wherein the abstract layout includes setting the area of ​​the apron and defining obstacles and service lanes in the apron area; Step 2, combining the aircraft types to be parked according to their available taxiing methods to form multiple combinations of aircraft types and taxiing methods, calculating the footprint of each combination of aircraft types and taxiing methods, and calculating the width of the right taxiway based on the footprint; Step 3, treating the parking space planning problem as a complete knapsack problem; each combination of aircraft types is regarded as an item to be packed, the value of each aircraft type is regarded as the item value, the available area of ​​the apron is regarded as the knapsack capacity, determining whether each combination of aircraft types can be parked on the apron according to the parking conditions, and obtaining all possible parking space planning results in the order of each row.

Description

Technical Field

[0001] This invention relates to the field of air transport, and is mainly a method for planning parking positions on large aprons in emergency situations. Background Technology

[0002] Currently, airports rely solely on manual planning to address the parking space planning issue within large aprons. The typical process involves planners manually planning the parking spaces based on factors such as the frequently served aircraft types and their safety distance standards, the most common taxiing methods for different aircraft types (automatic taxiing, sequential taxiing, push-in), the coordinates and width of the service lanes within the apron, and the coordinates and dimensions of surrounding ground obstacles. While manual planning offers good flexibility, it suffers from drawbacks such as long planning cycles, limited adaptability, and a high probability of error due to significant differences in the actual layout of different aprons and the types of aircraft commonly served. Furthermore, planners need a deep understanding of airport systems, airport configurations, and airfield pavements before planning, resulting in high time and learning costs for manual planning.

[0003] Under normal circumstances, when a large apron at a civilian or military airport is used for the first time, its parking positions need to be planned. However, in certain emergency situations, it is necessary to accommodate as many aircraft and a wider variety of aircraft types as possible on the apron within a short period of time. In such cases, the parking positions, parking lines, and taxiways should be quickly replanned. For example, air force combat training missions often require military airports to provide parking spaces for a large number of main combat aircraft at a specific time. Therefore, in the above scenarios, to plan the parking position layout accurately and in real time, it is urgent to establish an efficient and precise algorithm to effectively reduce planning time, strictly meet safety standards, maximize apron utilization, and provide airports with parking position planning solutions that meet parking needs, safety requirements, and real-time response requirements. Summary of the Invention

[0004] In view of this, the present invention provides a parking space planning method based on dynamic programming and bin packing algorithm. This method can effectively reduce planning time, strictly meet safety standards, and maximize the utilization rate of the parking apron. The method includes:

[0005] Step 1: Construct an abstract layout for the helipad, which includes the area of ​​the helipad and defines obstacles and service lanes within the helipad area.

[0006] Step 2: Combine the models to be parked into multiple groups according to their available taxiing methods, calculate the footprint of each group of models to be parked and taxiing methods, and calculate the width of the right taxiway based on the footprint.

[0007] Step 3: Treat the parking space planning problem as a complete knapsack problem; each aircraft combination is regarded as an item to be loaded, the value of each aircraft is regarded as the value of the item, and the available area of ​​the apron is regarded as the capacity of the knapsack. Determine whether each aircraft combination can be parked on the apron according to the parking conditions, and obtain all possible parking space plans in the order of each row. Compare and obtain the optimal parking space planning result.

[0008] Specifically, in step 1, defining obstacles and service lanes in the apron area includes defining the number and location coordinates of obstacles and defining the location coordinates and width of service lanes.

[0009] Specifically, in step 2, the sliding method includes convenient self-sliding, sequential self-sliding, and pushing into place;

[0010] When the aircraft of the type to be parked adopts the aforementioned convenient self-gliding sliding method, Length = F a Width = F b The area occupied is calculated by combining the type of aircraft to be parked with a convenient self-tapping method;

[0011] When the aircraft of the type to be parked adopts the aforementioned sequential self-gliding sliding method, the following is used: Width = F b The area occupied by the aircraft type to be parked and the sequential self-gliding method is calculated.

[0012] When the aircraft of the type to be parked is positioned using the aforementioned push-and-slide method, Length = F a +D5、Width=F b The footprint is calculated by combining the aircraft type to be parked with the aforementioned pushing placement method; where Length and Width represent the length and width of the space occupied by the aircraft, respectively, and the footprint of the aircraft can be calculated by multiplying the length and width; F a F b a, b, c, d, e, and R represent the aircraft's length, wingspan, distance from the nose landing gear to the nose, distance from the nose landing gear to the main landing gear, taxiing distance when the pilot adjusts the aircraft's parking position due to taxiing deviation, main landing gear wheelbase, equivalent main wheel width, and main landing gear inner wheel turning radius, respectively. D5 represents the safe distance between the aircraft's tail and the edge of the parking apron.

[0013] The calculation of the width of the right-side taxiway specifically includes:

[0014] Where α represents the safe distance between the wingtip of the aircraft in taxiing and an obstacle, β represents the safe distance between the outer main landing gear wheel of the aircraft in taxiing and the edge line of the apron, and Right represents the width of the taxiway on the right side; where x o This represents the x-coordinate of the nearest obstacle on the right side of the apron. This represents the safe distance between the i-th aircraft and the obstacle. The distance between the i-th aircraft and the edge of the apron is represented by N, and N represents the total number of different types of aircraft to be parked.

[0015] Specifically, in step 3, the available area of ​​the helipad is considered as the backpack capacity, and the backpack capacity is calculated according to the following formula:

[0016]

[0017] In the formula, T represents the backpack capacity, L and W represent the length and width of the tarmac, respectively, and E... h This represents the width of the h-th service lane.

[0018] Specifically, determining whether each aircraft combination can be parked on the apron based on parking conditions includes the following steps: calculating the upper and lower taxiway widths required for the aircraft type and taxiing method combination to be parked; and calculating the safe distance that a certain aircraft combination should maintain from the left edge of the apron.

[0019] Specifically, the required widths of the upper and lower taxiways for calculating the combination of the vehicle type and taxiing method to be parked are obtained using the following formula:

[0020]

[0021] Top and Bottom represent the upper and lower taxiway widths required for the combination of the parking model and the sliding method, respectively; F b i d i e i Let represent the wingspan, main landing gear wheelbase, and equivalent main wheel width of the i-th aircraft, respectively. This represents the safe distance between the i-th aircraft in taxiing and the nose or tail of a parked aircraft, or obstacles outside the apron. This represents the safe distance between the i-th aircraft and the obstacle. Let y represent the safe distance between the i-th aircraft in taxiing position and the edge line of the apron. Taking the value of i from 1 to n gives the Top value; taking the value of i from 1 to N gives the Bottom value. oThis represents the ordinate of the nearest obstacle on the upper side of the helipad.

[0022] Specifically, calculating the safe distance that a certain aircraft combination should maintain from the left edge of the apron includes the following: It can be calculated using the following formula:

[0023]

[0024] Where α represents the safe distance between the wingtip of the aircraft in taxiing and an obstacle, and β represents the safe distance between the outer main landing gear wheel of the aircraft in taxiing and the edge line of the apron; if there is an obstacle outside the left edge line of the apron and α>β, then according to Calculate the width of the left taxiway; otherwise, calculate using Left = β.

[0025] Specifically, all possible parking space plans are obtained in the order of each row, and the best parking space plan result is obtained by comparison. Further, a global variable hash table is defined to record the solutions to subproblems, and then the problem is solved recursively, finally resulting in an aircraft parking sequence that stores the number of aircraft types that can be packed into a backpack for each combination.

[0026] Beneficial effects:

[0027] (1) This invention abstracts the basic layout of the airport and embeds the aircraft parking safety standards and rules into the algorithm, making the final solution more standardized, safe and universal;

[0028] (2) In this invention, the aircraft parking is flexibly adapted and managed according to different sliding methods and aircraft types;

[0029] (3) In this invention, the upper and lower taxiway widths required for the combination of the aircraft type to be parked and the taxiing method are calculated, taking into full account the characteristics of different aircraft types and runways;

[0030] (4) In the basic layout of the airport, the present invention also fully considers facilities such as obstacles and fully considers the configuration of aircraft and obstacles at equal distances to ensure parking safety.

[0031] (5) The present invention directly uses an exact algorithm to solve the problem and does not involve algorithm iteration. Compared with manual planning or heuristic algorithm planning, the present invention can solve the optimal solution and is more efficient, which can directly improve the efficiency of parking space planning in the apron. Attached Figure Description

[0032] Figure 1 This is a flowchart illustrating the steps involved in establishing a parking space planning algorithm based on dynamic programming and packing strategies.

[0033] Figure 2This is a flowchart of the parking space planning algorithm based on dynamic programming and packing strategy;

[0034] Figure 3 This is a schematic diagram of the basic layout of the helipad;

[0035] Figure 4 These are the results of case analysis obtained using this invention. Detailed Implementation

[0036] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0037] This invention provides a parking space planning method based on dynamic programming and a packing algorithm for large helipads, the specific process of which is as follows: Figure 1 As shown. This invention proposes a two-stage solution method: the first stage transforms the parking space planning problem into a complete knapsack problem, and solves for an aircraft parking sequence through dynamic programming; the second stage uses the aircraft parking sequence output by the first stage as the sequence of items to be packed, and solves for the parking position of each aircraft through a combination of the bottom-left filling method and the maximum stack algorithm; the output of the second stage is the final output of this solution algorithm.

[0038] The following uses the actual geometric parameters of three commonly used civil aircraft models, along with the assumed dimensions of the apron and its internal facilities, as input samples for the algorithm. Based on actual conditions, the three aircraft models to be parked are: "Airbus A320A", "Boeing B777-300", and "Boeing 787-8", all of which can be parked using either "convenient self-tariffing" or "sequential self-tariffing" methods. The apron dimensions are set to 1500(m) × 500(m). Three obstacles are set with coordinates (1500.5, 350), (650, -2), and (-1.5, 150). Two lanes, each 8m wide, are set at one-third and two-thirds of the apron's x-axis direction, respectively.

[0039] The overall flow of the parking space planning algorithm provided by this invention is as follows: Figure 1 As shown, the specific steps are as follows: Step 1, abstract the basic layout of the apron. The schematic diagram of the basic layout of the apron is shown below. Figure 3As shown. The apron can be abstracted as a two-dimensional rectangle, where aircraft taxiing and parking activities take place. Let the upper left corner of the rectangle be the origin (0,0), the right side be the positive X-axis, and the lower side be the positive Y-axis. During parking, the aircraft needs to enter the apron through the entrance / exit (lower right corner of the rectangle). Additionally, the apron may have one or more service lanes to assist airfield personnel in scheduled aircraft maintenance. When taxiing on the apron, the aircraft's wings are allowed to extend beyond the apron's edge, but a safe distance must be maintained between the wings and any external obstacles. Aircraft need to taxi along taxiways within the apron. There are four types of taxiways: right-side taxiway, upper taxiway, lower taxiway, and middle taxiway. The actual width of each taxiway will be calculated during the problem-solving process.

[0040] Step 2: Divide each type of aircraft to be parked into multiple aircraft type combinations according to its available taxiing methods. That is, each aircraft type combination corresponds to one aircraft type and one taxiing method, and calculate the footprint of each aircraft type combination (the actual length and width of the space occupied by the aircraft when using different taxiing methods):

[0041] Length = F a (1)

[0042]

[0043] Length = F a +D5 (3)

[0044] Width = F b (4)

[0045] Equations (1) and (4) represent the calculation formulas for the footprint when "facilitating self-gliding", Equations (2) and (4) represent the calculation formulas for the footprint when "sequential self-gliding", and Equations (3) and (4) represent the calculation formulas for the footprint when "pushing into position". In the formulas, Length and Width represent the length and width of the space occupied by the aircraft, respectively, and F... a F b a, b, c, d, e, and R represent the aircraft's length, wingspan, distance from the nose landing gear to the nose, distance from the nose landing gear to the main landing gear, taxiing distance when the pilot adjusts the aircraft's parking position due to taxiing deviation, main landing gear wheelbase, equivalent main wheel width, and main landing gear inner wheel turning radius, respectively. D5 represents the safe distance between the aircraft's tail and the edge of the parking apron.

[0046] Specifically, in this embodiment, each type of parking machine is divided into multiple groups according to its available gliding methods, and the footprint of each group is calculated. "Convenient self-gliding" is denoted by the character "c", and "sequential self-gliding" is denoted by the character "s".

[0047]

[0048] Then, based on the dimensions of all the models to be parked, the width of the right-side taxiway was calculated:

[0049]

[0050] Equation (5) calculates α to ensure a safe distance between the wingtip of the aircraft and an obstacle while taxiing; Equation (6) calculates β to ensure a safe distance between the outer main landing gear wheel of the aircraft and the edge line of the apron while taxiing; and Equation (7) calculates the width of the right-hand taxiway. Where x o This represents the x-coordinate of the nearest obstacle on the right side of the apron. This represents the safe distance between the i-th aircraft and the obstacle. The distance between the i-th aircraft and the edge of the apron is represented by N, and N represents the total number of different types of aircraft to be parked.

[0051]

[0052] Step 3: Treat the parking space planning problem as a complete knapsack problem. Each aircraft combination is considered an item to be loaded, the value of each aircraft is considered the item value, and the available area of ​​the parking apron is considered the knapsack capacity. Calculate the knapsack capacity using the following formula:

[0053]

[0054] In the formula, T represents the backpack capacity, L and W represent the length and width of the tarmac, respectively, and E... h This represents the width of the h-th service lane.

[0055]

[0056] The knapsack problem is solved using dynamic programming. A global variable hash table is defined to record the solutions to subproblems. The problem is then solved recursively, resulting in a parking sequence B containing the number of aircraft to be packed into each combination of aircraft types. This sequence is then sorted in descending order of footprint size.

[0057] B=[{("B777-300","c"):4},{("B787-8","c"):23},{("A320A","c"):264}]

[0058] The parking space planning problem is viewed as a series of bin packing problems, that is, multiple bin packing algorithms are applied to the parking apron. The parking planning behavior of each row of aircraft is regarded as a "two-dimensional rectangular bin packing problem that cannot be orthogonally rotated". The problem is solved serially for each row. The left bottom with fill method is combined with a data structure - max stack - as the solution algorithm. The algorithm process is shown in Algorithm 1:

[0059]

[0060]

[0061]

[0062] In the pseudocode above, the entrance function controls the outer loop used to determine whether to perform the next packing, and completes the parameter initialization and update and output organization; the packingAuxiliary function, based on the bottom left filling method, embeds a maximum stack to support the retrieval of the current maximum lower taxiway width in constant time; the stackPush, stackPop, and stackGetMax functions are used for pushing onto the stack, popping from the stack, and retrieving the maximum value, respectively; the calculateTop and calculateBottom functions refer to equations (9), (10), and (11) to calculate the upper and lower taxiway widths required for a certain aircraft combination; the calculateLeftDistance function refers to equations (14) and (15) to calculate the safe distance that a certain aircraft combination should maintain from the left edge of the apron; line 15 of the algorithm reflects the calculation process of the middle taxiway, which will not be elaborated here.

[0063] The width of the upper and lower taxiways can be calculated using the following formula:

[0064]

[0065] In the formula, Top and Bottom represent the widths of the upper and lower slides, respectively. This represents the safe distance between the i-th aircraft in taxiing and the nose or tail of a parked aircraft, or obstacles outside the apron. This represents the safe distance between the i-th aircraft and the obstacle. y represents the safe distance between the i-th aircraft in taxiing position and the edge line of the apron. o This represents the ordinate of the nearest obstacle on the upper side of the apron.

[0066] d i e iLet represent the wingspan, main landing gear wheelbase, and equivalent main wheel width of the i-th aircraft, respectively.

[0067] The safe distance between the aircraft and the left edge of the apron can be calculated using the following formula:

[0068]

[0069]

[0070] Left = β (15)

[0071] The α calculated by equation (12) is used to ensure a safe distance between the wingtip of the aircraft in taxiing state and the obstacle. The β calculated by equation (13) is used to ensure a safe distance between the outer wheel of the main landing gear of the aircraft in taxiing state and the edge line of the parking apron. If there is an obstacle outside the left edge line of the parking apron and α>β, the width of the left taxiway is calculated according to equation (14). Otherwise, it is calculated according to equation (15).

[0072] In this embodiment, the aircraft parking planning behavior for each row is treated as a "two-dimensional rectangular bin packing problem with non-orthogonal rotation". A combined algorithm of the bottom-left filling method and the maximum stack is used to solve each bin packing problem sequentially, ultimately obtaining the parking position of each aircraft, i.e., the coordinates of the parking spot. Figure 4 As shown. Figure 4 In the diagram, each dot represents the position of the nose landing gear of each aircraft. Different colors are used to distinguish different aircraft models, and the size of the dots is proportional to the wingspan of each aircraft model. From the results, we can see that: 53 Airbus A320As, 4 Boeing B777-300s, and 23 Boeing B787-8s were parked.

[0073] In summary, the above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

[0074] It will be apparent to those skilled in the art that the embodiments of the present invention are not limited to the details of the exemplary embodiments described above, and that the embodiments of the present invention can be implemented in other specific forms without departing from the spirit or essential characteristics of the embodiments of the present invention. Therefore, the embodiments should be considered exemplary and non-limiting in all respects, and the scope of the embodiments of the present invention is defined by the appended claims rather than the foregoing description. Therefore, all variations falling within the meaning and scope of equivalents of the claims are intended to be encompassed within the embodiments of the present invention. No reference numerals in the claims should be construed as limiting the scope of the claims. Furthermore, it is clear that the word "comprising" does not exclude other units or steps, and the singular does not exclude the plural. Multiple units, modules, or devices recited in the system, apparatus, or terminal claims may also be implemented by the same unit, module, or device through software or hardware. The terms "first," "second," etc., are used to indicate names and do not indicate any particular order.

[0075] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the embodiments of the present invention and are not intended to limit them. Although the embodiments of the present invention have been described in detail with reference to the above preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions to the technical solutions of the embodiments of the present invention should not depart from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A parking space planning method based on dynamic programming and bin packing algorithm, characterized in that, include: Step 1: Construct an abstract layout for the helipad, which includes the area of ​​the helipad and defines obstacles and service lanes within the helipad area. Step 2: Combine the models to be parked according to their sliding methods to form multiple sets of models to be parked and sliding methods. Calculate the floor area of ​​each set of models to be parked and sliding methods, and calculate the width of the right-side sliding lane based on the floor area. In Step 2, the sliding methods include convenient self-sliding, sequential self-sliding, and push-in positioning. When the aircraft of the type to be parked adopts the aforementioned convenient self-gliding sliding method, Length = F a Width = F b The area occupied is calculated by combining the type of aircraft to be parked with a convenient self-tapping method; When the aircraft of the type to be parked adopts the aforementioned sequential self-gliding sliding method, the following is used: Width = F b The area occupied by the aircraft type to be parked and the sequential self-gliding method is calculated. When the aircraft of the type to be parked is positioned using the aforementioned push-and-slide method, Length = F a +D5、Width=F b The footprint is calculated by combining the aircraft type to be parked with the aforementioned pushing placement method; where Length and Width represent the length and width of the space occupied by the aircraft, respectively, and the footprint is calculated by multiplying the length and width; F a F b a, b, c, d, e, and R represent the aircraft's length, wingspan, distance from the nose landing gear to the nose, distance from the nose landing gear to the main landing gear, taxiing distance when the pilot adjusts the aircraft's parking position due to taxiing deviation, main landing gear wheelbase, equivalent main wheel width, and main landing gear inner wheel turning radius, respectively. D5 represents the safe distance between the aircraft's tail and the edge of the parking apron. The calculation of the width of the right-side taxiway specifically includes: Where α represents the safe distance between the wingtip of the aircraft in taxiing and an obstacle, β represents the safe distance between the outer main landing gear wheel of the aircraft in taxiing and the edge line of the apron, and Right represents the width of the taxiway on the right side; where x o This represents the x-coordinate of the nearest obstacle on the right side of the apron. This represents the safe distance between the i-th aircraft and the obstacle. represents the safe distance between the i-th aircraft and the edge line of the parking apron, and N represents the total number of different types of aircraft to be parked; Step 3: Treat the parking space planning problem as a complete knapsack problem; each aircraft combination is regarded as an item to be loaded, the value of each aircraft is regarded as the value of the item, and the available area of ​​the apron is regarded as the capacity of the knapsack. Determine whether each aircraft combination can be parked on the apron according to the parking conditions, and obtain all possible parking space plans in the order of each row. Compare and obtain the optimal parking space planning result.

2. The parking space planning method based on dynamic programming and bin packing algorithm as described in claim 1, characterized in that: Step 1 involves defining obstacles and service lanes in the apron area, including defining the number and location coordinates of obstacles and defining the location coordinates and width of service lanes.

3. The parking space planning method based on dynamic programming and bin packing algorithm as described in claim 1, characterized in that: In step 3, the usable area of ​​the helipad is considered as the backpack capacity, and the backpack capacity is calculated according to the following formula: In the formula, T represents the backpack capacity, L and W represent the length and width of the tarmac, respectively, and E... h This represents the width of the h-th service lane.

4. The parking space planning method based on dynamic programming and bin packing algorithm as described in claim 3, characterized in that: Determining whether each aircraft combination can be parked on the apron based on parking conditions includes the following steps: calculating the required upper and lower taxiway widths for the aircraft type and taxiing method combination to be parked; and calculating the safe distance that a certain aircraft combination should maintain from the left edge of the apron.

5. The parking space planning method based on dynamic programming and bin packing algorithm as described in claim 4, characterized in that: The required widths of the upper and lower taxiways for the combination of the parking model and the taxiing method are calculated using the following formula: Top and Bottom represent the upper and lower taxiway widths required for the combination of the parking model and the sliding method, respectively; F b i d i e i Let represent the wingspan, main landing gear wheelbase, and equivalent main wheel width of the i-th aircraft, respectively. This represents the safe distance between the i-th aircraft in taxiing and the nose or tail of a parked aircraft, or obstacles outside the apron. This represents the safe distance between the i-th aircraft and the obstacle. This represents the safe distance between the i-th aircraft in taxiing position and the edge line of the apron. Taking the value of i from 1 to n gives the Top value; taking the value of i from 1 to N gives the Bottom value. o This represents the ordinate of the nearest obstacle on the upper side of the helipad.

6. The parking space planning method based on dynamic programming and bin packing algorithm as described in claim 5, characterized in that: Calculating the safe distance between a certain aircraft combination and the left edge of the apron, specifically including: calculation according to the following formula: Where α represents the safe distance between the wingtip of the aircraft in taxiing and an obstacle, and β represents the safe distance between the outer main landing gear wheel of the aircraft in taxiing and the edge line of the apron; if there is an obstacle outside the left edge line of the apron and α>β, then according to Calculate the width of the left taxiway; otherwise, calculate using Left = β.

7. The parking space planning method based on dynamic programming and bin packing algorithm as described in any one of claims 1-6, characterized in that: The process involves obtaining all possible parking space plans in the order of each row, comparing them to obtain the optimal parking space plan, further including defining a global variable hash table to record the solutions to subproblems, and then using a recursive approach to solve the problem, finally obtaining an aircraft parking sequence that stores the number of aircraft types that can be packed into a backpack for each combination.

Images