A path optimization method for branch route network

Abstract

This invention discloses a path optimization method for feeder air route networks, belonging to the field of neural network technology. It simplifies the algorithm process, improves computation speed, and reduces the existence of equivalent solutions in the algorithm. The method includes: Step 11, obtaining the distance d between cities in the network. xy Step 12: Based on the input U of the neural network xi (t) and dynamic equations, calculate step 13: based on the input U of the neural network at the next time step. xi (t+1); Step 14, based on distance d xy Obtain the access route matrix between cities, and based on U xi (t+1) Calculate the minimum constraint condition that each row and column of the access route matrix contains only one 1 and the rest are zero; Step 15: Calculate the energy function E of the neural network according to the minimum constraint condition; Step 16: When the energy function E is minimized, stop the iteration and record the path corresponding to the minimum energy function E as the optimal path; otherwise, execute step 12; Step 17: Output the optimal path. This invention is used for path optimization of branch line airway networks.

Description

Technical Field

[0001] This invention relates to a path optimization method for feeder airway networks, belonging to the field of neural network technology. Background Technology

[0002] With the rapid development of the civil aviation industry in recent years, passenger turnover has increased significantly, including domestic trunk airports and domestic feeder airports. At present, my country's civil aviation economic structure is mainly based on air transport to capital cities and large and medium-sized cities, while the development of feeder airports is relatively lagging behind. However, as an important part of the modern air transport system, feeder aviation can improve the coverage of air transport and meet diverse travel needs.

[0003] For the optimization of air route networks, researchers both domestically and internationally have adopted different approaches. Most methods involve selecting a suitable neural network algorithm, establishing an objective function, and performing convex optimization. However, this approach can cause the network to get stuck in a minimum value. Some researchers have combined the Yen algorithm with the A* algorithm to reduce the search space and decrease the search size and running time for solving the KSP problem. However, as the number of network nodes increases, the number of selection results also increases, leading to the inability to make the optimal decision. In route networks, the inversion algorithm in dynamic programming can be used to solve network problems, but this algorithm is limited to theoretical research and has no practical application value, failing to be applicable to real-world situations. Summary of the Invention

[0004] This invention provides a path optimization method for feeder airway networks, which simplifies the algorithm calculation process, improves the calculation speed, and reduces the existence of equivalent solutions in the algorithm.

[0005] This invention provides a path optimization method for feeder airway networks, the method comprising:

[0006] Step 11: Obtain the distance d between cities in the feeder route network. xy Where x, y = 1, 2, ..., n; n is the number of cities, and also the neurons of the neural network;

[0007] Step 12: Based on the input U of the neural network xi Given the initial values ​​of (t) and the dynamic equations of the neural network, calculate... Among them, U i This represents the sum of inputs to the i-th neuron.

[0008] Step 13, according to the above Solving for the input U of the neural network at the next time step xi (t+1), where

[0009] Step 14: Based on the distance d xy Obtain the access route matrix between cities, and based on the U... xi (t+1), calculate the minimum constraint condition that satisfies the condition that each row and column of the access route matrix has only one 1 and the rest are zero;

[0010] Step 15: Calculate the energy function E of the neural network based on the minimum constraint condition; the energy function E is:

[0011]

[0012] Where A, B, and D are preset weight parameters; l represents the weights of the neural network; v i From the formula get, Here, T is the activation function, and T is the control parameter.

[0013] Step 16: When the energy function E is minimized, stop the iteration and record the path corresponding to the minimum energy function E as the optimal path; otherwise, proceed to step 12.

[0014] Step 17: Output the original path and the optimal path of the feeder route network.

[0015] Optionally, the calculation satisfies the constraint that each row and column of the access route matrix contains only one 1 and the rest are zero, specifically:

[0016] The Sigmoid function is used to calculate the minimum constraint that satisfies the requirement that each row and column of the access route matrix contains only one 1 and the rest are zero.

[0017] Optionally, the calculation satisfies the constraint that each row and column of the access route matrix contains only one 1 and the rest are zero, specifically:

[0018] The min-max function is used to calculate the minimum constraint that satisfies the condition that each row and column of the access route matrix has only one 1 and the rest are zero.

[0019] Optionally, the dynamic equation of the neural network is:

[0020]

[0021] Among them, C i R is the clustering coefficient of i; i From the formula Obtain, r i w is the additional resistance of the i-th neuron; ij y represents the link weights between neurons ij; jI is the output of the j-th neuron; i is the external bias current for the i-th neuron.

[0022] Optionally, the distance d between cities in the obtained feeder route network is... xy Previously, the method also included:

[0023] Set the initial value of the neural network to t = 0, and set the weight parameters A, B, and D of the energy function E.

[0024] The beneficial effects that this invention can produce include:

[0025] The path optimization method for regional air route networks provided by this invention applies a Hopfield neural network to the optimization problem of regional air route networks, transforming the objective function into an energy function. By converting the problem to be solved into the corresponding states of network nodes, the optimal solution can be found. Since the Hopfield neural network has the advantage of parallel computing, and the computational cost does not increase exponentially with increasing dimensionality, this effectively reduces the number of neurons and nodes, improves computational efficiency, and can effectively solve the daily utilization optimization problem. Attached Figure Description

[0026] Figure 1 A flowchart of a path optimization method for feeder airway networks provided in an embodiment of the present invention;

[0027] Figure 2 This is a schematic diagram illustrating the relationship between the neural network and the target problem provided in an embodiment of the present invention. Detailed Implementation

[0028] The present invention will now be described in detail with reference to the embodiments, but the present invention is not limited to these embodiments.

[0029] This invention provides a path optimization method for feeder airway networks, such as... Figure 1 As shown, the method includes:

[0030] Step 11: Obtain the distance d between cities in the feeder route network. xy Where x, y = 1, 2, ..., n; n is the number of cities, and also the neurons of the neural network.

[0031] In practical applications, before step 11, the method may further include: setting the initial value of the neural network t = 0, and setting the weight parameters A, B, and D of the energy function E.

[0032] Step 12: Based on the input U of the neural network xi Given the initial values ​​of (t) and the dynamic equations of the neural network, calculate... Among them, Ui This represents the sum of inputs to the i-th neuron.

[0033] The dynamic equations of the aforementioned neural network can be:

[0034]

[0035] Among them, C i R is the clustering coefficient of i; i From the formula Obtain, r i w is the additional resistance of the i-th neuron; ij y represents the link weights between neurons ij; j I is the output of the j-th neuron; i is the external bias current for the i-th neuron.

[0036] Step 13, according to Solving for the input U of the neural network at the next time step xi (t+1), where

[0037] Step 14: Based on distance d xy Obtain the access route matrix between cities, and based on U xi (t+1), calculate the minimum constraint that satisfies the condition that each row and column of the access route matrix has only one 1 and the rest are zero.

[0038] In practical applications, the Sigmoid function or the min-max function can be used to calculate the minimum constraint that satisfies the condition that each row and column of the access route matrix has only one 1 and the rest are zero.

[0039] For example, if the number of cities is 4, and the set is represented as {abc,d}, the route matrix can be shown in the table below, which requires starting from city b, passing through several other cities in sequence, and finally returning to city b.

[0040] a b c d a 0 1 0 0 b 1 0 0 0 c 0 0 1 0 d 0 0 0 1

[0041] In the access route matrix above, 1 indicates arrival and 0 indicates no arrival. The elements in each row and column of this access route matrix follow a pattern: each row contains only one 1 element, and the rest are zero elements.

[0042] Step 15: Calculate the energy function E of the neural network based on the minimum constraint condition; the energy function E is:

[0043]

[0044] Where A, B, and D are preset weight parameters; l represents the weights of the neural network; vi From the formula get, Here, T is the activation function, and T is the control parameter.

[0045] Step 16: When the energy function E is minimized, stop the iteration and record the path corresponding to the minimum energy function E as the optimal path; otherwise, proceed to step 12.

[0046] Step 17: Output the original path and optimal path of the branch route network.

[0047] The energy function of the optimal solution maps to the equilibrium point of the system. As the iteration process continues, the energy function value and the system tend to converge. The implementation of the system and the optimization problem can be correlated one-to-one. The initial conditions of the problem to be solved correspond to the initial state of the system's Hopfield network, such as... Figure 2 As shown.

[0048] The regional flight path data was simulated using Matlab software. The coordinates of cities 1 to 9 were selected as (2, 3); (4, 4); (3, 6); (9, 7); (10, 5); (6, 4); (5, 8); (2, 2); (9, 1). The optimal path was selected using the above path optimization method. The optimal path was calculated to be 2-5-3-6-7-1-9-8-4.

[0049] By transforming the problem to be solved into the corresponding states of network nodes, the optimal solution can be found, and the computational efficiency of the algorithm can be improved. When the number of network nodes increases, the daily utilization rate of the branch network can be effectively improved, and it can be well applied to practical problems.

[0050] The above description is merely a few embodiments of this application and is not intended to limit this application in any way. Although this application discloses preferred embodiments as described above, it is not intended to limit this application. Any changes or modifications made by those skilled in the art without departing from the scope of the technical solution of this application using the disclosed technical content are equivalent to equivalent implementation cases and fall within the scope of the technical solution.

Claims

1. A method for path optimization for a network of branch routes, characterized in that, The method comprises: Setting initial value t=0 of the neural network and setting weight parameters A, B, D of an energy function E; Step 11, obtaining the distance between each city in the branch route network ; wherein, x , y =1,2,……, n ; the n is the number of cities, also the neurons of the neural network; Step 12, calculating the initial value of the input of the neural network according to the initial value of the input of the neural network and the dynamic equation of the neural network ; wherein, U i is the input sum of the i th neuron​ The dynamic equation of the neural network is: ； wherein, is the clustering coefficient of i ; is obtained from the formula , r i is the additional resistance of the i-th neuron; i is the output of the i-th neuron; is the link weight between the neurons ij ; y j is the output of the i-th neuron; j is the output of the i-th neuron; I i is the additional bias current of the i-th neuron; Step 13, according to the , solving the input of the neural network at the next time U xi ( t +1), wherein ; Step 14, according to the distance , access route matrix between cities is obtained, and according to the U xi ( t +1), the constraint minimum condition that each row and each column in the access route matrix has only one 1 and the rest is zero is calculated; Step 15, calculating the energy function E of the neural network according to the constraint minimum condition; the energy function E is: ； wherein A, B and D are all preset weight parameters; l for weights of the neural network; v i obtained by the formula , is an activation function, and T is a control parameter; Step 16, when the energy function E is minimum, stopping iteration, and recording the path corresponding to the minimum energy function E as an optimal path; otherwise, executing step 12; Step 17, outputting the original path and the optimal path of the branch air route network.

2. The method of claim 1, wherein, The calculation satisfies the constraint minimum condition that each row and each column in the access route matrix has only one 1 and the rest is zero, and the constraint minimum condition is specifically: The Sigmoid function is used to calculate the constraint minimum condition that each row and each column in the access route matrix has only one 1 and the rest is zero.

3. The method of claim 1, wherein, The calculation satisfies the constraint minimum condition that each row and each column in the access route matrix has only one 1 and the rest is zero, and the constraint minimum condition is specifically: The min-max function is used to calculate the constraint minimum condition that each row and each column in the access route matrix has only one 1 and the rest is zero.

Images