Path optimization method based on memristor bidirectional coupling fractional order network model

Abstract

The invention discloses a path optimization method based on a memristor bidirectional coupling fractional order network model. The method comprises the following steps: step 1, determining a fractional order derivative expression by adopting a Caputo definition; 2, constructing a fractional order Hopfield neural network model, and determining a hyperbolic tangent memristor in the fractional order Hopfield neural network model; step 3, determining a coupled hyperbolic tangent memristor; and step 4, based on a specific TSP problem, obtaining an optimal solution through a fractional order Hopfield neural network model, and completing path planning. The invention belongs to the technical field of neural network application, and solves the problem that an integer order Hopfield neural network (HNN) model in the prior art is insufficient in precision when solving complex problems. Two hyperbolic tangent memristors are used for coupling two neurons to simulate a synaptic crosstalk phenomenon, and the coupling strategy is expanded to a fractional order system, so that dynamic behaviors of the model are greatly enriched, and more complex and diversified dynamic characteristics are shown.

Description

Technical Field

[0001] The present invention belongs to the technical field of neural network applications and relates to a path optimization method based on a memristor bidirectional coupling fractional-order network model. Background Art

[0002] Neurons are the core components of the nervous system, showing extremely complex electrical signal activities and rich nonlinear dynamic characteristics. Neurons are connected through synapses to form a complex and interwoven network. The various parts of the network cooperate with each other to jointly realize multiple functions of the brain. In 1984, John Hopfield proposed the Hopfield neural network model (HNN). HNN is a neural network model with a feedback mechanism that simulates the interaction between neurons in the brain through a series of interconnected nodes. Each node represents a simplified "neuron" that can receive input signals from other nodes in the network and decide whether to transmit signals to other nodes in the network based on its own state. When these "neurons" use nonlinear activation functions, HNN can exhibit a variety of complex dynamic behaviors such as chaos, hyperchaos, periodicity or quasi-periodicity. This feature makes HNN show great application value in many fields such as pattern recognition, image restoration, combinatorial optimization and information processing.

[0003] At present, most memristor-based HNN models use a single memristor to achieve coupling. This design may limit the full expression of the nonlinear characteristics and dynamic range of neural networks in some cases. If two memristors are coupled, more complex nonlinear dynamic phenomena can be induced, making artificial neural networks closer to real biological neural networks, thereby improving the accuracy and stability of the model. Dual memristor coupling can not only expand the adjustment range of the intensity of interaction between neurons, ensuring that the network works stably under diverse input conditions, but also enhance the model's ability to adapt to different application scenarios.

[0004] With the help of the theory of fractional calculus, the traditional integer-order neuron model is extended to the fractional-order model. Compared with the first-order system, the fractional-order model can more accurately reflect the dynamic behavior of the actual nonlinear system and further improve the simulation accuracy of the model. However, the application of integrating these technologies is not mature enough, and the accuracy of the model still needs to be improved, which requires further research and optimization. Summary of the invention

[0005] The purpose of the present invention is to provide a path optimization method based on a memristor bidirectional coupled fractional-order network model, which solves the problem of insufficient accuracy of the prior art integer-order Hopfield neural network (HNN) model when solving complex problems.

[0006] The technical solution adopted by the present invention is a path optimization method based on a memristor bidirectional coupled fractional-order network model, which is implemented according to the following steps: Step 1. Use Caputo definition to determine the fractional derivative expression; Step 2. Construct a fractional-order Hopfield neural network model and determine the hyperbolic tangent memristor therein; Step 3. Determine the coupled hyperbolic tangent memristor; Step 4. Based on the specific TSP problem, the optimal solution is obtained through the fractional-order Hopfield neural network model to complete the path planning.

[0007] The beneficial effects of the present invention are that the new fractional-order Hopfield neural network model (FOHNN) successfully extends the coupling strategy to the fractional-order system by using a dual-memristor coupling mechanism to simulate the synaptic crosstalk phenomenon in the Hopfield neural network; this method not only greatly enriches the dynamic behavior of the model, but also exhibits more complex and diverse dynamic characteristics, and verifies its effectiveness and accuracy through numerical simulation, theoretically advancing the research in the field of neural networks; according to the specific requirements of the TSP problem, an energy function is designed to guide the fractional-order Hopfield neural network model to search for the optimal solution, perform iterative operations, and obtain the optimal solution to the TSP problem, that is, the shortest inspection path. BRIEF DESCRIPTION OF THE DRAWINGS

[0008] Figure 1 In Example 1 of the present invention =0.96, the new fractional-order Hopfield neural network model changes with the strength of memristor electromagnetic induction coupling Changing bifurcation diagrams; Figure 2a In Example 1 of the present invention =0.96, =7.1, the state quantity of neuron I Timing diagram of Figure 2b is based on Figure 2a The parameters obtained by plotting Planar phase diagram; Figure 2c is based on Figure 2a The parameters obtained by plotting Planar phase diagram; Figure 2d is based on Figure 2a The parameters obtained by plotting Planar phase diagram; Figure 3a In Example 1 of the present invention =0.96, =10, the state quantity of neuron I Timing diagram of Figure 3b is based on Figure 3a The parameters obtained by plotting Planar phase diagram; Figure 3c is based on Figure 3a The parameters obtained by plotting Planar phase diagram; Figure 3d is based on Figure 3a The parameters obtained by plotting Planar phase diagram; Figure 4a In Example 1 of the present invention =0.96, =11.6, the state quantity of neuron I Timing diagram of Figure 4b is based on Figure 4a The parameters obtained by plotting Planar phase diagram; Figure 4c is based on Figure 4a The parameters obtained by plotting Planar phase diagram; Figure 4d is based on Figure 4a The parameters obtained by plotting Planar phase diagram; Figure 5a In Example 1 of the present invention =0.96, =12.6, the state quantity of neuron I Timing diagram of Figure 5b is based on Figure 5a The parameters obtained by plotting Planar phase diagram; Figure 5c is based on Figure 5a The parameters obtained by plotting Planar phase diagram; Figure 5d is based on Figure 5a The parameters obtained by plotting Planar phase diagram; Figure 6a In Example 1 of the present invention =0.96, =14.2, the state quantity of neuron I Timing diagram of Figure 6b is based on Figure 6a The parameters obtained by plotting Planar phase diagram; Figure 6c is based on Figure 6a The parameters obtained by plotting Planar phase diagram; Figure 6d is based on Figure 6a The parameters obtained by plotting Planar phase diagram; Figure 7a In Example 2 of the method of the present invention, =0.96, the fractional-order Hopfield neural network model optimizes the wind turbine inspection path planning TSP in the two-dimensional wind farm, and the random inspection path when there is no planning; Figure 7b The display is based on Figure 7a The optimal path matrix of the parameters in multiple iterations; Figure 7c The display is based on Figure 7a The parameters of change with the number of iterations, and the energy function changes; Figure 8a In Example 3 of the method of the present invention, =0.96, the fractional-order Hopfield neural network model optimizes the three-dimensional wind turbine blade inspection path planning TSP, and the random inspection path when there is no planning; Figure 8b The display is based on Figure 8a The optimal path matrix of the parameters in multiple iterations; Figure 8c The display is based on Figure 8a The parameters of the energy function change as the number of iterations changes. DETAILED DESCRIPTION

[0009] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0010] The method of the present invention adopts a fractional-order Hopfield neural network model with bidirectional memristor coupling. The model takes into account the synaptic crosstalk phenomenon and uses two hyperbolic tangent memristors for coupling between neurons, successfully extending this coupling strategy to fractional-order systems.

[0011] The present invention is based on the path optimization method of the memristor bidirectional coupled fractional-order network model, by establishing a memristor bidirectional coupled fractional-order Hopfield neural network model, and is implemented according to the following steps: Step 1: Use Caputo definition to determine the fractional derivative expression. Based on Caputo's definition of fractional derivative, the expression is: (1) in, is the fractional order, ; is not less than The smallest integer of ; a and t are the upper and lower limits of the integral respectively; is a unary function of Derivatives; is the Gamma function; Step 2: Construct a fractional-order Hopfield neural network model and determine the hyperbolic tangent memristor in it. 2.1) Based on the expression of fractional derivatives, fractional orders are introduced into the traditional integer-order Hopfield neural network model , and considering the mutual influence between synapses, coupled hyperbolic tangent memristors are used to replace the original neural synapses to achieve the coupling of fractional-order Hopfield neurons, and a fractional-order Hopfield neural network model containing three neurons is constructed, as shown in formula (2): (2) Among them, the order of the fractional order Pick ; They are the activation functions of neuron I, neuron II, and neuron III respectively; They are the state variables of neuron I, neuron II, and neuron III respectively; is the state variable of the hyperbolic tangent memristor; tanh( u ), tanh( w ) is the memristor function of the hyperbolic tangent memristor; w 11 is the synaptic weight of neuron I itself; w 13 It is the synaptic weight of the connection where neuron I affects neuron III; w 22 is the synaptic weight of neuron II itself; w 23 It is the synaptic weight of the connection that affects neuron III by neuron II; w 31 It is the synaptic weight of the connection that affects neuron I by neuron III; w 32 It is the synaptic weight of the connection that affects neuron II by neuron III; w 33 is the synaptic weight of neuron III itself; It is the synaptic weight of the connection where neuron I affects neuron II; It is the synaptic weight of the connection that affects neuron I by neuron II; yes Strength parameters of yes Strength parameters of is the crosstalk strength of the memristor; 2.2) The expression of the hyperbolic tangent memristor used in the fractional-order Hopfield neural network model is: (3) in, v is the input port of the memristor; i is the output port of the memristor; x is an internal variable; G ( x ) is the memetic derivative function.

[0012] Step 3: Determine the coupled hyperbolic tangent memristor, simulate the synaptic crosstalk phenomenon in the HNN model, couple two fractional-order hyperbolic tangent memristors, and obtain a coupled hyperbolic tangent memristor, as shown in formula (4): (4) in, is the state variable of the hyperbolic tangent memristor; is the crosstalk strength of the hyperbolic tangent memristor, is the memristor of the coupled hyperbolic tangent memristor.

[0013] Step 4: Based on the specific TSP problem, the optimal solution is obtained through the fractional-order Hopfield neural network model to complete the path planning. The specific process is: according to the specific requirements of the TSP problem, the corresponding fractional-order Hopfield neural network model guided by the energy function is designed, the optimal solution is searched, and the model is used for iterative calculation to obtain the optimal solution of the TSP problem, that is, the shortest inspection path.

[0014] Through the above steps, the coupled hyperbolic tangent memristor is used to simulate the synaptic crosstalk phenomenon in the HNN model, and neuron I is coupled with neuron II; the remaining coupling strengths of neuron I, neuron II, and neuron III are given by It means that the whole model construction is completed at this point; then according to the specific TSP problem, the relevant parameters are set and the optimal solution is predicted.

[0015] Test verification 1. Stability (equilibrium point) analysis of the model of the present invention: In order to obtain the equilibrium point of the system, the left side of equation (3) is set to 0, and after conversion, equation (4) is obtained as follows: (4) The equilibrium point is obtained from formula (4), as shown in formula (5): (5) is the intersection of the following two functions, expressed as formula (6): (6) The system equation (5) is at the equilibrium point ( x 1 , x 2 , x 3 , x 4 , x 5 ) is expressed as follows: (7) in, ; then the eigenvalue of the system's equilibrium point is: , in, Regarding variables Table 1 shows the relationship between the equilibrium state of the system and Partial value relationship.

[0016] Table 1. Eigenvalues ​​of fractional-order Hopfield neural network model

[0017] From Table 1, we can see that the fractional-order Hopfield neural network model has a good equilibrium point. There is a solution at , and all eigenvalues ​​are greater than or equal to 0, thus it can be determined that the model created by the present invention is a complex unstable system.

[0018] According to the above analysis and verification, the model constructed by the present invention takes into account the mutual influence between neuronal synapses, and proposes a fractional-order Hopfield neural network model by coupling two hyperbolic tangent memristors to connect Hopfield neurons. This model can not only show more diverse and complex dynamic characteristics and chaotic phenomena, but also is more in line with the actual operation mode of the brain.

[0019] Example 1 According to the aforementioned steps of the present invention, the following is implemented: 1) Establish a fractional-order Hopfield neural network model, A new hyperbolic tangent memristor model is established, and its mathematical form is shown in formula (9): (9) in, and are the input and output ports of the memristor; is an internal variable; is the memetic derivative function.

[0020] Select the memristor electromagnetic induction coupling strength k between neuron I and neuron II 1 are variables, and the values ​​of the other parameters are shown in Table 2. Substitute the parameters in Table 2 into formula (2), where two hyperbolic tangent memristors are used to replace the synapses of neuron I and neuron II, and the complete bidirectional synaptic connection between neurons is retained; at the same time, the model is generalized from integer order to fractional order, and a specific fractional-order Hopfield neural network model is established, as shown in formula (10): (10) In the formula, q is the fractional order; k 1 is the memristor coupling strength. Table 2. Parameter values ​​of fractional-order Hopfield neural network model

[0021] In terms of stability, in order to find the equilibrium point of the system, the left side of equation (9) is set to 0, and we get: (11) From formula (11), the equilibrium point can be obtained as formula (12): (12) is the intersection of the following two functions, expressed as formula (13): (13) The system equation (10) is at the equilibrium point ( x 1 , x 2 , x 3 , x 4 ) is expressed as: (14) The eigenvalue of the system's equilibrium point is obtained by equation (15): (15) in, Regarding variables The fractional-order Hopfield neural network model is at the equilibrium point. There is a solution at , and all eigenvalues ​​are greater than or equal to 0. This shows that the new model created by the present invention is a complex unstable system.

[0022] 2) Verification of the rich dynamic behavior of the fractional-order Hopfield neural network model.

[0023] When other parameters remain unchanged, when the order of the fractional order is =0.96, select the initial value ,like Figure 1 , which shows the 0.96-order fractional-order Hopfield neural network model with the electromagnetic induction coupling intensity is the bifurcation diagram of the variable. Figure 1 It can be seen that the 0.96-order fractional-order Hopfield neural network model exhibits rich dynamic behavior characteristics. When , the 0.96-order fractional-order Hopfield neural network model is in a single-cycle state; when When , the 0.96-order fractional-order Hopfield neural network model is in a double-periodic state; when When , the 0.96-order fractional-order Hopfield neural network model goes through a short four-cycle state. When it instantly jumps to the chaotic state; when After that, the 0.96-order fractional-order Hopfield neural network model jumps from the chaotic state to the double-periodic state. Through the above analysis, the rich dynamic behavior of the 0.96-order fractional-order Hopfield neural network model is fully demonstrated. The following analysis is based on the fractional order =0.96 as a prerequisite.

[0024] when =7.1, draw the state quantity of neuron I in the 0.96-order fractional-order Hopfield neural network model Timing diagram Figure 2a ,draw Planar phase diagram Figure 2b , Figure 2c , Figure 2d As shown, at this time, the 0.96-order fractional-order Hopfield neural network model is in a single-cycle state.

[0025] when =10, draw the state quantity of neuron I in the 0.96-order fractional-order Hopfield neural network model Timing diagram Figure 3a ,draw Planar phase diagram Figure 3b , Figure 3c , Figure 3dAs shown, the 0.96-order fractional-order Hopfield neural network model is in a double-periodic state.

[0026] when =11.6, draw the state quantity of neuron I in the 0.96-order fractional-order Hopfield neural network model Timing diagram Figure 4a ,draw Planar phase diagram Figure 4b , Figure 4c , Figure 4d As shown, the 0.96-order fractional-order Hopfield neural network model is in a four-cycle state.

[0027] when =12.6, draw the state quantity of neuron I in the 0.96-order fractional-order Hopfield neural network model Timing diagram Figure 5a ,draw Planar phase diagram Figure 5b , Figure 5c , Figure 5d As shown, the 0.96-order fractional-order Hopfield neural network model is in a chaotic state.

[0028] when =14.2, draw the state quantity of neuron I in the 0.96-order fractional-order Hopfield neural network model Timing diagram Figure 6a ,draw Planar phase diagram Figure 6b , Figure 6c , Figure 6d As shown, the 0.96-order fractional-order Hopfield neural network model is in a single-cycle state.

[0029] Through detailed analysis of phase diagrams, timing diagrams and bifurcation diagrams, it is proved that the method of the present invention fully takes into account the synaptic crosstalk phenomenon, uses coupled hyperbolic tangent memristors to connect Hopfield neurons, and expands the three neural networks to fractional orders, successfully constructing a new fractional-order Hopfield neural network model, which exhibits diverse and complex dynamic behaviors and more accurately reflects the nonlinear characteristics of the real human brain.

[0030] Example 2 Embodiment 2 of the present invention is similar to Embodiment 1.

[0031] After the model is built, a TSP problem with 28 wind turbine coordinates in a two-dimensional space is designed. The specific parameter information of these coordinates is shown in Table 3. For the TSP problem, when designing the energy function of the fractional-order Hopfield neural network, a Matrix to representn The rows of the matrix represent the coordinates of each position, and the columns of the matrix indicate the order of access. In addition, according to the definition of the TSP problem, the following constraints must be observed: (1) Each position can only be accessed once, and only one element in each row is "1", and the rest are "0"; (2) Only one position can be accessed at a time, and only one element in each column is "1", and the rest are "0"; (3) All positions must be visited, and the sum of all "1" elements in the matrix must be n; The energy function of the fractional-order Hopfield neural network corresponding to the TSP problem is as follows: (16) in, The output of the neuron is represented in the order j Access Location i ,in Indicates location i and location j The distance between Only when the constraints are met, the first three items in formula (16) will reach the minimum value of 0; the fourth item in formula (16) is the objective function. =0, means in order j Access Location i When you need to determine the position in the matrix i The adjacent previous and next positions , and the position i The distance to these two locations is included in the total distance.

[0032] According to the above analysis, it can be obtained that the shortest path found in the iterative process corresponds to the state matrix when the energy function of the fractional-order Hopfield neural network reaches its minimum value.

[0033] Then, the fractional-order Hopfield neural network model of the present invention is used to iteratively optimize the TSP problem in Example 2, and the results are as follows: Figure 7a , Figure 7b , Figure 7c shown. Figure 7a The figure shows the random inspection path without planning. Figure 7b It shows the optimal path matrix during multiple iterations. Figure 7cIt shows the changing trend of the energy function value as the number of iterations increases during the entire iteration process, reflecting the process of the algorithm converging to the optimal solution. It can be seen that the energy function curve of the fractional-order Hopfield neural network model in the method of the present invention decreases rapidly, indicating that it has an efficient convergence speed and excellent convergence performance.

[0034] Table 3. Fan location information

[0035] Example 3 The implementation object and implementation process of Example 3 are similar to those of Example 2, and the goal is to apply the fractional-order Hopfield neural network model to the inspection path planning problem of three-dimensional wind turbine blades, namely the three-dimensional traveling salesman problem (3D TSP).

[0036] In the inspection work of wind farms, in addition to the need to solve the traditional two-dimensional wind turbine inspection path planning problem, the limited endurance of quadcopter drones is still a problem that needs to be solved. To this end, the shortest path planning problem of the quadcopter drone's power inspection is converted into a three-dimensional TSP problem, and the fractional-order Hopfield neural network model in the method of the present invention is used to solve it. A three-dimensional inspection path planning TSP problem containing 30 wind turbine blade observation points is now constructed. The specific location information of each observation point is detailed in Table 4. Through iterative calculation, when the defined energy function reaches the minimum value, the corresponding inspection path is the optimal solution. The method of the present invention is used to iteratively optimize the power inspection TSP problem in Example 3 using a fractional-order Hopfield neural network model, and the results are as follows: Figure 8a , Figure 8b , Figure 8c shown. Figure 8a The figure shows the random inspection path without planning. Figure 8b It shows the optimal path matrix during multiple iterations. Figure 8c It shows the law of energy function change with the change of iteration number. It can be seen that the energy function curve of the fractional-order Hopfield neural network model in the method of the present invention decreases rapidly, indicating that it has efficient convergence speed and excellent convergence performance.

[0037] Table 4. Observation point location information

[0038] Example 4 The implementation object and implementation process of Example 4 are similar to those of Example 2. After the model is constructed, a TSP problem with 30 wind turbine coordinates in a two-dimensional space is designed. The specific parameter information of these coordinates is shown in Table 5. According to the specific requirements of the TSP problem, an energy function is designed to guide the fractional-order Hopfield neural network model to search for the optimal solution. The model is used for iterative calculation to obtain the optimal solution of the TSP problem, that is, the shortest inspection path.

[0039] The method of the present invention is adopted to iteratively optimize the inspection TSP problem in Example 4 using a fractional-order Hopfield neural network model. The energy function curve of the fractional-order Hopfield neural network model in the method of the present invention decreases rapidly, indicating that it has an efficient convergence speed and excellent convergence performance.

[0040] Table 5. Fan location information

[0041] Example 5 The implementation object and implementation process of Example 5 are similar to those of Example 3, and the goal is to apply the fractional-order Hopfield neural network model to the inspection path planning problem of three-dimensional wind turbine blades, namely the three-dimensional traveling salesman problem (3D TSP).

[0042] The shortest path planning problem of the power inspection of the quadcopter drone is transformed into a three-dimensional TSP problem, and the fractional-order Hopfield neural network model in the method of the present invention is used to solve it. A three-dimensional inspection path planning TSP problem containing 24 wind turbine blade observation points is now constructed. The specific location information of each observation point is shown in Table 6. Through iterative calculation, when the defined energy function reaches the minimum value, the corresponding inspection path is the optimal solution. The method of the present invention is adopted to iteratively optimize the inspection TSP problem in Example 5 using a fractional-order Hopfield neural network model. The energy function curve of the fractional-order Hopfield neural network model in the method of the present invention decreases rapidly, indicating that it has an efficient convergence speed and excellent convergence performance.

[0043] Table 6. Observation point location information

[0044] Example 6 The implementation object and implementation process of Example 6 are similar to those of Example 3, and the goal is to apply the fractional-order Hopfield neural network model to the inspection path planning problem of three-dimensional wind turbine blades, namely the three-dimensional traveling salesman problem (3D TSP).

[0045] The shortest path planning problem of the power inspection of the quadcopter drone is transformed into a three-dimensional TSP problem, and the fractional-order Hopfield neural network model in the method of the present invention is used to solve it. A three-dimensional inspection path planning TSP problem containing 36 wind turbine blade observation points is now constructed. The specific location information of each observation point is shown in Table 7. Through iterative calculation, when the defined energy function reaches the minimum value, the corresponding inspection path is the optimal solution. Table 7. Observation point location information

[0046] The method of the present invention is adopted to iteratively optimize the inspection TSP problem in Example 6 using a fractional-order Hopfield neural network model. The energy function curve of the fractional-order Hopfield neural network model in the method of the present invention decreases rapidly, indicating that it has an efficient convergence speed and excellent convergence performance.

Claims

1. A path optimization method based on a memristor bidirectional coupled fractional-order network model, characterized in that: Follow these steps to implement: Step 1: Use Caputo definition to determine the fractional derivative expression; Step 2: construct a fractional-order Hopfield neural network model and determine the hyperbolic tangent memristor therein; Step 3, determining a coupled hyperbolic tangent memristor; Step 4: Based on the specific TSP problem, the optimal solution is obtained through the fractional-order Hopfield neural network model to complete the path planning.

2. The path optimization method based on the memristor bidirectional coupled fractional-order network model according to claim 1 is characterized in that: In step 1, the specific process is: Based on the fractional derivative defined by Caputo, the expression is: (1) in, is the fractional order, ; is not less than The smallest integer of ; a and t are the upper and lower limits of the integral respectively; is a unary function of Derivatives; is the Gamma function.

3. The path optimization method based on the memristor bidirectional coupled fractional-order network model according to claim 1 is characterized in that: In step 2, a fractional-order Hopfield neural network model is constructed. The specific process is: Based on the expression of fractional derivatives, fractional orders are introduced into the traditional integer-order Hopfield neural network model. , and considering the mutual influence between synapses, coupled hyperbolic tangent memristors are used to replace the original neural synapses to achieve the coupling of fractional-order Hopfield neurons, and a fractional-order Hopfield neural network model containing three neurons is constructed, as shown in formula (2): (2) Among them, the order of the fractional order Pick ; They are the activation functions of neuron I, neuron II, and neuron III respectively; They are the state variables of neuron I, neuron II, and neuron III respectively; is the state variable of the hyperbolic tangent memristor; tanh( u ), tanh( w ) is the memristor function of the hyperbolic tangent memristor; w 11 is the synaptic weight of neuron I itself; w 13 It is the synaptic weight of the connection where neuron I affects neuron III; w 22 is the synaptic weight of neuron II itself; w 23 It is the synaptic weight of the connection that affects neuron III by neuron II; w 31 It is the synaptic weight of the connection that affects neuron I by neuron III; w 32 It is the synaptic weight of the connection that affects neuron II by neuron III; w 33 is the synaptic weight of neuron III itself; It is the synaptic weight of the connection where neuron I affects neuron II; It is the synaptic weight of the connection that affects neuron I by neuron II; yes Strength parameters of yes Strength parameters of is the crosstalk strength of the memristor.

4. The path optimization method based on the memristor bidirectional coupled fractional-order network model according to claim 3 is characterized in that: In step 1, the order of the fractional order is =0.

96.

5. The path optimization method based on the memristor bidirectional coupled fractional-order network model according to claim 3 is characterized in that: In step 1, The value range is 7~14.

2.

6. The path optimization method based on the memristor bidirectional coupling fractional-order network model according to claim 1 is characterized in that: In step 2, the expression of the hyperbolic tangent memristor is: (3) in, v is the input port of the memristor; i is the output port of the memristor; x is an internal variable; G ( x ) is the memetic derivative function.

7. The path optimization method based on the memristor bidirectional coupled fractional-order network model according to claim 1 is characterized in that: In step 3, To simulate the synaptic crosstalk phenomenon in the HNN model, two fractional-order hyperbolic tangent memristors are coupled to obtain a coupled hyperbolic tangent memristor, which is expressed as follows: (4) in, is the state variable of the hyperbolic tangent memristor; is the crosstalk strength of the hyperbolic tangent memristor, is the memristor of the coupled hyperbolic tangent memristor.

8. The path optimization method based on the memristor bidirectional coupling fractional-order network model according to claim 1 is characterized in that: In step 4, the specific process is: According to the specific requirements of the TSP problem, a fractional-order Hopfield neural network model guided by the corresponding energy function is designed to search for the optimal solution. The model is used for iterative calculation to obtain the optimal solution of the TSP problem, that is, the shortest inspection path.

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