Underwater multi-objective routing method based on improved non-dominated sorting genetic algorithm

Abstract

The application discloses an underwater multi-target routing method based on an improved non-dominated sorting genetic algorithm. Firstly, sensor nodes are arranged in a target water area and networking is performed, and a segmented structure is adopted to encode feasible paths from a source node to a target node; secondly, a routing multi-target fitness function is constructed, and a dynamic weight function is introduced to form a comprehensive fitness index; finally, the improved non-dominated sorting genetic algorithm is used to divide a population into grades, and a better path is explored through a crossover and mutation operation; and a reference point elite selection strategy is designed to improve the coverage of a solution set in a target space, and the optimal routing path is output after the algorithm converges. The application can realize dynamic balance among different optimization targets, reduce energy consumption and time delay while taking into account link quality, and thus improve network routing performance.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of underwater routing, and particularly relates to an underwater multi-objective routing method based on an improved non-dominated sorting genetic algorithm. BACKGROUND

[0002] With the continuous advancement of ocean resource development and intelligent ocean construction, underwater wireless sensor networks (UWSN) as a key information infrastructure have been widely used in environmental monitoring, target detection and disaster warning tasks. UWSN is usually composed of distributed underwater sensor nodes, and data transmission is realized through multi-hop communication between nodes, and finally uploaded to the shore-based monitoring center via a buoy. However, due to the complex and variable underwater physical environment, UWSN generally has performance bottlenecks in terms of routing energy consumption, communication delay and link quality.

[0003] Existing underwater network routing methods are mostly based on a single optimization target, such as minimizing energy consumption or minimizing delay, which is difficult to balance multiple performance indicators such as energy consumption, delay and link quality in practical applications. At the same time, traditional multi-objective routing algorithms mostly use fixed weights or static fitness functions, lack dynamic adaptive mechanisms, and are difficult to effectively cope with the uncertainty and complexity of the underwater environment. For example, the method proposed by Guilin University of Electronic Technology in the patent "Method for multi-objective optimization opportunistic routing of underwater sensor network" (Application No.: 201911185266.7, Publication No.: CN 110933676 A) uses a fixed fitness function, only focuses on the optimization of routing energy consumption and delay, and fails to consider link quality in the comprehensive consideration, and routing energy consumption and delay are mutually conflicting optimization targets, so the overall network performance is difficult to guarantee when the link quality deteriorates.

[0004] In recent years, multi-objective evolutionary algorithms (such as NSGA-II, NSGA-III) have received widespread attention due to their ability to simultaneously optimize multiple conflicting objectives. However, traditional methods still have many shortcomings in terms of path encoding, fitness evaluation indicators and solution set diversity maintenance. For example, the fixed weight strategy is difficult to achieve dynamic guidance during optimization, which easily leads to local optimization; the conventional crowding distance mechanism has limited ability to distinguish sparse regions, affecting the distribution balance of the solution set. In addition, multi-objective routing schemes based on genetic algorithms also have obvious limitations in terms of Pareto solution set diversity and path feasibility guarantee.

[0005] In summary, existing UWSN routing algorithms are difficult to balance key performance indicators such as energy consumption, delay and link quality, thereby limiting the improvement of the overall routing performance of the network. Therefore, it is urgent to propose an efficient routing method that adapts to dynamic underwater environments, has flexible path encoding, and balances multiple optimization targets, in order to comprehensively improve the routing performance of UWSN. SUMMARY

[0006] The purpose of the present application is to overcome the shortcomings of the prior art, and provide an underwater multi-objective routing method based on an improved non-dominated sorting genetic algorithm, to solve the problem that the existing underwater routing method has poor adaptability, and it is difficult to balance energy consumption, time delay and link quality, resulting in poor overall network routing performance. Specifically, the present application encodes the feasible path from the source node to the destination node into a chromosome individual using a segmented structure, and reasonably represents the solution space. Then a multi-objective fitness function considering energy consumption, time delay and link quality is established, and a weight function dynamically adjusted with iteration is introduced to balance the optimization objectives. Finally, through cross and mutation operations, better solutions are continuously explored, and the reference point elitist selection strategy is combined to improve the coverage of the solution set in the objective space.

[0007] The present application provides an underwater multi-objective routing method based on an improved non-dominated sorting genetic algorithm to overcome the shortcomings of the above technology.

[0008] To achieve the above-mentioned purpose of the present application, the technical scheme adopted by the present application is as follows:

[0009] An underwater multi-objective routing method based on an improved non-dominated sorting genetic algorithm, comprising the following steps:

[0010] S1: Deploy sensor nodes in the target water area and network, and encode the feasible path from the source node to the destination node using a segmented structure;

[0011] S2: Construct a routing multi-objective fitness function, and introduce a dynamic weight function to form a comprehensive fitness index;

[0012] S3: Use the improved non-dominated sorting genetic algorithm to divide the population into grades, and explore better paths through cross and mutation operations;

[0013] S4: Design a reference point elitist selection strategy to improve the coverage of the solution set in the objective space, until the algorithm converges and outputs the optimal routing path.

[0014] Further, the step S1 is specifically as follows:

[0015] S1-1: Deploy sensor nodes in the target water area and network:

[0016] Deploy underwater sensor nodes anchored on the seabed in the target water area, and form a network with buoy nodes deployed on the sea surface; wherein the underwater sensor nodes are used to monitor and collect marine environmental data, and transmit the monitoring data to the buoy nodes through multi-hop routing; the set of underwater sensor nodes is denoted as , and the set of buoy nodes is denoted as ;

[0017] The whole network is represented as a directed graph , wherein represents a node set, represents a directed link set between nodes, represents a directed link from node to node , wherein node is an underwater sensor node, and node is an underwater sensor node or a buoy node; represents a communication distance between node and node , is a maximum communication radius of underwater sensor node ; the buoy node periodically uploads the collected data to a low-orbit satellite, and the low-orbit satellite transmits the data to a monitoring center located on the shore through a radio link;

[0018] S1-2: encode the feasible paths from the source node to the target node by using a segmented structure:

[0019] Encode each feasible path from the source node to the target node as a chromosome individual by using the segmented structure:

[0020]

[0021] wherein, represents a terminal subscript of the first path encoding segment, and satisfies 2≤ ≤ -2, represents the th node on the feasible path, represents the number of nodes on the feasible path; , , and are the first path encoding segment, the second path encoding segment and the third path encoding segment, respectively.

[0022] Further, the step S2 is specifically as follows:

[0023] S2-1: construct a routing multi-objective fitness function:

[0024] The multi-objective fitness function includes a total routing energy consumption function , a total routing delay function , and a total routing link quality loss function ​Three objective fitness functions are as follows:

[0025]

[0026]

[0027]

[0028] wherein, is the routing energy consumption from the i th node to the i+1 th node, is the routing delay from the i th node to the i+1 th node, is the routing link quality loss from the i th node to the i+1 th node.

[0029] S2-2: Introducing a dynamic weight function to form a comprehensive fitness index:

[0030] Introducing a dynamic weight function, adaptively fusing the multi-objective fitness function, and forming a comprehensive fitness index :

[0031]

[0032] wherein, is a routing energy consumption weight function dynamically adjusted with the iteration number, is a routing delay weight function dynamically adjusted with the iteration number, is a routing link quality loss weight function dynamically adjusted with the iteration number, and satisfies and the following variable weight strategy is set:

[0033]

[0034]

[0035]

[0036] wherein, and are the maximum value and the minimum value of the routing energy consumption weight function, respectively; and ​​​​​​​​​​​​​​​Set the maximum and minimum values ​​of the routing delay weight function respectively; This represents the maximum number of iterations.

[0037] Furthermore, step S3 is specifically as follows:

[0038] S3-1: Using an improved non-dominated sorting genetic algorithm to classify the population into hierarchical levels:

[0039] An improved non-dominated sorting genetic algorithm was used to analyze the parent population composed of chromosome individuals. The hierarchy is determined by grouping all chromosomes that are not dominated by any solution into a frontier. ;

[0040] S3-2: Exploring better paths through crossover and mutation operations:

[0041] ① Crossover: Use partial matching to crossover while preserving the source node. Under the premise of keeping the parent population unchanged, exchange parent populations The intermediate path of the two chromosome individuals is encoded and the path repair is performed to obtain two offspring chromosome individuals after the crossover operation;

[0042] ② Variation: In the parent population In an individual with a single chromosome, a relay node that is not the source node is randomly selected, and the mutation probability is... Replace it with another neighbor node and perform path repair to obtain a offspring chromosome individual after the mutation operation. The mutation probability is adaptively adjusted according to the chromosome individual level, and the calculation formula is:

[0043]

[0044] in, To rank individuals, and These are the maximum and minimum values ​​of the individual ranking rank, respectively. and These are the maximum and minimum values ​​of the mutation probability, respectively;

[0045] The crossover and mutation operations between the first, second, and third path coding segments in S1-2 are performed independently, and the offspring chromosomes after path repair must still be directed graphs. Feasible paths on the road.

[0046] Furthermore, step S4 is specifically as follows:

[0047] S4-1: Design a reference point elite selection strategy to improve the coverage of the solution set in the target space:

[0048] Merge the offspring chromosome individuals after the crossover and mutation operations into the parent population , and perform hierarchical partitioning again using the improved non-dominated sorting genetic algorithm; design a reference point elite selection strategy to fill the next generation population in sequence from the front . The steps are as follows:

[0049] ① Normalize the comprehensive fitness index of each solution in the front to a unit hyperplane;

[0050] ② Project the comprehensive fitness index normalized to the unit hyperplane to the nearest reference point, which is its membership reference point;

[0051] ③ Count the number of currently assigned solutions for each reference point , and preferentially select solutions associated with the reference point of ;

[0052] ④ If the number of currently assigned solutions for a reference point is more than one, select the solution with the smallest projection angle;

[0053] ⑤ Repeat ①-④ to assign solutions to each reference point one by one until the next generation population reaches the size limit .

[0054] S4-2: Output the optimal routing path after the algorithm converges:

[0055] When the algorithm iterates to the maximum number of iterations or the Pareto front is no longer updated, output the optimal routing path closest to the reference point.

[0056] The advantages and technical effects of the present application are as follows:

[0057] The present application introduces a dynamic weight function to form a comprehensive fitness index, which can adjust the weights of each objective in real time according to the iteration process, achieving dynamic balance among the three optimization objectives of energy consumption, delay and link quality, and overcoming the shortcomings of traditional routing optimization methods that fixed weights cannot dynamically consider multiple conflicting optimization objectives. Secondly, global optimization is performed by the improved non-dominated sorting genetic algorithm, combined with crossover, mutation operations and reference point elite selection strategy, which improves the optimization efficiency and diversity of solutions and avoids falling into local optimum.

[0058] ​The simulation results show that when the number of network nodes reaches 50, compared with the traditional multi-objective optimization opportunistic routing method (applicant: Guilin University of Electronic Technology, application number: 201911185266.7, publication number: CN 110933676A), the average end-to-end delay is reduced by about 37.7%, the routing energy consumption is reduced by about 14.9%, and the link reliability is increased by about 19.5%.

[0059] The application can realize dynamic balance between different optimization objectives, reduce energy consumption and delay while considering link quality, and thus improve network routing performance. BRIEF DESCRIPTION OF DRAWINGS

[0060] Figure 1 is the overall flowchart of an embodiment of the application;

[0061] Figure 2 is a network architecture diagram of an embodiment of the application;

[0062] Figure 3 is a schematic diagram of path encoding using a segmented structure according to an embodiment of the application;

[0063] Figure 4 is a simulation result comparison diagram of average end-to-end delay between the method provided by the application and the traditional multi-objective optimization opportunistic routing method according to an embodiment of the application;

[0064] Figure 5 is a simulation result comparison diagram of routing energy consumption between the method provided by the application and the traditional multi-objective optimization opportunistic routing method according to an embodiment of the application.

[0065] Figure 6 is a simulation result comparison diagram of link reliability between the method provided by the application and the traditional multi-objective optimization opportunistic routing method according to an embodiment of the application. DETAILED DESCRIPTION

[0066] In order to make the purpose, technical scheme and advantages of the application clearer, further detailed description will be made to the application in combination with the drawings and embodiments.

[0067] The embodiment proposes an underwater multi-objective routing method based on an improved non-dominated sorting genetic algorithm, and the overall flowchart is as shown in Figure 1 The method comprises the following steps:

[0068] S1: Deploy sensor nodes in the target water area and network, encode the feasible paths from the source node to the target node using a segmented structure, and the specific steps are as follows:

[0069] S1-1: Deploy sensor nodes in the target water area and network:

[0070] like Figure 2 As shown, deployment in the target water area An underwater sensor node anchored on the seabed, and with =A network consisting of 2 buoy nodes deployed on the sea surface; wherein, underwater sensor nodes are used to monitor and collect marine environmental data, and transmit the monitoring data to the buoy nodes through multi-hop routing; the set of underwater sensor nodes is denoted as . The set of buoy nodes is denoted as ;

[0071] The entire network is represented as a directed graph. ,in Represents a set of nodes. Represents the set of directed links between nodes. Indicates from node To the node A directed link, in which nodes It is an underwater sensor node, node These are underwater sensor nodes or buoy nodes; Represents a node With nodes Communication distance between them underwater sensor node The maximum communication radius; the buoy nodes periodically upload the collected data to a low-Earth orbit satellite, which then transmits the data to the monitoring center on shore via a radio link;

[0072] S1-2: Encode the feasible path from the source node to the target node using a segmented structure:

[0073] like Figure 3 As shown, the network consists of 12 underwater sensor nodes and 2 buoy nodes, forming a directed graph with 14 vertices. The 14 vertices of the directed graph are labeled as follows: ; Figure 3 From the source node To the target node A feasible path has 6 vertices, which means the number of nodes on the feasible path is... =6; In this embodiment, we take... =3, using a segmented structure for path encoding, dividing each path from the source node To the target node Feasible path Encoded as a single chromosome:

[0074]

[0075] in, Indicates a feasible path the first path encoding segment is = 0 = 1 ; the second path encoding segment is = 0 = 1 ; the third path encoding segment is = 0 = 1

[0076] .

[0077] S2: build a routing multi-objective fitness function, and introduce a dynamic weight function to form a comprehensive fitness index, the specific steps are as follows:

[0078] S2-1: build a routing multi-objective fitness function: The multi-objective fitness function includes a total routing energy consumption function , a total routing delay function , and a total routing link quality loss function

[0079] three objective fitness functions, as shown in the following formula:

[0080]

[0081]

[0082] wherein, is the routing energy consumption of the i th node to the i+1 th node , is the routing delay of the i th node to the i+1 th node , and is the routing link quality loss of the i th node to the i+1 th node . S2-2: introduce a dynamic weight function to form a comprehensive fitness index: The dynamic weight function is introduced to adaptively fuse the multi-objective fitness function to form a comprehensive fitness index :

[0083] wherein, is a routing energy consumption weight function dynamically adjusted with the iteration number

[0084] .

[0085]

[0086] .​​​​​ Number of iterations Dynamically adjusted routing delay weight function Number of iterations A dynamically adjusted routing link quality loss weight function that satisfies... And set the following variable power strategy:

[0087]

[0088]

[0089]

[0090] in, and The maximum and minimum values ​​of the energy consumption weight function are routed separately; and Set the maximum and minimum values ​​of the routing delay weight function respectively; To determine the maximum number of iterations, in this embodiment, we take... =0.6, =0.2, =0.4, =0.2, =14.

[0091] S3: The population is hierarchically divided using an improved non-dominated sorting genetic algorithm, and better paths are explored through crossover and mutation operations. The specific steps are as follows:

[0092] S3-1: Using an improved non-dominated sorting genetic algorithm to classify the population into hierarchical levels:

[0093] An improved non-dominated sorting genetic algorithm was used to analyze the parent population composed of chromosome individuals. The hierarchy is determined by grouping all chromosomes that are not dominated by any solution into a frontier. ;

[0094] S3-2: Exploring better paths through crossover and mutation operations:

[0095] ① Crossover: Use partial matching to crossover while preserving the source node. Under the premise of keeping the parent population unchanged, exchange parent populations The intermediate path of the two chromosome individuals is encoded and the path repair is performed to obtain two offspring chromosome individuals after the crossover operation;

[0096] ② Variation: In the parent population In an individual with a single chromosome, a relay node that is not the source node is randomly selected, and the mutation probability is... Replace it with another neighbor node and perform path repair to obtain a sub-child chromosome individual after mutation operation, and the mutation probability is adaptively adjusted according to the chromosome individual level, and the calculation formula is:

[0097]

[0098] Wherein, is the individual ranking, and are the maximum and minimum values of the individual ranking, and are the maximum and minimum values of the mutation probability; in this embodiment, the maximum value of the mutation probability =0.3, and the minimum value of the mutation probability =0.05.

[0099] The crossover and mutation operations among the first path encoding segment, the second path encoding segment and the third path encoding segment in S1-2 are independently performed, and the sub-child chromosome individual after performing path repair still needs to be a feasible path on the directed graph.

[0100] S4: design reference point elitist selection strategy to improve the coverage of the solution set in the target space, and output the optimal routing path after the algorithm converges, and the specific steps are as follows:

[0101] S4-1: design reference point elitist selection strategy to improve the coverage of the solution set in the target space:

[0102] Combine the sub-child chromosome individuals after the crossover and mutation operations into the parent population , and perform level division again by using the improved non-dominated sorting genetic algorithm; design reference point elitist selection strategy to fill the next generation population from the front , and the steps are as follows:

[0103] ① Normalize the comprehensive fitness index of each solution in the front to the unit hyperplane;

[0104] ② Project the comprehensive fitness index normalized to the unit hyperplane to the nearest reference point, which is its affiliated reference point;

[0105] ③ Count the number of currently allocated solutions for each reference point , and preferentially select the solution associated with the reference point;

[0106] ④ If the number of currently allocated solutions for a reference point is more than one, select the solution with the smallest projection angle; ​​​​

[0107] V. Repeat 1-IV, assign solutions to each reference point one by one until the next generation population reach the size limit ;

[0108] S4-2: Output the optimal routing path after the algorithm converges:

[0109] When the algorithm iterates to the maximum number of iterations or the Pareto front is no longer updated, output the optimal routing path closest to the reference point.

[0110] The average end-to-end delay comparison results of the method provided by the application and the traditional multi-objective optimization opportunistic routing method (application number: 201911185266.7, publication number: CN110933676A) are shown in Figure 4 This embodiment is completed in Python3.7, and the computer memory used is 32GB, and the processor is Intel Core i5-12400F CPU based on x64 architecture. The specific parameters of all simulations in this embodiment are listed in Table 1. All experiments are carried out under the same parameter conditions to ensure the fairness of comparison.

[0111] Table 1 Simulation parameters

[0112]

[0113] From the simulation results of Figure 4 It can be seen that as the network size increases, the method of the application is always superior to the comparison method in terms of average end-to-end delay. When the number of network nodes is 50, the average end-to-end delay of the method of the application is reduced by about 37.7% compared with the traditional multi-objective optimization opportunistic routing method. The average end-to-end delay is obtained by averaging the transmission time of all data packets from the source node to the destination buoy node.

[0114] The routing energy consumption comparison results of the method provided by the application and the comparison method are shown in Figure 5 The routing energy consumption is obtained by accumulating the energy consumption of all links in the transmission path of the data packet. From the simulation results, it can be seen that the method of the application can effectively reduce the routing energy consumption, and when the number of nodes reaches 50, it is reduced by about 14.9% compared with the comparison method. The main reason is that the method of the application introduces a dynamic weight function to adaptively adjust the energy consumption target, avoiding the frequent use of long-distance or inefficient links.

[0115] The link reliability comparison results of the method provided by the application and the comparison method are shown in Figure 6 The link reliability is calculated by normalizing the link quality index, reflecting the reliable transmission capability of the path in the dynamic marine environment. From the simulation results of Figure 6It can be seen that the method of the application always keeps higher link reliability under the same condition, and when the number of nodes reaches 50, it is improved by about 19.5% compared with the comparative method. This is because the reference point elite selection strategy enhances the distribution of the solution set in the target space, so that the finally selected path achieves a better balance between energy consumption, delay and link quality.

[0116] In summary, the application can achieve dynamic balance between different optimization objectives, reduce energy consumption and delay while considering link quality, thereby improving network routing performance.

[0117] The above examples are only used to illustrate the technical solutions of the application, but not to limit it; although the application has been described in detail with reference to the foregoing examples, the technical solutions recorded in the foregoing examples can still be modified or some technical features can be replaced by equivalents for ordinary skilled in the art; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions claimed by the application.

Claims

1. An improved non-dominated sorting genetic algorithm based underwater multi-objective routing method, characterized in that, The method comprises the following steps: S1: deploying sensor nodes and networking in a target water area, and encoding the feasible paths from a source node to a target node by using a segmented structure; S2: constructing a routing multi-objective fitness function, and introducing a dynamic weight function to form a comprehensive fitness index, specifically as follows: S2-1: constructing a routing multi-objective fitness function: The multi-objective fitness function comprises a total route energy consumption function a total route latency function a total route link quality loss function The three objective fitness functions are as follows: in, For the first Nodes To the +1 node Router power consumption For the first Nodes To the +1 node routing latency, For the first Nodes To the +1 node Routing link quality loss; S2-2: introducing a dynamic weight function to form a comprehensive fitness index: A dynamic weight function is introduced to adaptively fuse the multi-objective fitness functions to form a comprehensive fitness index : wherein, is the iteration number a dynamically adjusted routing energy consumption weight function, is the iteration number a dynamically adjusted routing time delay weight function, is the iteration number a dynamically adjusted routing link quality loss weight function, and satisfies and the following variable weight strategy is set: wherein, and routing the maximum and minimum values of the energy consumption weight function, respectively; and routing the maximum and minimum values of the latency weight function, respectively; is the maximum number of iterations. S3: using an improved non-dominated sorting genetic algorithm to divide the population into grades, and exploring better paths through crossover and mutation operations, specifically as follows: S3-1: using an improved non-dominated sorting genetic algorithm to divide the population into grades: using an improved non-dominated sorting genetic algorithm on a parent population of chromosome individuals performing a rank partitioning to form a front of all chromosome individuals that are not dominated by any solution ; S3-2: exploring better paths through crossover and mutation operations: ① Crossover: using partial match crossover to keep the source node unchanged, exchange the parent population the middle path encoding of two chromosome individuals in the parent population, and perform path repair to obtain two child chromosome individuals after the crossover operation. ② Variation: in a chromosome individual of the parent population , a relay node of a non-source node is randomly selected to replace another neighbor node with a variation probability , and path repair is performed to obtain a child chromosome individual after variation operation, and the variation probability is adaptively adjusted according to the chromosome individual level, and the calculation formula is: wherein, is the rank of the individual, and are the maximum and minimum of the rank of the individual, respectively, and are the maximum and minimum of the mutation probability, respectively; The crossing and mutation operations among the first path encoding segment, the second path encoding segment and the third path encoding segment in S1-2 are independently performed, and the offspring chromosome individual after path repair still needs to be a feasible path on a directed graph . S4: designing a reference point elite selection strategy to improve the coverage of the solution set in the target space, and outputting the optimal routing path after the algorithm converges.

2. The underwater multi-objective routing method based on improved non-dominated sorting genetic algorithm of claim 1, wherein, The step S1 is specifically as follows: S1-1: deploying sensor nodes and networking in a target water area: Deployment in the target waters An underwater sensor node anchored on the seabed, and with A network of buoy nodes deployed on the sea surface is formed; among them, underwater sensor nodes are used to monitor and collect marine environmental data, and transmit the monitoring data to the buoy nodes through multi-hop routing; the set of underwater sensor nodes is denoted as . The set of buoy nodes is denoted as ; The entire network is represented as a directed graph wherein represents a set of nodes, represents a set of directed links between nodes, represents a directed link from node to node , wherein node is an underwater sensor node and node is either an underwater sensor node or a buoy node; represents the communication distance between node and node , and is the maximum communication radius of an underwater sensor node ; the buoy node periodically uploads the collected data to a low earth orbit satellite, which then transmits the data to a monitoring center located on shore via a radio link; S1-2: encoding the feasible paths from a source node to a target node by using a segmented structure: The path is encoded by using a section structure, and each feasible path from the source node to the target node is encoded as a chromosome individual: ​ wherein denotes a termination index of the first path encoding segment and satisfies 2≤ -2, denotes the th node on a feasible path ; denotes the number of nodes on a feasible path; , and are the first path encoding segment, the second path encoding segment and the third path encoding segment, respectively.​ 3. The underwater multi-objective routing method based on improved non-dominated sorting genetic algorithm of claim 1, wherein, The step S4 is specifically as follows: S4-1: designing a reference point elite selection strategy to improve the coverage of the solution set in the target space: Merging the offspring chromosome individuals after the crossover and mutation operations into the parent population Again, the improved non-dominated sorting genetic algorithm is used for rank division; a reference point elite selection strategy is designed to fill the next generation population from the front , step by step , the steps are: frontier comprehensive fitness indicator for each solution normalized to the unit hyperplane; ② projecting the comprehensive fitness index normalized to a unit hyperplane to the nearest reference point, which is the membership reference point of the point; iii. count the number of currently assigned solutions for each reference point , prefer the solution associated with the reference point of ; ④ if the number of currently allocated solutions of a reference point is more than one, selecting the solution with the smallest projection angle with the reference point; • Repeat 1-4, assigning solutions to each reference point one by one until the next generation population reached size limit ; S4-2: outputting the optimal routing path after the algorithm converges: When the algorithm iterates to the maximum number of iterations or the Pareto front is no longer updated, the optimal routing path closest to the reference point is output.

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