A network traffic distribution method based on knowledge-driven multi-objective particle swarm optimization

Abstract

The application discloses a network flow distribution method based on knowledge-driven multi-objective particle swarm optimization, a double-layer coding mode is modeled and designed to represent a scheduling scheme, a double-population evolution method is adopted to optimize two proposed objectives respectively, and an external archive is introduced to provide a channel for information exchange between the two populations, so that an optimal solution is obtained; through comprehensively considering mathematical models of minimum maximum link utilization and global link average utilization, adopting a knowledge-driven dynamic link analysis strategy, an efficient indirect coding mode, and an elite mutation strategy and non-dominated sorting method in the external archive, and with the help of the above strategies, the proposed data-driven multi-objective particle swarm optimization algorithm achieves excellent results when solving large-scale dynamic traffic engineering problems.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of network traffic engineering, and particularly relates to a network traffic distribution method based on knowledge-driven multi-objective particle swarm optimization. BACKGROUND

[0002] With the continuous development of network technology, traffic engineering plays an increasingly important role in modern network management. However, the traditional traffic engineering methods are difficult to quickly adapt and adjust in the face of rapid changes in network conditions. Moreover, mainstream TE technologies mainly focus on a single network performance optimization target, such as minimizing the maximum link utilization, while ignoring other important network performance indicators. These traditional methods often appear to be inadequate in dealing with complex network environments, and new solutions are urgently needed.

[0003] Currently, network traffic engineering can be divided into the following methods and deficiencies: 1) Configuration of link state protocols (such as OSPF): network traffic is managed and optimized through link state protocols, and path selection is based on link costs. This method usually requires a lot of manual involvement and intervention control, making it difficult to achieve automatic driving and management of the network. 2) Distributed traffic monitoring and control: traffic monitoring and bandwidth reservation are carried out through distributed mechanisms to respond to changes in network traffic demand. However, for large-scale networks or complex topologies, maintaining and updating the link state database requires a large amount of computing and storage resources, leading to increased packet loss or delay. 3) Optimization techniques based on constraint programming and local search: mathematical models and algorithms are used to optimize network resource allocation and traffic path selection. This method is difficult to quickly adapt and adjust in the face of rapid changes in network conditions. This can lead to decreased network performance and wasted resources in modern network environments, especially in large-scale networks. In summary, traditional TE methods have deficiencies in terms of automation, multi-objective optimization capability, adaptability, and computational efficiency. Therefore, new solutions are needed to solve the problem of multi-objective network performance optimization in traffic engineering. SUMMARY

[0004] To address the problems of the prior art, the application provides a network traffic distribution method based on knowledge-driven multi-objective particle swarm optimization, which models and designs a double-layer coding method to represent the scheduling scheme, adopts a double-population evolution method to optimize the two proposed objectives, and introduces an external archive to provide a channel for information exchange between the two populations, thereby obtaining the optimal solution.

[0005] The technical solution of the application is as follows:

[0006] A network traffic distribution method based on knowledge-driven multi-objective particle swarm optimization, comprising the following steps:

[0007] S1, a network model is established, weights are assigned to links in the network, segment identifiers are assigned to nodes or links through segment routing, paths with the same cost between nodes are obtained through equal-cost multi-path routing method, data is transmitted according to the shortest path according to the weights of the links as cost indicators, and a multi-objective optimization mathematical model is constructed;

[0008] S2, parameters are initialized, particle swarm and evolution generation MaxGen are set, particle swarm coding mode is constructed, and the weight of the link in the actual network is configured by manipulating the code in each particle in the particle swarm; the particle is decoded to obtain the lowest cost path;

[0009] S3, according to the lowest cost path obtained by decoding the particle, the data is transmitted according to the shortest path, the network performance is calculated, and the fitness value of the particle swarm is obtained, and is updated to pBest;

[0010] S4, the non-dominated solution of the current particle swarm is obtained by non-dominated sorting, and the non-dominated solution is added to the external archive A;

[0011] S5, the optimal solution of a single particle is found from all particles in the current particle swarm, and is updated to gBest;

[0012] S6, a dynamic link analysis strategy is used to guide and update the current particle swarm to generate a new generation of particle swarm;

[0013] S7, the new generation of particle swarm obtained in S6 is compared with pBest in S3 to obtain the updated pBest 更新 ; the non-dominated solution of the new particle swarm is obtained by non-dominated sorting, and the non-dominated solution is added to the external archive A;

[0014] S8, the external archive A is updated by an elite mutation strategy, Gaussian disturbance is performed on each non-dominated solution and a random dimension to obtain a hybrid population solution; then the hybrid population solution is non-dominated sorted, and the non-dominated solution in the hybrid population solution is selected; the final non-dominated solution is determined according to the number of non-dominated solutions and the crowding degree calculation method; according to the particle swarm evolution generation MaxGen, S3 is repeatedly executed to obtain the final non-dominated solution after iteration.

[0015] Further, in S1, the network is modeled as a weighted directed graph G=(V,E), where V represents nodes in the network, and E represents directed links; each link is assigned a weight, and the calculation method of the maximum link utilization MLU is:

[0016] ;

[0017] MLU = f Lis the flow on link L, C L is the capacity of link L; the value of MLU is between 0 and 1;

[0018] The calculation method of average link utilization ALU of all links on the network is:

[0019] ;

[0020] wherein, ALU is average link utilization, f L is the flow on link L, C L is the capacity of link L; |E| is the total number of links in the network.

[0021] Further, to minimize MLU and ALU, the specific method of constructing a multi-objective optimization mathematical model is:

[0022] ;

[0023] ;

[0024] wherein, the multi-objective optimization mathematical model satisfies four constraints, which are flow conservation constraint, link capacity constraint, flow demand constraint and non-negative flow constraint.

[0025] Further, the flow conservation constraint is that for each node in the network, the total flow flowing in is equal to the total flow flowing out, which is expressed by formula:

[0026] ;

[0027] wherein, i is an intermediate node, n is all predecessor nodes of i, m is all successor nodes of i, f （n，i） is the total flow flowing into intermediate node i from all predecessor nodes n, f （i，m） is the total flow flowing out of intermediate node i to all successor nodes m;

[0028] The link capacity constraint is that the flow through each link does not exceed the specified capacity of the link, that is:

[0029] ;

[0030] wherein, f i，j is the flow on the link connecting node i and node j, C i，j is the capacity on the link connecting node i and node j;

[0031] The flow demand constraint is to meet the flow demand from the source node to the destination node, that is:

[0032] ;

[0033] where s is the source node, t is the destination node, f （s，i） is the total flow from the source node s into the intermediate node i, f （i，t） is the total flow into the destination node t, D s，t is the flow demand;

[0034] The non-negative flow constraint is that the flow on all links is kept non-negative, i.e.

[0035] ;

[0036] where f i，j is the flow on the link connecting node i and node j.

[0037] Further, the equal-cost multi-path routing method specifically comprises the following steps: identifying all possible paths between two nodes in the network, and selecting paths with the same cost; and for the paths with the same cost, evenly distributing the flow on the paths to the next hop node.

[0038] Further, in the S2, the particle swarm coding mode is constructed, specifically comprising the following steps: representing the network as a graph, the nodes as routers or switches, and the edges as the connections between the nodes; assigning a unique identifier to each edge, the identifier corresponding to the position of the edge in the network topology; associating the identifier with a specific integer value, representing the cost weight of the corresponding link; and compiling the cost weights into a vector to construct a particle, each element of the vector corresponding to the cost weight of the corresponding link.

[0039] The position of the particle is configured in an integer range through the equal-cost multi-path routing method.

[0040] Further, in the S2, the particle is decoded, specifically comprising the following steps:

[0041] The decoding mode is applied to each particle, the configured cost weight of the link is converted into a routing instruction; and according to the current flow matrix information, for each pair of nodes, the cost weight of the link specified by the particle is used as the cost metric, and the Dijkstra algorithm is used to calculate and obtain the lowest cost path.

[0042] Further, in the S6, the dynamic link analysis strategy specifically comprises the following steps:

[0043] The direction of the change of the position of the particle is determined through a sign function (sign (*)) in the discrete particle swarm optimization method, i.e.

[0044] ;

[0045] ;

[0046] where i = 1, 2, …, N, N is the number of particles; j = 1, 2, …, D, D is the dimension of particles; pBest ij represents the jth dimension of pBest i ; c1, c2, c3 are acceleration factors; r1, r2, r3 are random numbers in the interval [0, 1]; X ij is the position of the ith particle in the jth dimension; Arch ij represents the position of the ith solution in the jth dimension in the non-dominated solution archive; V ij is the velocity of the ith particle in the jth dimension; evo ij represents the change value of the ith particle in the jth dimension, used to determine the direction of velocity update; represents the value of the changed velocity that needs to be added to the original velocity V ij ; klg(l j ) is the knowledge-driven rule multiplier for link l j ;

[0047] If klg(l j ) = 1, then the velocity V ij is definitely added with evo ij ; if klg(l j ) = 0.5, then evo ij has a 50% probability of being added to V ij ;

[0048] The rules of klg(l j ) include bandwidth rules, link centrality rules, and dynamic demand rules.

[0049] The bandwidth rule is that the links with the top 25% bandwidth availability follow a special update rule. If the velocity update sign is positive, indicating that the link weight increases, then klg(l j ) is set to 0.5.

[0050] The link centrality rule is that for links with the top 50% centrality and the bottom 50% bandwidth ranking, if the velocity update sign is negative, indicating that the link weight decreases, then klg(l j ) is set to 0.5.

[0051] The dynamic demand rule is that for links with the top 10% traffic demand usage and the bottom 50% bandwidth ranking, when the velocity update sign is negative, then klg(l j ) is adjusted to 0.5.

[0052] For cases that do not meet the bandwidth rule, the link centrality rule, and the dynamic demand rule, klg(l j ) remains at 1.

[0053] Further, the S8, the specific method of updating the external archive A by elitist mutation strategy includes:

[0054] For each non-dominated solution Arch in the external archive A i , set a new solution E i , and set a new solution E i equal to Arch i , then select a random dimension d to perform Gaussian disturbance, the formula is:

[0055] ;

[0056] Where E id is the solution after performing Gaussian disturbance, d th represents the dimension, X max，d is the upper bound of the d th th dimension, X min，d is the lower bound of the d th th dimension, Gaussian (0, 1) is a random value generated by a Gaussian distribution with mean 0 and standard deviation 1;

[0057] After disturbance, judge whether E id is within the search range of ; if not, set E id to the corresponding boundary;

[0058] After calculating the fitness value of the new solution E i , add E i and Arch i to the mixed population S to obtain the mixed population solution.

[0059] Further, the non-dominated sorting of the obtained mixed population solution is performed to obtain a new generation of non-dominated solutions and store them in the external archive A; set NP as the upper limit of the number of non-dominated solutions in the external archive A;

[0060] If the number of non-dominated solutions contained in the mixed population solution is less than NP, replace the non-dominated solutions in the external archive A directly with the non-dominated solutions in the mixed population solution;

[0061] If the number of non-dominated solutions contained in the mixed population solution exceeds NP, perform crowding degree calculation, and select the non-dominated solution with large crowding degree value as the non-dominated solution in the external archive A;

[0062] The specific method of crowding degree calculation includes:

[0063] All particles are sorted according to the fitness value under the current target, and the maximum fitness value is set as f max , and the minimum fitness value is set as f min ;

[0064] The crowding degree of the particle with the maximum fitness value and the minimum fitness value is infinite, and the current particle is set as the rs-th particle in the order, and the fitness value of the current target is f rs The crowding degree is:

[0065] ;

[0066] That is, after calculating the difference between the fitness values of adjacent particles, the result of normalization is performed.

[0067] Compared with the prior art, the present application has the following beneficial effects:

[0068] 1. The present application proposes a mathematical model that comprehensively considers the minimum maximum link utilization (MLU) and the global link average utilization (ALU) for the multi-objective optimization problem in modern network traffic engineering. By optimizing these two key indicators simultaneously, the present application can more comprehensively improve network performance and avoid the shortcomings caused by single optimization target in traditional methods.

[0069] 2. The present application adopts a knowledge-driven dynamic link analysis strategy, which classifies and adjusts the weights of links by deeply analyzing network graph and traffic matrix data. This strategy can intelligently adjust link weights according to bandwidth, centrality and dynamic demand attributes of links, thereby optimizing network traffic distribution and improving network adaptability and flexibility.

[0070] 3. The present application proposes an efficient indirect encoding method to make each particle represent a potential network solution. By manipulating the encoded link weights in each particle and combining with the equal-cost multi-path routing technology, the initialization method of the particle individual is defined, and the particle swarm optimization algorithm can efficiently navigate and optimize the routing configuration of the network. This method is not only intuitive but also easy to implement, which can significantly improve the convergence speed and optimization effect of the algorithm.

[0071] 4. The present application adopts the elitist mutation strategy and non-dominated sorting method in the external archive A, which can retain non-dominated solutions with better diversity. This strategy not only improves the exploration ability of the algorithm, but also ensures the quality of solutions in the learning process of each generation of particles, further improving the optimization effect. BRIEF DESCRIPTION OF DRAWINGS

[0072] Figure 1 is a flowchart of a network traffic distribution method based on knowledge-driven multi-objective particle swarm optimization provided by the present application;

[0073] Figure 2 is one of the flowcharts of the equal-cost multi-path routing technology provided by the present application;

[0074] Figure 3Figure 2 is a flowchart of the equal-cost multi-path routing technology provided by the present application;

[0075] Figure 4 Figure 4 is a schematic diagram of a mapping method for encoding a specific structure of a particle configured for a network topology. DETAILED DESCRIPTION

[0076] In order to make the objectives, technical solutions and advantages of the present application clearer, the technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by a person of ordinary skill in the art without creative work fall within the protection scope of the present application. EMBODIMENT

[0077] As Figures 1 to 4 A network traffic distribution method based on knowledge-driven multi-objective particle swarm optimization, comprising the following steps:

[0078] S1, establishing a network model, assigning weights to the links in the network; through segment routing, assigning segment identifiers to nodes or links; through an equal-cost multi-path routing method, obtaining paths between nodes with the same cost; according to the weights of the links as cost indicators, making data transmit according to the shortest path, and constructing a multi-objective optimization mathematical model;

[0079] In S1, the network is modeled as a weighted directed graph G=(V,E), where V represents nodes (such as routers or switches) in the network, and E represents directed links; each link is assigned a weight, and the weights dynamically change to affect the selection of the traffic path. The change of the link weight will affect the transmission path of the data packet, and further affect the network performance indicators. In the construction of the model, the maximum link utilization and the global average link utilization are mainly considered; the MLU is used to measure the utilization of the busiest link in the network, i.e. the calculation method of the maximum link utilization MLU is:

[0080] ;

[0081] Where, MLU is the maximum link utilization, f L is the traffic on the link L, C L is the capacity of the link L; the value of MLU is between 0 and 1; close to 0 indicates low link utilization, close to 1 indicates high link utilization, and more than 1 usually indicates link overload.

[0082] ALU represents the average utilization of all links in the network, and the calculation method of the average link utilization ALU of all links on the network is:

[0083] ;

[0084] where ALU is the average link utilization, f L is the traffic on link L, C L is the capacity of link L; |E| is the total number of links in the network. ALU, as an important indicator for evaluating the overall efficiency of the network, provides network administrators with a global perspective of network load distribution, thus simplifying the strategic planning and network optimization process.

[0085] In the multi-objective optimization problem, the goal is to minimize both MLU and ALU. There may be conflicts between these two objectives. To this end, we aim to efficiently explore the possible routing configuration space and find solutions that balance the minimum MLU and ALU. In the segmented routing, we use link weights as cost indicators to guide traffic through the shortest path transmission. This method can dynamically change the traffic load on the network links, thus affecting the results of these objectives.

[0086] To minimize MLU and ALU, the specific method for constructing a multi-objective optimization mathematical model is as follows:

[0087] ;

[0088] ;

[0089] This framework includes four constraints: flow conservation constraint, link capacity constraint, traffic demand constraint, and non-negative flow constraint.

[0090] The flow conservation constraint is that for each node in the network (excluding the source node and the destination node), the total flow into the node is equal to the total flow out of the node, which can be expressed as:

[0091] ;

[0092] where i is the intermediate node, n is all the predecessor nodes of i, m is all the successor nodes of i, f （n，i） is the total flow from all predecessor nodes n into the intermediate node i, f （i，m） is the total flow from the intermediate node i to all successor nodes m;

[0093] This constraint ensures the conservation of flow in the network, maintaining balance at intermediate nodes and not generating or disappearing flow.

[0094] The link capacity constraint is that the flow through each link does not exceed the specified capacity of that link, i.e.:

[0095] ;

[0096] where f i，j is the flow on the link connecting node i and node j, C i，j is the capacity of the link connecting node i and node j.

[0097] This requirement prevents network links from being overloaded, thus avoiding potential bottlenecks and ensuring the integrity of network operation.

[0098] The flow demand constraint is to meet the flow demand from the source node to the destination node, that is:

[0099] ;

[0100] where s is the source node, t is the destination node, f （s，i） is the total flow from the source node s to the intermediate node i, f （i，t） is the total flow to the destination node t, D s，t is the flow demand.

[0101] Meeting this condition ensures that the network capacity is sufficient to meet the specified demand, supporting seamless end-to-end connection.

[0102] The non-negative flow constraint is to meet the flow of all links remaining non-negative, that is:

[0103] ;

[0104] where f i，j is the flow on the link connecting node i and node j.

[0105] This inherent provision verifies that the flow value is consistent with the feasible network flow scenario, eliminating the possibility of reverse or abnormal flow.

[0106] Equal-cost multi-path routing technology specifically splits traffic in the following way: it identifies all possible paths between two nodes in the network and selects paths with the same cost. For paths with the same cost, it evenly distributes traffic to the next hop node on the path.

[0107] Equal-cost multi-path routing is a load balancing technique that evenly distributes traffic to multiple links with the same cost. It first identifies all possible paths from one node to another in the network and selects those with the same cost.

[0108] The equal-cost multi-path routing mentioned in the invention is equivalent to the expression of equal-cost multi-path.

[0109] Figures 2-3 It shows how network traffic is effectively distributed on multiple paths with the same cost.

[0110] As Figure 2, the configured link weights result in the identification of two shortest paths from node v1 to v5: v1-v2-v3 and v1-v3-v5. Thus, employing equal-cost multi-path routing for load balancing can result in the fair distribution of traffic between next-hop nodes v2 and v3, as shown in Figure 3

[0111] S2, initialize parameters, set particle swarm pop and evolution generation MaxGen, construct particle swarm coding mode, configure the weight of the link in the actual network by manipulating the code in each particle in the particle swarm; decode the particle to obtain the lowest cost path;

[0112] Constructing a particle swarm coding mode specifically includes: representing the network as a graph, nodes as routers or switches, edges as connections between nodes, assigning each edge a unique identifier corresponding to its position in the network topology, associating the identifier with a specific integer value representing the cost weight of the corresponding link, and compiling the cost weight into a vector to construct a particle, each element of the vector corresponding to the cost weight of the corresponding link;

[0113] The position of the particle is configured in the integer range by the equal-cost multi-path routing method.

[0114] The present application is based on the principle of particle swarm optimization, and adopts an encoding method, in which each particle in the particle swarm represents a potential solution, reflecting the topology of the network graph, as shown in Figure 4 The encoding process starts with representing the network as a graph, where nodes are routers or switches and edges are connections between them. Then each edge is assigned a unique identifier corresponding to its position in the network topology. These identifiers are associated with specific integer values representing the cost weight of the corresponding link, similar to the metrics used in OSPF configuration to determine the traversal cost of each link. By compiling these cost weights into a vector to construct a particle, each element of the vector corresponds to the weight of a specific link, effectively refreshing the state of the network according to the link cost. Moreover, by applying the equal-cost multi-path routing strategy, the particle position is configured in the integer range of [0, 30] to meet specific optimization requirements, for example, in a network with three links (Link1, Link 2, Link 3), their weights are 10, 20 and 30 respectively, the particle will be encoded as [10, 20, 30]. This method is not only intuitive, but also easy to implement, enabling the particle swarm algorithm to efficiently navigate and optimize the routing configuration of the network by manipulating the encoded link weights in each particle.

[0115] Decoding the particle specifically includes: ​

[0116] For each particle, a decoding method is applied, the cost weight of the encoded link is configured, and it is converted into a routing instruction. Based on the current traffic matrix information, for each pair of nodes, the cost weight of the link specified by the particle is used as the cost metric, and the Dijkstra algorithm is used to calculate and obtain the lowest cost path.

[0117] Decoding each particle is a unique and essential process that transforms the encoded particle data into an actionable network routing configuration. We first apply a function mapping method to each particle to interpret the encoded link weights and translate them into routing instructions. Incorporating the current traffic matrix information is crucial, as it provides traffic demand data between each pair of source-destination nodes. For each node pair, the link weights specified by the particle are used as a cost metric, and Dijkstra's algorithm is employed to calculate the lowest-cost path, ensuring efficient routing. Equal-cost multipath routing is then applied to distribute traffic across multiple equal-cost paths, enhancing load balancing. After routing all node pairs according to the particle configuration, we calculate the maximum and average link utilization values ​​to evaluate the network performance under the represented routing scheme. These objective values ​​constitute a Pareto solution, representing a potential routing configuration for each particle, allowing us to evaluate its effectiveness and optimize network traffic flow.

[0118] S3. Based on the lowest cost path obtained after decoding the particles, transmit the data along the shortest path, calculate the network performance and obtain the fitness value of the particle swarm, and update it to pBest.

[0119] S4. Obtain the non-dominated solution of the current particle swarm through non-dominated sorting and add the non-dominated solution to the external archive A.

[0120] S5. Find the optimal solution for a single particle from all particles in the current particle swarm and update it to gBest;

[0121] The non-dominated sorting used in this invention is an existing design. The particle swarm algorithm used is based on the existing design but changes the mutation and evolution strategy of particles. A corresponding strategy is also designed on the external archive A, which promotes faster convergence of the algorithm overall.

[0122] S6. Employ a dynamic link analysis strategy to guide and update the current particle swarm, generating a new generation of particle swarms.

[0123] To achieve a more accurate and intelligent link weight adjustment method and overcome the shortcomings of arbitrary and unguided particle updates, this invention leverages in-depth analysis of existing network graph and traffic matrix data. This analysis enables us to classify network links in a way that supports a knowledge-driven strategy. We focus on three pieces of information that are crucial to shaping this knowledge-driven strategy.

[0124] First, consider link bandwidth. Greater link bandwidth means higher link availability, suggesting that lower link weight costs may be more advantageous. Therefore, links with higher bandwidth are assigned lower weights to promote their utilization.

[0125] Second, the static property of link connectivity is evaluated by calculating link centrality. This is determined by the sum of the in-degree and out-degree of the nodes it connects to, reflecting the link's importance in the network topology. Links with high centrality are often considered critical or "hub" links. However, when these highly centralized links have limited bandwidth, they require higher weights to represent the higher routing cost through them, in order to prevent congestion.

[0126] Third, analyze the dynamic attributes of link demand, focusing primarily on the top 10% of source-destination (OD) pairs with the highest traffic forwarding demand. By performing shortest path searches on these 10% of OD pairs and compiling the paths they traverse, links that frequently appear (more than three times) on these paths can be identified. Links that appear frequently on these paths are considered active under the current TM conditions. Similarly, active links with limited bandwidth will have their weight increased to prevent congestion.

[0127] The knowledge-driven strategy aims to optimize particle updates in particle swarm optimization, ensuring they are both data-driven and efficient. This approach is driven by both the inherent characteristics of the network and current traffic demands, collectively improving network performance. By integrating complex link weight adjustment strategies that consider bandwidth, centrality, and dynamic demand attributes, a smarter and more responsive framework is established for optimizing network routing configuration.

[0128] In this invention, the evolution of particles is primarily driven by updates to their positions and velocities, with each particle's position reflecting the cost weight of a network link. In traditional particle swarm optimization algorithms, the velocity update of each particle is influenced by two key factors: the individual's current optimal position (pBest) and the swarm's globally optimal position (gBest). However, in our update method, pBest... i It is redefined as the optimal position for the current particle to reach. iThis represents a position in the non-dominated solution archive. Each particle learns from different randomly selected archive members, adding randomness to the learning process. This approach ensures that each particle's update is influenced by a unique combination of the historical best position and the current objective, resulting in a more dynamic and faster-responding optimization process.

[0129] The improved particle swarm optimization algorithm provided by this invention can intelligently adjust network link weights. First, an equivalent multipath routing strategy is applied, and particle positions are configured within the integer range [0, 30] to meet specific optimization requirements. Given the discrete nature of this optimization space, a knowledge-driven strategy borrows the sign function (sign(*)) from discrete particle swarm optimization methods to determine the direction of position changes. This innovative method distinguishes itself through different learning interactions with pBest, gBest, and the archive.

[0130] Dynamic link analysis strategies specifically include:

[0131] The direction of particle position change is determined by the sign function (sign(*)) in the discrete particle swarm optimization method, i.e.:

[0132] ;

[0133] ;

[0134] Where i = 1, 2, ..., N, N is the number of particles; j = 1, 2, ..., D, D is the dimension of the particle; pBest ij pBest i The j-th dimension; c1, c2, c3 are acceleration factors; r1, r2, r3 are random numbers in the interval [0, 1]; X ij Arch represents the position of the i-th particle in the j-th dimension. ij V represents the position of the i-th solution in the j-th dimension of the non-dominated solution archive; ij Let be the velocity of the i-th particle in the j-th dimension; evo ij This represents the change value of the i-th particle in the j-th dimension, used to determine the direction of velocity update; This indicates that at the original speed V ij Based on this, the value of the changed speed needs to be added; klg(l j ) for link l j Knowledge-driven rule multipliers;

[0135] The sign function (sign(∗)) can simplify the computational complexity in discrete space by converting velocity updates into direction decisions (-1 for moving backward and 1 for moving forward).

[0136] For the link l j Knowledge-driven rule multiplier klg(l j This will affect the use of evo ij The probability of performing a speed update.

[0137] If klg(l) j If )=1, then the velocity V ij definitely add evo ij If klg(l) j If ) = 0.5, then evo ij There is a 50% probability that it will be added to V. ij ;

[0138] klg(l j The rules include bandwidth rules, link centrality rules, and dynamic demand rules;

[0139] The bandwidth rule is as follows: the top 25% of links in bandwidth availability follow a special update rule. If the speed update sign is positive, it indicates that the link weight has increased, and klg(l) will be increased. j Set it to 0.5;

[0140] The link centrality rule is as follows: for links that rank in the top 50% in centrality but in the bottom 50% in bandwidth, if the speed update sign is negative, it indicates a reduction in link weight, and klg(l) will be adjusted accordingly. j Set it to 0.5;

[0141] The dynamic demand rule is as follows: for links used by the top 10% of traffic demand and ranked in the bottom 50% of bandwidth, when the speed update sign is negative, then klg(l) will be used. j Adjusted to 0.5;

[0142] For cases that do not comply with bandwidth rules, link centrality rules, and dynamic demand rules, klg(l j Keep it at 1.

[0143] S7. Compare the new generation of particle swarm obtained in S6 with pBest in S3 to obtain the updated pBest. 更新 Obtain the non-dominated solution of the new particle swarm through non-dominated sorting, and add the non-dominated solution to the external archive A.

[0144] S8. Update the external archive A using an elite mutation strategy. Perform Gaussian perturbation on each non-dominated solution and random dimension to obtain a mixed population solution. Then, sort the mixed population solutions by non-dominated nature and select the non-dominated solutions from the mixed population solutions. Determine the final non-dominated solution based on the number of non-dominated solutions and the crowding calculation method. Repeat S3 based on the particle swarm evolution generation MaxGen to obtain the final non-dominated solution after iteration.

[0145] Finally, an elite strategy-based file update mechanism is implemented. First, the previous generation's file solution and the current pBest are input to form a hybrid population solution. Second, an elite strategy is applied to the previous generation's file solution to perform a local search, exploring the possibility of optimal positions around the particles, and the resulting new solution is added to the current hybrid population S.

[0146] Specific methods for updating external archive A using the elite mutation strategy include:

[0147] For each non-dominated solution Arch in external archive A i Set a new solution E i And set a new solution E i Equal to Arch i Then, a Gaussian perturbation is performed on a random dimension d, with the following formula:

[0148] ;

[0149] Among them, E id To perform the solution after Gaussian perturbation, use d th X represents dimension. max，d For the dth th The upper bound of dimension, X min，d For the dth th The lower bound of the dimension, Gaussian(0,1), is a random value generated by a Gaussian distribution with a mean of 0 and a standard deviation of 1;

[0150] New solution E i It means iterating through the Arch. i Each subsequent solution is processed by performing a new operation (Gaussian perturbation) on a newly copied solution, followed by E. i and Arch i Add them together to the mixed population S;

[0151] After the perturbation, determine E id Is it in Within the search range; if not, then E id Set the corresponding boundaries;

[0152] Then the new solution E is calculated. i After the fitness value is determined, E will be... i and Arch i Add it to the mixed population S to obtain the mixed population solution.

[0153] Finally, the solutions of the mixed population are sorted by non-dominated ordering to obtain a set of excellent non-dominated solutions, which are then stored in the external archive as a new generation of archive solutions.

[0154] The obtained mixed population solutions are sorted non-dominated to obtain a new generation of non-dominated solutions, which are then stored in external archive A; NP is set as the upper limit of the number of non-dominated solutions in external archive A.

[0155] If the number of non-dominated solutions in the mixed population solution is less than NP, then the non-dominated solutions in the external archive A are directly replaced by the non-dominated solutions in the mixed population solution.

[0156] If the number of non-dominated solutions in the mixed population solution exceeds NP, then the crowding degree is calculated, and the non-dominated solution with the larger crowding degree value is selected as the non-dominated solution in the external archive A.

[0157] The specific methods for calculating congestion include:

[0158] All particles are sorted according to their fitness values ​​under the current target, with the maximum fitness value set to f. max The minimum fitness value is f min ;

[0159] The crowding of the particles with the highest and lowest fitness values ​​is infinite. Let the current particle be the rs-th particle after sorting, and its fitness value in the current target be f. rs Its congestion level is:

[0160] ;

[0161] That is, the result of normalizing the difference in fitness values ​​between adjacent particles.

[0162] By calculating the crowding degree of each particle separately in a dual-objective model and summing them as the final crowding degree of the individual, this method can better preserve the diversity of non-dominated solutions. By incorporating an elitist strategy and a file update strategy after non-dominated sorting, the algorithm's exploration ability can be improved during the learning process of each generation of particles, and the file solutions can, in turn, guide the update of the next generation of particles, improving the quality of the solutions.

[0163] This invention addresses the distributed, multi-stage production model of modern enterprises by proposing a distributed, end-to-end job shop scheduling problem. It discloses a distributed, end-to-end job shop scheduling method based on an evolutionary algorithm. This method simultaneously considers two objectives: the maximum product completion time and the total machine operating cost, to provide a set of Pareto optimal solutions for the enterprise. First, the invention models the proposed problem and designs a two-layer encoding method to represent the scheduling scheme. To locate more Pareto solutions, this invention employs a dual-population evolutionary approach to optimize the two proposed objectives separately. An external archive is introduced to provide a channel for information exchange between the two populations, thereby obtaining a set of Pareto optimal solutions.

[0164] The key points of this invention include the following four points:

[0165] 1. An efficient indirect network coding method is proposed to address the characteristics of the problem, as well as a decoding method for path finding under Dijkstra's algorithm by using the weights of the coding. At the same time, an individual initialization strategy is designed based on equal-cost multi-path routing.

[0166] 2. To address the shortcomings of traditional traffic engineering's single optimization objective, this invention proposes a dual-objective optimization model based on minimum and maximum link utilization and global average link utilization, and designs dynamic link weight adjustment rules. By modeling the network as a weighted directed graph and combining traffic conservation, link capacity, traffic demand, and non-negative traffic constraints, a multi-objective mathematical programming framework is constructed, which helps to achieve network load balancing and performance improvement.

[0167] 3. To address the need for dynamic optimization of link cost weights, a knowledge-driven dynamic particle update strategy is proposed. By ranking link bandwidth, analyzing centrality, and identifying dynamic traffic demand, a knowledge-driven particle velocity update rule is designed. This helps individuals in the population improve their problem-solving exploration capabilities and enhances the algorithm's convergence ability.

[0168] 4. In response to the characteristics of the problem, a corresponding archive elite mutation strategy was designed to perform Gaussian perturbation on the found non-dominated solutions to improve the accuracy of the solutions. This mechanism helps to break through local optima and improve the coverage of Pareto fronts through interactive learning between external archives and particle swarms.

[0169] With the help of the above strategies, the proposed data-driven multi-objective particle swarm optimization algorithm has achieved excellent results in solving large-scale dynamic flow engineering problems.

[0170] Based on the disclosure and teachings of the foregoing specification, those skilled in the art can make changes and modifications to the above embodiments. Therefore, the present invention is not limited to the specific embodiments disclosed and described above, and some modifications and changes to the present invention should also fall within the protection scope of the claims of the present invention. Furthermore, although some specific terms are used in this specification, these terms are only for convenience of explanation and do not constitute any limitation on the present invention.

Claims

1. A network traffic allocation method based on knowledge-driven multi-objective particle swarm optimization, characterized in that, Includes the following steps: S1. Establish a network model and assign weights to links in the network; assign segment identifiers to nodes or links through segmented routing. The equal-cost multipath routing method is used to obtain paths between nodes with the same cost; the link weight is used as the cost index to ensure that data is transmitted along the shortest path, and a multi-objective optimization mathematical model is constructed. S2. Initialize parameters, set the particle swarm and the number of generations MaxGen, construct the particle swarm encoding method, and configure the weight of the links in the actual network by manipulating the encoding of each particle in the particle swarm; decode the particles to obtain the lowest cost path. S3. Based on the lowest cost path obtained after decoding the particles, transmit the data along the shortest path, calculate the network performance and obtain the fitness value of the particle swarm, and update it to pBest. S4. Obtain the non-dominated solution of the current particle swarm through non-dominated sorting and add the non-dominated solution to the external archive A. S5. Find the optimal solution for a single particle from all particles in the current particle swarm and update it to gBest; S6. Employ a dynamic link analysis strategy to guide and update the current particle swarm, generating a new generation of particle swarms; the dynamic link analysis strategy specifically includes: The direction of particle position change is determined by the sign function (sign(*)) in the discrete particle swarm optimization method, i.e.: ； ； Where i = 1, 2, ..., N, N is the number of particles; j = 1, 2, ..., D, D is the dimension of the particle; pBest ij pBest i The j-th dimension; c1, c2, c3 are acceleration factors; r1, r2, r3 are random numbers in the interval [0, 1]; X ij Arch represents the position of the i-th particle in the j-th dimension. ij V represents the position of the i-th solution in the j-th dimension of the non-dominated solution archive; ij Let be the velocity of the i-th particle in the j-th dimension; evo ij This represents the change in the j-th dimension of the i-th particle, used to determine the direction of velocity update; klg(l j ) for link l j Knowledge-driven rule multipliers; This indicates that at the original speed V ij Based on this, there will be klg(l j The probability plus the rate of change evo ij ; If klg(l) j If )=1, then the velocity V ij definitely add evo ij If klg(l) j If ) = 0.5, then evo ij There is a 50% probability that it will be added to V. ij ; klg(l j The rules include bandwidth rules, link centrality rules, and dynamic demand rules; The bandwidth rule is as follows: the top 25% of links in bandwidth availability follow a special update rule. If the speed update sign is positive, it indicates that the link weight has increased, and klg(l) will be increased. j Set it to 0.5; The link centrality rule is as follows: for links that rank in the top 50% in centrality but in the bottom 50% in bandwidth, if the speed update sign is negative, it indicates a reduction in link weight, and klg(l) will be adjusted accordingly. j Set it to 0.5; The dynamic demand rule is as follows: for links used by the top 10% of traffic demand and ranked in the bottom 50% of bandwidth, when the speed update sign is negative, then klg(l) will be used. j Adjusted to 0.5; For cases that do not comply with bandwidth rules, link centrality rules, and dynamic demand rules, klg(l j Keep it at 1; S7. Compare the new generation of particle swarm obtained in S6 with pBest in S3 to obtain the updated pBest. 更新 Obtain the non-dominated solution of the new particle swarm through non-dominated sorting, and add the non-dominated solution to the external archive A. S8. Update the external archive A using an elite mutation strategy. Perform Gaussian perturbation on each non-dominated solution and random dimension to obtain a mixed population solution. Then, sort the mixed population solutions by non-dominated nature and select the non-dominated solutions from the mixed population solutions. Determine the final non-dominated solution based on the number of non-dominated solutions and the crowding calculation method. Repeat S3 based on the particle swarm evolution generation MaxGen to obtain the final non-dominated solution after iteration. Specific methods for updating external archive A using the elite mutation strategy include: For each non-dominated solution Arch in external archive A i Set a new solution E i And set a new solution E i Equal to Arch i Then, a Gaussian perturbation is performed on a random dimension d, with the following formula: ； Among them, E id To perform the solution after Gaussian perturbation, use d th X represents dimension. max，d For the dth th The upper bound of dimension, X min，d For the dth th The lower bound of the dimension, Gaussian(0,1), is a random value generated by a Gaussian distribution with a mean of 0 and a standard deviation of 1; After the perturbation, determine E id Is it in Within the search range; if not, then E id Set the corresponding boundaries; Calculate the new solution E i After the fitness value is determined, E will be... i and Arch i Add it to the mixed population S to obtain the mixed population solution.

2. The network traffic allocation method based on knowledge-driven multi-objective particle swarm optimization according to claim 1, characterized in that, In step S1, the network is modeled as a weighted directed graph G=(V,E), where V represents nodes in the network and E represents directed links; each link is assigned a weight, and the maximum link utilization (MLU) is calculated as follows: ； Where MLU is the maximum link utilization, f L For traffic on link L, C L The capacity of link L; the value of MLU is between 0 and 1; The method for calculating the average link utilization (ALU) of all links on the network is as follows: ； Where ALU is the average link utilization, f L For traffic on link L, C L Let L be the capacity of link L; |E| is the total number of links in the network.

3. The network traffic allocation method based on knowledge-driven multi-objective particle swarm optimization according to claim 2, characterized in that, The specific method for constructing a multi-objective optimization mathematical model by minimizing MLU and ALU is as follows: ； ； The multi-objective optimization mathematical model satisfies four constraints: flow conservation constraint, link capacity constraint, flow demand constraint, and non-negative flow constraint.

4. The network traffic allocation method based on knowledge-driven multi-objective particle swarm optimization according to claim 3, characterized in that, The flow conservation constraint states that for each node in the network, the total inflow equals the total outflow, expressed by the formula: ； Where i is the intermediate node, n is all the predecessor nodes of i, m is all the successor nodes of i, and f （n，i） f is the total flow from all predecessor nodes n into intermediate node i. （i，m） This represents the total flow from intermediate node i to all successor nodes m. The link capacity constraint is that the traffic through each link shall not exceed the specified capacity of that link, that is: ； Among them, f i，j For the traffic on the link connecting node i and node j, C i，j Capacity of the link connecting node i and node j; The traffic demand constraint is to satisfy the traffic demand from the source node to the destination node, that is: ； Where s is the source node, t is the destination node, and f is the destination node. （s，i） f represents the total flow from source node s into intermediate node i. （i，t） D represents the total flow into destination node t. s，t For traffic demand; The non-negative flow constraint is that the flow of all links remains non-negative, that is: ； Where f i，j Traffic on the link connecting node i and node j.

5. The network traffic allocation method based on knowledge-driven multi-objective particle swarm optimization according to claim 1, characterized in that, The equal-cost multi-path routing method specifically includes identifying all possible paths between two nodes in the network and selecting paths with the same cost. For paths with the same cost, traffic is evenly distributed on the path to the next hop node.

6. The network traffic allocation method based on knowledge-driven multi-objective particle swarm optimization according to claim 1, characterized in that, In S2, the construction of the particle swarm encoding method specifically includes: representing the network as a graph, with nodes as routers or switches, edges as connections between nodes, assigning a unique identifier to each edge, the identifier corresponding to its position in the network topology, associating the identifier with a specific integer value to represent the cost weight of the corresponding link, and compiling the cost weight into a vector to construct particles, with each element of the vector corresponding to the cost weight of the corresponding link. The particle position is configured within an integer range using an equal-cost multipath routing method.

7. A network traffic allocation method based on knowledge-driven multi-objective particle swarm optimization according to claim 6, characterized in that, In step S2, decoding the particles specifically includes: For each particle, a decoding method is applied, the cost weight of the encoded link is configured, and it is converted into a routing instruction. Based on the current traffic matrix information, for each pair of nodes, the cost weight of the link specified by the particle is used as the cost metric, and the Dijkstra algorithm is used to calculate and obtain the lowest cost path.

8. The network traffic allocation method based on knowledge-driven multi-objective particle swarm optimization according to claim 1, characterized in that, The obtained mixed population solutions are sorted non-dominated to obtain a new generation of non-dominated solutions, which are then stored in external archive A; NP is set as the upper limit of the number of non-dominated solutions in external archive A. If the number of non-dominated solutions in the mixed population solution is less than NP, then the non-dominated solutions in the external archive A are directly replaced by the non-dominated solutions in the mixed population solution. If the number of non-dominated solutions in the mixed population solution exceeds NP, then the crowding degree is calculated, and the non-dominated solution with the larger crowding degree value is selected as the non-dominated solution in the external archive A. The specific methods for calculating congestion include: All particles are sorted according to their fitness values ​​under the current target, with the maximum fitness value set to f. max The minimum fitness value is f min ; The crowding of the particles with the highest and lowest fitness values ​​is infinite. Let the current particle be the rs-th particle after sorting, and its fitness value in the current target be f. rs Its congestion level is: ； That is, the result of normalizing the difference in fitness values ​​between adjacent particles.

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