Network flow distribution method based on knowledge-driven multi-objective particle swarm optimization

Abstract

The invention discloses a network flow distribution method based on knowledge-driven multi-objective particle swarm optimization, which comprises the following steps: modeling and designing a double-layer coding mode to represent a scheduling scheme, and adopting a double-population evolution method to respectively optimize two proposed objectives; a channel is provided for information exchange between the two populations by introducing an external archiving mode, so that an optimal solution is obtained; by comprehensively considering a mathematical model of the minimum and maximum link utilization rate and the global link average utilization rate, a knowledge-driven dynamic link analysis strategy, a high-efficiency indirect coding mode and an elitist variation strategy, a non-dominated sorting method and the like are adopted in an external archive, and under the help of the strategies, the optimal link utilization rate is obtained. The multi-target particle swarm algorithm based on data driving obtains an excellent result when solving a large-scale dynamic traffic engineering problem.

Description

Technical Field

[0001] The present invention belongs to the technical field of network traffic engineering, and particularly relates to a network traffic allocation method based on knowledge-driven multi-objective particle swarm optimization. Background Art

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

[0003] At present, network traffic engineering can be divided into the following methods and deficiencies: 1) Configuration of link state protocols (such as OSPF): Manage and optimize network traffic through link state protocols, and select paths according to link costs. This method usually requires a large amount of manual participation and intervention control, and it is difficult to achieve network automatic driving and management. 2) Distributed traffic monitoring and control: Perform traffic monitoring and bandwidth reservation through a distributed mechanism to cope with changes in traffic demand in the network. However, for large-scale networks or complex topological structures, maintaining and updating the link state database requires a large amount of computing and storage resources, resulting in packet loss or increased latency. 3) Optimization technologies based on constraint programming and local search: Use mathematical models and algorithms to optimize network resource allocation and traffic path selection. This method is usually difficult to quickly adapt and adjust when facing the rapid changes of network conditions. In a modern network environment, especially in a large-scale network, this may lead to network performance degradation and resource waste. In summary, traditional TE methods have deficiencies in terms of automation level, multi-objective optimization ability, adaptability, and computational efficiency. Therefore, new solutions are urgently needed to solve the traffic engineering problem of multi-objective network performance optimization. Summary of the Invention

[0004] Aiming at the problems existing in the prior art, the present invention provides a network traffic allocation method based on knowledge-driven multi-objective particle swarm optimization. By modeling and designing a double-layer coding method to represent the scheduling scheme, a two-population evolution method is adopted to optimize the two proposed objectives respectively, and an external archive is introduced to provide a channel for information exchange between the two populations, so as to obtain the optimal solution.

[0005] The technical solution of the present invention is realized as follows:

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

[0007] S1. Establish a network model, assign weights to the links in the network; through segment routing, assign paragraph identifiers to nodes or links; by means of equal-cost multi-path routing method, obtain paths with the same cost between nodes; take the weight of the link as the cost metric to make data transmit along the shortest path, and construct a multi-objective optimization mathematical model;

[0008] S2. Initialize parameters, set the particle swarm and the maximum number of generations MaxGen, construct the particle swarm coding method, and configure the weights of the links in the actual network by manipulating the codes in each particle of the particle swarm; decode the particles to obtain the lowest-cost path;

[0009] S3. According to the lowest-cost path obtained after decoding the particles, after making the data transmit along the shortest path, calculate the network performance and obtain the fitness value of the particle swarm, and update it to pBest;

[0010] S4. Obtain the non-dominated solutions of the current particle swarm through non-dominated sorting, and add the non-dominated solutions to the external archive A;

[0011] S5. Find the optimal solution of a single particle from all the particles of the current particle swarm, and update it to gBest;

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

[0013] 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 solutions of the new particle swarm through non-dominated sorting, and add the non-dominated solutions to the external archive A;

[0014] S8. Update the external archive A through an elite mutation strategy, perform Gaussian perturbation on each non-dominated solution and a random dimension to obtain a mixed population solution; then perform non-dominated sorting on the mixed population solution, and select the non-dominated solutions in the mixed population solution; determine the final non-dominated solutions according to the number of non-dominated solutions and the crowding degree calculation method; according to the maximum number of generations MaxGen of the particle swarm evolution, repeat S3 to obtain the final non-dominated solutions after iteration.

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

[0016]

[0017] where MLU is the maximum link utilization rate, f Lis the traffic on link L, C L is the capacity of link L; the value of MLU ranges between 0 and 1;

[0018] The average link utilization ALU of all links on the network is calculated as follows:

[0019]

[0020] 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.

[0021] Furthermore, to minimize MLU and ALU, the specific method for constructing the multi-objective optimization mathematical model is as follows:

[0022] min MLU;

[0023] min ALU;

[0024] Among them, the multi-objective optimization mathematical model satisfies four constraints, namely the traffic conservation constraint, the link capacity constraint, the traffic demand constraint, and the non-negative traffic constraint.

[0025] Furthermore, the traffic conservation constraint means that for each node in the network, the total inflow traffic is equal to the total outflow traffic, which is expressed by the formula:

[0026]

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

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

[0029] f i,j ≤ C i,j ;

[0030] where f i，j is the traffic on the link connecting node i and node j, C i，j is the capacity of the link connecting node i and node j;

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

[0032]

[0033] where s is the source node, t is the destination node, and f (s，i) is the total flow out of the source node s, and f (i，t) is the total flow into the destination node t, and D s，t is the traffic demand;

[0034] The non - negative flow constraint is that the flow on all links is non - negative, that is:

[0035] f i,j ≥0, for all i, j ∈ V;

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

[0037] Furthermore, 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, the traffic is evenly distributed among the paths for transmitting to the next - hop node.

[0038] Furthermore, in S2, constructing the particle swarm encoding method specifically includes: representing the network as a graph, with nodes as routers or switches and edges as connections between nodes, assigning a unique identifier to each edge, where the identifier corresponds 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 weights into a vector to construct a particle, where each element of the vector corresponds to the cost weight of the corresponding link;

[0039] Configure the position of the particle within the integer range through the equal - cost multi - path routing method.

[0040] Furthermore, in S2, decoding the particle specifically includes:

[0041] Applying the decoding method to each particle, configuring the cost weights of the links, and converting them into routing instructions; according to the current traffic matrix information, for each pair of nodes, using the cost weights of the links specified by the particle as the cost metric, and using the Dijkstra algorithm to calculate and obtain the lowest - cost path.

[0042] Furthermore, in S6, the dynamic link analysis strategy specifically includes:

[0043] Determine the direction of the particle position change through the sign function (sign(*)) in the discrete particle swarm optimization method, that is:

[0044] evo ij = sign(c1 * r1 * (pBest ij - X ij ) + c2 * r2 * (gBestij -X ij ) + c3 * r3 * (Arch ij -X ij ));

[0045] V ij = V ij + evo ij ⊙ klg(l j ));

[0046] where i = 1, 2, …, N, N is the number of particles; j = 1, 2, …, D, D is the dimension of the particles; pBest ij represents the j-th dimension of pBest i ; c1, c2, c3 are acceleration factors; r1, r2, r3 are random numbers within the interval [0, 1]; X ij is the position of the i-th particle in the j-th dimension; Arch i represents a position in the non-dominated solution archive; V ij is the velocity of the i-th particle in the j-th dimension; evo ij represents the change value of the i-th particle in the j-th dimension, used to determine the direction of velocity update; evo ij ⊙ klg(l j ) 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 will definitely add 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 top 25% of the links with bandwidth availability follow special update rules. If the velocity update sign is positive, indicating an increase in link weight, then set klg(l j ) to 0.5;

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

[0051] The dynamic demand rule is that for the traffic demands ranked in the top 10%, and for the links ranked in the bottom 50% in terms of bandwidth, when the speed update symbol is negative, then klg(l j ) is adjusted to 0.5;

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

[0053] Furthermore, in the step S8, the specific method for updating the external archive A through the elite mutation strategy includes:

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

[0055] E id = E id + (X max,d - X min,d ) * Gaussian(0,1);

[0056] Among them, E id is the solution after performing Gaussian perturbation, 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, and Gaussian(0, 1) is a random value generated by a Gaussian distribution with a mean of 0 and a standard deviation of 1;

[0057] After perturbation, it is judged whether E id is within the search range of [X max,d , X min,d ; if not, then E id is set to the corresponding boundary;

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

[0059] Furthermore, non-dominated sorting is performed on the obtained mixed population solution to obtain a new generation of non-dominated solutions and store them in the external archive A; NP is set 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, directly replace the non-dominated solutions in the external archive A 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, calculate the crowding degree, and select the non-dominated solution with a large crowding degree value as the non-dominated solution in the external archive A;

[0062] The specific method for calculating the crowding degree includes:

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

[0064] The crowding degrees of the particles with the maximum and minimum fitness values are infinite. Set the current particle as the rs-th particle after sorting, and its fitness value under the current objective is f rs , and its crowding degree distance is:

[0065] (f rs+1 - f rs-1 )(f max - f min );

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

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

[0068] 1. The present invention 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 simultaneously optimizing these two key indicators, the present invention can more comprehensively improve network performance and avoid the deficiencies brought by a single optimization objective in traditional methods.

[0069] 2. The present invention adopts a knowledge-driven dynamic link analysis strategy. By deeply analyzing the network diagram and traffic matrix data, the links are classified and the weights are adjusted. This strategy can intelligently adjust the link weights according to the bandwidth, centrality, and dynamic demand attributes of the links, thereby optimizing the network traffic distribution and improving the adaptability and flexibility of the network.

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

[0071] 4. The present invention adopts an elite mutation strategy and a 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 the solutions in the learning process of each generation of particles, further enhancing the optimization effect. Description of the Drawings

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

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

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

[0075] Figure 4 is a schematic diagram of the mapping method of the specific structure for encoding the particles configured for the network topology provided by the present invention. Detailed Embodiment

[0076] In order to make the objectives, technical solutions and advantages of the present invention clearer and more understandable, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0077] Embodiment

[0078] Such as Figures 1 to 4 , a network traffic allocation method based on knowledge-driven multi-objective particle swarm optimization, includes the following steps:

[0079] S1. Establish a network model, assign weights to the links in the network; through segmented routing, assign paragraph identifiers to nodes or links; through the equal-cost multi-path routing method, obtain paths with the same cost between nodes; use the weight of the link as a cost index to make data transmit along the shortest path, and construct a multi-objective optimization mathematical model;

[0080] In S1, the network is modeled as a weighted directed graph G=(V, E), where V represents the nodes in the network (such as routers or switches), and E represents the directed links; each link is assigned a weight, and these weights change dynamically to affect the selection of traffic paths. The change in link weights will affect the transmission path of data packets, and thus affect the network performance metrics. In the construction of the model, the maximum link utilization and the global average link utilization are mainly considered; MLU is used to measure the utilization of the busiest link in the network, that is, the calculation method of the maximum link utilization MLU is:

[0081]

[0082] where MLU is the maximum link utilization, f L is the traffic on link L, and C L is the capacity of link L; the value of MLU ranges between 0 and 1; close to 0 indicates low link utilization, close to 1 indicates high link utilization, and exceeding 1 usually indicates link overload.

[0083] ALU represents the average utilization of all links in the network. The calculation method of the average link utilization ALU of all links on the network is:

[0084]

[0085] where ALU is the average link utilization, f L is the traffic on link L, and C L is the capacity of link L; ∣E∣ is the total number of links in the network. As an important indicator for evaluating the comprehensive efficiency of the network, ALU provides a global perspective on the network load distribution for network administrators, thus simplifying the strategic planning and network optimization processes.

[0086] In the multi-objective optimization problem, the goal is to minimize MLU and ALU simultaneously. There may be conflicts between these two goals. Therefore, we aim to efficiently explore the possible routing configuration space and find solutions that balance minimizing MLU and ALU. When performing segment routing, the link weights are used as cost metrics to guide the traffic to be transmitted through the shortest path. This method can dynamically change the traffic load on the network links, thereby affecting the results of these goals.

[0087] The specific method for constructing a multi-objective optimization mathematical model by minimizing MLU and ALU is:

[0088] minMLU;

[0089] minALU;

[0090] This framework includes four constraint conditions, namely the flow conservation constraint, the link capacity constraint, the traffic demand constraint, and the non - negative flow constraint.

[0091] The flow conservation constraint means that for each node in the network (excluding the source node and the destination node), the total inflow traffic is equal to the total outflow traffic, which is expressed by the formula:

[0092]

[0093] where i is an intermediate node, n is all the predecessor nodes of i, m is all the successor nodes of i, and f (n，i) is the total traffic flowing into the intermediate node i from all predecessor nodes n, and f (i，m) is the total traffic flowing out from the intermediate node i to all successor nodes m;

[0094] This constraint ensures the conservation of traffic in the network, maintaining balance at intermediate nodes and preventing traffic from being generated or disappearing.

[0095] The link capacity constraint means that the traffic passing through each link does not exceed the specified capacity of that link, that is:

[0096] f i,j ≤C i,j ;

[0097] where f i，j is the traffic on the link connecting node i and node j, and C i，j is the capacity of the link connecting node i and node j;

[0098] This requirement prevents network links from being overloaded, thus avoiding potential bottlenecks and ensuring the integrity of network operation.

[0099] The traffic demand constraint means that the traffic demand from the source node to the destination node is satisfied, that is:

[0100]

[0101] where s is the source node, t is the destination node, f (s，i) is the total traffic flowing out from the source node s, f (i，t) is the total traffic flowing into the destination node t, and D s，t is the traffic demand;

[0102] Meeting this condition ensures that the network capacity is sufficient to handle the specified demand and supports seamless end - to - end connections. The non - negative flow constraint means that the traffic on all links satisfies non - negativity, that is:

[0103] f i,j ≥0, for all i,j∈V;

[0104] where fi，j is the traffic on the link connecting node i and node j.

[0105] This internal regulation verifies that the traffic value is consistent with a feasible network traffic scenario, excluding the possibility of reverse or abnormal traffic.

[0106] For the specific traffic splitting method of equal-cost multi-path routing technology, all possible paths between two nodes in the network are identified, and paths with the same cost are selected. For paths with the same cost, the traffic is evenly distributed on the paths to the next-hop node.

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

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

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

[0110] Such as Figure 2 , the configured link weights result in the identification of two shortest paths from node v1 to v5:

[0111] v1 - v2 - v3 and v1 - v3 - v5. Therefore, using equal-cost multi-path routing for load balancing can evenly distribute the traffic between the next-hop nodes v2 and v3, as shown in Figure 3 . Conversely, node v4, as the next-hop of another non-shortest path, does not participate in traffic distribution in this scenario.

[0112] S2. Initialize parameters, set the particle swarm pop and the number of evolution generations MaxGen, construct the particle swarm encoding method, and configure the weights of the links in the actual network by manipulating the encoding in each particle in the particle swarm; decode the particles to obtain the lowest-cost path;

[0113] Construct the particle swarm encoding method, specifically including: representing the network as a graph, with nodes as routers or switches and edges as connections between nodes, assigning a unique identifier to each edge, where the identifier corresponds 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 weights into a vector to construct a particle, where each element of the vector corresponds to the cost weight of the corresponding link;

[0114] Configure the position of the particles within the integer range by the equal-cost multi-path routing method.

[0115] Based on the particle swarm optimization principle, the present invention adopts a coding method, where each particle in the particle swarm represents a potential solution, reflecting the topological structure of the network graph, such as Figure 4 shown. The coding process starts from representing the network as a graph, where nodes are routers or switches and edges are the connections between them. Then a unique identifier is assigned to each edge, corresponding to its position in the network topology. These identifiers are associated with specific integer values, representing the cost weights of the corresponding links, similar to the metrics used in OSPF configuration to determine the traversal cost of each link. A particle is constructed by compiling these cost weights into a vector, with each element of the vector corresponding to the weight of a specific link, effectively refreshing the state of the network according to the link costs. Moreover, the equal-cost multi-path routing strategy is applied, and the particle positions are configured within the integer range of [0, 30] to meet specific optimization requirements. For example, in a network with three links (Link1, Link 2, Link3) whose 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.

[0116] Decoding the particles specifically includes:

[0117] Applying a decoding method to each particle, configuring the cost weights of the encoded links, and converting them into routing instructions; according to the current traffic matrix information, for each pair of nodes, using the cost weights of the links specified by the particle as the cost metric, and adopting the Dijkstra algorithm to calculate and obtain the lowest-cost path.

[0118] Decoding each particle is a unique and essential process, which converts the encoded particle data into an operable network routing configuration. We first apply a function mapping method to each particle to interpret the encoded link weights and convert them into routing instructions. Combining the current traffic matrix information is crucial because it provides the traffic demand data between each pair of source-destination nodes. For each pair of nodes, using the link weights specified by the particle as the cost metric and adopting the Dijkstra algorithm to calculate and obtain the lowest-cost path to ensure efficient routing. Then the equal-cost multi-path routing is applied to distribute the traffic over multiple equal-cost paths to enhance load balancing. After routing all pairs of nodes according to the particle configuration, we calculate the maximum link utilization rate and the average link utilization rate values to evaluate the performance of the network under the represented routing scheme. The Pareto solutions formed by these objective values represent a potential routing configuration scheme for each particle, enabling us to evaluate its effectiveness and optimize the network traffic flow.

[0119] S3. According to the lowest-cost path obtained after decoding the particles, after the data is transmitted along the shortest path, calculate the network performance and obtain the fitness value of the particle swarm, and update it as pBest;

[0120] S4. Obtain the non-dominated solutions of the current particle swarm through non-dominated sorting, and add the non-dominated solutions to the external archive A;

[0121] S5. Find the optimal solution of a single particle from all the particles in the current particle swarm, and update it as gBest;

[0122] The non-dominated sorting adopted by the present invention is an existing design. The particle swarm algorithm adopted changes the strategies of particle mutation and evolution on the basis of the existing design, and corresponding strategies are also designed for the external archive A, which generally promotes the faster convergence of the algorithm.

[0123] S6. Adopt the dynamic link analysis strategy to guide and update the current particle swarm to generate a new generation of particle swarm;

[0124] In order to implement a more accurate and intelligent link weight adjustment method and overcome the defects of arbitrary and unguided particle updates, the present invention utilizes in-depth analysis of the existing network graph and traffic matrix data. This analysis enables us to classify the links of the network in a way that supports knowledge-driven strategies. We focus on three pieces of information that are crucial for shaping knowledge-driven strategies.

[0125] First, consider the link bandwidth. A larger link bandwidth means higher link availability, which indicates that a lower link weight cost may be more beneficial. Therefore, links with larger bandwidths are assigned smaller weights to promote their utilization.

[0126] Second, evaluate the static property of link connectivity by calculating the centrality of the link. This is determined by the sum of the in-degree and out-degree of the nodes it connects, reflecting the importance of the link in the network topology. Links with high centrality are usually considered key or "hub" links. However, when these highly centralized links have limited bandwidth, they require higher weights to represent higher routing costs through them to prevent congestion.

[0127] Third, analyze the dynamic property of link demand, mainly focusing on the top 10% of source-destination (OD) pairs with the highest traffic forwarding demands. By performing the shortest path search on these 10% of OD pairs and compiling the paths they pass through, links that frequently appear (more than three times) in these paths can be identified. Links that appear frequently in these paths are regarded as active under the current TM conditions. Similarly, active links with limited bandwidth will increase their weights to prevent congestion.

[0128] The knowledge-driven strategy aims to optimize the particle update in the particle swarm, ensuring that they are both data-based and efficient. This approach is driven by the inherent characteristics of the network and the current traffic demands, jointly enhancing the performance of the network. By integrating a complex link weight adjustment strategy that considers bandwidth, centrality, and dynamic demand attributes, a more intelligent and responsive framework is established for the optimization of network routing configurations.

[0129] In the present invention, the evolution process of particles is mainly driven by the update of particle positions and velocities. The position of each particle reflects the cost weight of network links. In the traditional particle swarm optimization algorithm, the velocity update of each particle is affected by two key factors: the optimal position found by the individual so far (pBest) and the global optimal position found by the swarm (gBest). However, in our update method, pBest i is redefined as the target best position reached by the current particle. Arch i represents a position in the non-dominated solution archive, and each particle learns from different randomly selected archive members, adding randomness to the learning process. This method ensures that the update of each particle is affected by a unique combination of historical optimal positions and current goals, resulting in a more dynamic and faster-responsive optimization process.

[0130] The improved particle swarm optimization algorithm provided by the present invention can intelligently adjust the network link weights. First, the equivalent multi-path routing strategy is applied, and the particle positions are configured within the integer range of [0, 30] to meet specific optimization requirements. Given the discrete nature of this optimization space, the knowledge-driven strategy borrows the sign function (sign(*)) in the discrete particle swarm optimization method to determine the direction of position change. This innovative method differentiates this approach through different learning interactions with pBest, gBest, and the archive.

[0131] The dynamic link analysis strategy specifically includes:

[0132] Determining the direction of particle position change through the sign function (sign(*)) in the discrete particle swarm optimization method, i.e.:

[0133] evo ij = sign(c1 * r1 * (pBest ij - X ij ) + c2 * r2 * (gBest ij - X ij ) + c3 * r3 * (Arch ij - X ij ));

[0134] V ij = V ij + evo ij⊙klg(l j );

[0135] where \(i = 1, 2, \ldots, N\), \(N\) is the number of particles; \(j = 1, 2, \ldots, D\), \(D\) is the dimension of the particles; pBest ij represents the \(j\)-th dimension of pBest i ; \(c_1\), \(c_2\), \(c_3\) are acceleration factors; \(r_1\), \(r_2\), \(r_3\) are random numbers in the interval \([0, 1]\); \(X\ ij is the position of the \(i\)-th particle in the \(j\)-th dimension; Arch i represents a position in the non-dominated solution archive; \(V\ ij is the velocity of the \(i\)-th particle in the \(j\)-th dimension; evo ij represents the change value of the \(i\)-th particle in the \(j\)-th dimension, which is used to determine the direction of velocity update; evo ij ⊙klg(l j ) 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 ;

[0136] The sign function \((sign(*))\) can simplify the computational complexity in the discrete space by converting the velocity update into a direction decision (-1 means moving backward, 1 means moving forward).

[0137] For the knowledge-driven rule multiplier \(klg(l j ) of link \(l\ j , it will affect the probability of using evo ij for velocity update.

[0138] If \(klg(l j ) = 1\), then the velocity \(V\ ij will definitely add evo ij ; if \(klg(l j ) = 0.5\), then evo ij has a 50% probability of being added to \(V\ ij ;

[0139] The rules of \(klg(l j ) include the bandwidth rule, the link centrality rule, and the dynamic demand rule;

[0140] The bandwidth rule is that the links in the top 25% of bandwidth availability follow special update rules. If the velocity update sign is positive, indicating an increase in link weight, then \(klg(l j ) is set to 0.5;

[0141] The link centrality rule is that for links with centrality ranking in the top 50% and bandwidth ranking in the bottom 50%, if the speed update symbol is negative, indicating a decrease in link weight, then set klg(l j ) to 0.5;

[0142] The dynamic demand rule is that for links used by the top 10% of traffic demands and with bandwidth ranking in the bottom 50%, when the speed update symbol is negative, then adjust klg(l j ) to 0.5;

[0143] For cases that do not conform to the bandwidth rule, link centrality rule, and dynamic demand rule, klg(l j ) remains at 1.

[0144] S7. Compare the new generation of particle swarm obtained in S6 with the pBest in S3 to obtain the updated pBest 更新 ; Obtain the non-dominated solutions of the new particle swarm through non-dominated sorting, and add the non-dominated solutions to the external archive A;

[0145] S8. Update the external archive A through the elite mutation strategy. Perform Gaussian perturbation on each non-dominated solution and a random dimension to obtain the mixed population solutions; then perform non-dominated sorting on the mixed population solutions and select the non-dominated solutions in the mixed population solutions; Determine the final non-dominated solutions according to the number of non-dominated solutions and the crowding degree calculation method; According to the particle swarm evolution algebra MaxGen, repeat S3 to obtain the final non-dominated solutions after iteration.

[0146] Finally, there is an archive update mechanism with an elite strategy. First, pass in the solutions of the previous generation archive and the current pBest to form a set of mixed population solutions. Secondly, perform an elite strategy on the solutions of the previous generation archive for local search to explore the possibility of the best position existing around the particles, and add the newly formed solutions to the current mixed population S.

[0147] The specific method for updating the external archive A through the elite mutation strategy includes:

[0148] For each non-dominated solution Arch i in the external archive A, set a new solution E i , and set the new solution E i to be equal to Arch i , then select a random dimension d to perform Gaussian perturbation, and its formula is:

[0149] E id = E id + (X max,d - X min,d ) * Gaussian(0, 1);

[0150] Among them, E id is the solution after performing Gaussian perturbation, where d th represents the dimension, X max，d is the upper bound of the d th -th dimension, and X min，d is the lower bound of the d th -th dimension. Gaussian(0, 1) is a random value generated from a Gaussian distribution with a mean of 0 and a standard deviation of 1;

[0151] The new solution E i is obtained by traversing each solution in Arch i . By performing a new operation (Gaussian perturbation) on a newly copied solution, and then adding it together with E i and Arch i to the mixed population S;

[0152] After perturbation, it is judged whether E id is within the search range of [X max,d , X min,d ; if not, then set E id to the corresponding boundary;

[0153] Subsequently, 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.

[0154] Finally, perform non-dominated sorting on the mixed population solution to obtain a set of excellent non-dominated solutions and store them as the new generation of archive solutions in the external archive.

[0155] Perform non-dominated sorting on the obtained mixed population solution to obtain the 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;

[0156] If the number of non-dominated solutions included in the mixed population solution is less than NP, then directly replace the non-dominated solutions in the external archive A with the non-dominated solutions in the mixed population solution;

[0157] If the number of non-dominated solutions included in the mixed population solution exceeds NP, then perform crowding degree calculation and select the non-dominated solutions with large crowding degree values as the non-dominated solutions in the external archive A;

[0158] The specific method for crowding degree calculation includes:

[0159] All particles are sorted according to the fitness value under the current objective, setting the maximum fitness value as f max , and the minimum fitness value as f min ;

[0160] The crowding degrees of the particles with the maximum and minimum fitness values are infinite. Assume that the current particle is the rs-th particle after sorting, and its fitness value for the current objective is f rs , and its crowding distance is:

[0161] (f rs+1 - f rs-1 )(f max - f min );

[0162] That is, after calculating the difference in fitness values between adjacent particles, it is the result of normalization.

[0163] For each particle, calculate the crowding degree for each of the two objectives and accumulate it as the final crowding degree of the individual. This method can retain non-dominated solutions with better diversity. By adding an elite strategy and an archive update strategy after non-dominated sorting, the exploration ability of the algorithm can be improved during the learning process of each generation of particles, and the archive solutions can in turn guide the update of the new generation of particles, improving the quality of the solutions.

[0164] The present invention proposes a distributed full-process job shop scheduling problem for the distributed multi-stage production mode of modern enterprise products, and discloses a distributed full-process job shop scheduling method based on an evolutionary algorithm. This method simultaneously considers two objectives, the maximum completion time of the product and the total operating cost of the machines, to provide a set of Pareto optimal solutions for the enterprise. First, the present invention models the proposed problem and designs a two-layer coding method to represent the scheduling scheme. To locate more Pareto solutions, the present invention adopts a two-population evolution method to optimize the two proposed objectives respectively, and provides a channel for information exchange between the two populations by introducing an external archive, thereby obtaining a set of Pareto optimal solutions.

[0165] The key points of the present invention include the following four points:

[0166] 1. An efficient indirect network coding method is proposed according to the characteristics of the problem, as well as a decoding method for finding paths under the Dijkstra algorithm through the weights of the coding, and an individual initialization strategy designed according to equal-cost multi-path routing.

[0167] 2. Aiming at the defect of the single optimization objective of traditional traffic engineering, the present invention proposes a two-objective optimization model based on the minimum-maximum link utilization rate and the global average link utilization rate, 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.

[0168] 3. To meet the requirement of dynamically optimizing the link cost weight, a knowledge-driven dynamic particle update strategy is proposed. By ranking link bandwidth, analyzing centrality, and identifying dynamic traffic demands, a knowledge-driven particle velocity update rule is designed, which helps individuals in the population improve their exploration ability to find solutions and enhances the convergence ability of the algorithm.

[0169] 4. According to the characteristics of the problem, a corresponding archived elite mutation strategy is designed to perform Gaussian perturbation on the found non-dominated solutions to improve the accuracy of the solutions. This mechanism enables interactive learning between the external archive and the particle swarm, which helps break through local optima and expand the coverage of the Pareto front.

[0170] With the help of the above strategies, the proposed data-driven multi-objective particle swarm algorithm has achieved excellent results in solving large-scale dynamic traffic engineering problems.

[0171] Based on the disclosure and teachings of the above specification, those skilled in the art to which the present invention pertains can also 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. In addition, although some specific terms are used in this specification, these terms are only for convenience of description and do not constitute any limitation to the present invention.

Claims

1. A network traffic allocation method based on knowledge-driven multi-objective particle swarm optimization, characterized in that It includes the following steps: S1. Establish a network model, assign weights to the links in the network; through segment routing, assign segment identifiers to nodes or links; Obtain paths with the same cost between nodes by the equal-cost multi-path routing method; use the weight of the link as a cost metric to make data transmit along the shortest path, and construct a multi-objective optimization mathematical model; S2. Initialize parameters, set the particle swarm and the evolutionary algebra MaxGen, construct the particle swarm coding method, and configure the weights of the links in the actual network by manipulating the coding in each particle in the particle swarm; decode the particles to obtain the lowest-cost path; S3. According to the lowest-cost path obtained after decoding the particles, after making the data transmit 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 solutions of the current particle swarm by non-dominated sorting, and add the non-dominated solutions to the external archive A; S5. Find the optimal solution of a single particle from all the particles in the current particle swarm, and update it to gBest; S6. Adopt a dynamic link analysis strategy to guide and update the current particle swarm to generate a new generation of particle swarms; S7. Compare the new generation of particle swarm obtained in S6 with the pBest in S3 to obtain the updated pBest 更新 ; Obtain the non-dominated solutions of the new particle swarm by non-dominated sorting, and add the non-dominated solutions to the external archive A; S8. Update the external archive A by the elite mutation strategy, perform Gaussian perturbation according to each non-dominated solution and a random dimension to obtain the mixed population solutions; then perform non-dominated sorting on the mixed population solutions, and select the non-dominated solutions in the mixed population solutions; determine the final non-dominated solutions according to the number of non-dominated solutions and the crowding degree calculation method; According to the particle swarm evolutionary algebra MaxGen, repeat S3 to obtain the final non-dominated solutions after iteration.

2. The network traffic allocation method based on knowledge-driven multi-objective particle swarm optimization according to claim 1, wherein In S1, the network is modeled as a weighted directed graph G=(V, E), where V represents the nodes in the network and E represents the directed links; assign a weight to each link, and the calculation method of the maximum link utilization MLU is: where MLU is the maximum link utilization, f L is the traffic on link L, and C L is the capacity of link L; the value of MLU ranges between 0 and 1; The calculation method of the average link utilization ALU of all the links on the network is: Among them, ALU is the average link utilization rate, f L is the traffic on link L, and C L is the capacity of link L; |E| is the total number of links in the network.

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

4. A network traffic allocation method based on knowledge-driven multi-objective particle swarm optimization according to claim 3, characterized in that The flow conservation constraint is that for each node in the network, the total inflow traffic is equal to the total outflow traffic, which is expressed by the formula: where i is an intermediate node, n is all the predecessor nodes of i, m is all the successor nodes of i, and f (n，i) is the total flow rate flowing into the intermediate node i from all the predecessor nodes n, and f (i，m) is the total flow rate flowing out from the intermediate node i to all the successor nodes m; The link capacity constraint is that the traffic passing through each link does not exceed the specified capacity of the link, that is: f i,j ≤C i,j ; where f i，j is the traffic on the link connecting node i and node j, and C i，j is the capacity of the link connecting node i and node j; The traffic demand constraint is to meet 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 (s，i) is the total flow flowing out of the source node s, and f (i，t) is the total flow flowing into the destination node t, and D s，t is the flow requirement; The non-negative flow constraint is to meet that the traffic of all links remains non-negative, that is: f i,j ≥0, for all i, j ∈ V; where f i，j is the traffic on the link connecting node i and node j.

5. A 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, evenly distribute the traffic on the paths for transmitting to the next-hop node.

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

7. A network traffic allocation method based on knowledge-driven multi-objective particle swarm optimization according to claim 6, characterized in that In S2, decoding the particle specifically includes: Applying a decoding method to each particle, configuring the cost weights of the encoded links, and converting them into routing instructions; according to the current traffic matrix information, for each pair of nodes, using the cost weights of the links specified by the particle as the cost metric, and using the Dijkstra algorithm to calculate and obtain the lowest-cost path.

8. A network traffic allocation method based on knowledge-driven multi-objective particle swarm optimization according to claim 1, characterized in that, In S6, the dynamic link analysis strategy specifically includes: Determining the direction of particle position change through the sign function (sign(*)) in the discrete particle swarm optimization method, that is: evo ij = sign(c1 * r1 * (pBest ij - X ij ) + c2 * r2 * (gBest ij - X ij ) + c3 * r3 * (Arch ij - X ij )); V ij = V ij + evo ij ⊙klg(l j ) 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 j-th dimension of pBest i ; c1, c2, c3 are acceleration factors; r1, r2, r3 are random numbers within the interval [0, 1]; X ij is the position of the i-th particle in the j-th dimension; Arch i represents a position in the non-dominated solution archive; V ij is the velocity of the i-th particle in the j-th dimension; evo ij represents the change value of the i-th particle in the j-th dimension, which is used to determine the direction of velocity update; klg(l j ) is the knowledge-driven rule multiplier for link l j ; evo ij ⊙ klg(l j ) means that on the basis of the original velocity V ij , there is a probability of klg(l j ) to add the changed velocity value evo ij ; If \(k\lg(l j ) = 1\), then the speed \(V ij will definitely add evo ij ; if \(k\lg(l j ) = 0.5\), then evo ij has a 50% probability of being added to \(V ij ; klg(l j )'s rules include bandwidth rules, link centrality rules, and dynamic demand rules; The bandwidth rule is that the links in the top 25% of bandwidth availability follow special update rules. If the speed update symbol is positive, indicating an increase in link weight, then set k lg(l j ) to 0.5; The link centrality rule is that for links with a centrality ranking in the top 50% and a bandwidth ranking in the bottom 50%, if the speed update symbol is negative, indicating a decrease in link weight, then set k lg(l j ) to 0.5; The dynamic demand rule is that for the top 10% of traffic demand usage and links with the bottom 50% in bandwidth ranking, when the speed update symbol is negative, then adjust klg(l j ) to 0.5; For cases that do not conform to the bandwidth rule, the link centrality rule, and the dynamic demand rule, klg(l j ) remains at 1.

9. A network traffic allocation method based on knowledge-driven multi-objective particle swarm optimization according to claim 1, characterized in that In S8, the specific method for updating the external archive A through the elite mutation strategy includes: For each non-dominated solution Arch in the external archive A i , a new solution E i is set, and the new solution E i is set to be equal to Arch i , and then a random dimension d is selected to perform Gaussian perturbation, and its formula is: E id = E id + (X max,d - X min,d ) * Gaussian(0,1); Among them, E id is the solution after performing Gaussian perturbation, where d th represents the dimension, X max，d is the upper bound of the d th -th dimension, and 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 a mean of 0 and a standard deviation of 1; After perturbation, determine E id is within the search range of [X max,d , X min,d ; if not, set E id to the corresponding boundary; Calculate the fitness value of the new solution E i After that, add E i and Arch i to the mixed population S to obtain the solution of the mixed population.

10. A network traffic allocation method based on knowledge-driven multi-objective particle swarm optimization according to claim 9, characterized in that, Performing non-dominated sorting on the obtained mixed population solutions, obtaining a new generation of non-dominated solutions and storing them in the external archive A; setting NP as the upper limit of the number of non-dominated solutions in the external archive A; If the number of non-dominated solutions included in the mixed population solutions is less than NP, directly replace the non-dominated solutions in the external archive A with the non-dominated solutions in the mixed population solutions; If the number of non-dominated solutions included in the mixed population solutions exceeds NP, perform crowding degree calculation, and select the non-dominated solution with a large crowding degree value as the non-dominated solution in the external archive A; The specific method for crowding degree calculation includes: 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 f min ; The crowding degrees of the particles with the maximum and minimum fitness values are infinite. Assume the current particle is the rs-th particle after sorting, and its fitness value for the current objective is f rs , and its crowding distance is as follows: (f rs+1 -f rs-1 )(f max -f min ); That is, the result after normalization is obtained after calculating the difference in fitness values between adjacent particles.

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