Method for identifying key node set under cascade failure of marine transportation network based on multi-population genetic algorithm

Abstract

The invention belongs to the field of combinatorial optimization, and relates to a heuristic algorithm combined with global marine transportation network priori knowledge, which is used for solving a key port set problem in a global marine transportation network, and comprises the following steps: modeling a marine transportation network, modeling a marine transportation network cascade failure phenomenon, and carrying out optimization on the marine transportation network cascade failure phenomenon; a key port gathering problem of the marine transportation network is converted into a single-target optimization problem; a multi-population genetic algorithm framework is adopted, priori knowledge of the marine transportation network is fused into initial population generation of all sub-populations, and therefore initial sub-populations with high quality are formed; a simulated annealing mechanism is introduced in the algorithm iteration process to improve the algorithm performance and enhance the search capability. The method is superior to a current mainstream heuristic method and an index method on a sea transportation data set, and an effective reference is provided for stable operation of a sea transportation network.

Description

Technical Field

[0001] The invention belongs to the field of combinatorial optimization, and in particular relates to a method for identifying key node sets under cascading failure of a shipping network based on a multi-population genetic algorithm. Background Art

[0002] The uninterrupted operation of the maritime transport network is essential to maintaining world trade and economic development. However, this network may be disrupted by various risks, especially port disruptions caused by factors such as natural disasters and epidemics. In recent years, congestion caused by port disruptions has become more frequent and spread to many other ports, causing adverse effects on trade. Therefore, understanding the propagation process of port congestion and identifying the key ports that cause severe congestion to spread are essential to improve the disaster resilience of maritime logistics.

[0003] The spread of port congestion is a typical phenomenon of cascading failures in shipping networks. For a long time, the identification of key ports has been an important research topic in the vulnerability analysis of shipping networks. Existing research on the identification of key ports in the vulnerability analysis of shipping networks can be roughly divided into two categories: topology-based analysis and cascading failure-based analysis. Topology-based research usually only uses the static topological connection information of the network. After defining the indicators for measuring network performance, a certain proportion of ports in the network are removed intentionally or randomly to simulate the destruction of ports, and the degree of degradation of network performance is used to characterize the importance of the removed ports. For example, literature 1 (H. Liu, Z. Tian, ​​A. Huang, and Z. Yang, “Analysis of vulnerabilities in maritime supply chains,” Reliab Eng Syst Saf, vol. 169, pp. 475–484, Jan. 2018, doi: 10.1016 / j.ress.2017.09.018.) removes 54 ports from the Asia-Europe route one by one and calculates the global network efficiency and local efficiency clustering coefficient to evaluate the impact of each port on the vulnerability of the shipping network. Reference 2 (D.Wu, N.Wang, A.Yu, and N.Wu, “Vulnerability analysis of global container shipping liner network based on main channel disruption,” Maritime Policy and Management, vol.46, no.4, pp.394–409, May 2019, doi:10.1080 / 03088839.2019.1571643.) simulated the disruption of the Strait of Malacca, the Suez Canal, and the Panama Canal, and calculated network performance indicators such as network average degree and clustering coefficient, and found that the disruption of the main canal would greatly affect the performance of the network. However, static analysis methods based on network topology structure rarely consider the dynamic process of traffic redistribution caused by port disruption.

[0004] Research based on cascading failure aims to identify ports where initial failures will lead to the most serious cascading failure consequences. These studies not only consider the topological structure of the shipping network, but also the traffic flow dynamics therein. However, existing research based on cascading failure often only models the cascading failure of a single port interruption, and cannot simulate the cascading failure phenomenon caused by the simultaneous interruption of multiple ports. However, the simultaneous congestion of multiple ports has more significant practical significance. However, the simultaneous congestion of multiple ports will make the cascading failure propagation process of the network more complicated. The congestion propagation process is not only affected by the characteristics of the triggering port, but also by the rotation adjustment behavior of the ports serving the routes. This complexity increases the difficulty of solving the optimization problem of identifying key port combinations under cascading failures in shipping networks. At the same time, there is currently no effective solution specifically for this problem. Summary of the invention

[0005] The present invention formulates the problem of identifying the key port set in the cascading vulnerability of the shipping network as an optimization problem, aiming to determine the port set whose simultaneous interruption will cause the maximum cascading failure scale (i.e., the most congested ports). In order to solve this problem, an improved multi-population genetic algorithm targeting the characteristics of the shipping network is proposed. The algorithm incorporates the characteristics of the shipping network into the generation of sub-populations, and helps generate a high-quality initial population based on the prior knowledge of the network incorporated into the multi-population genetic algorithm to obtain a high-quality initial solution. At the same time, in the process of sub-population evolution, in order to prevent the occurrence of duplicate genes due to crossover and mutation, and to maintain the search efficiency of the algorithm, the present invention adopts a replacement method based on gene importance ranking. In addition, in order to reduce the risk of falling into a local optimum, a simulated annealing strategy is adopted in the iteration process of the sub-population, that is, an inferior solution is accepted with a certain probability, which reduces the possibility of the algorithm falling into a local optimum and increases the diversity of solutions in the population. This strategy is particularly suitable for problems where there are multiple local optimal solutions in the solution space.

[0006] The technical solution of the present invention is as follows:

[0007] The key node set identification method under cascading failure of shipping network based on multi-population genetic algorithm has the following steps:

[0008] Step 1: Shipping network modeling. Based on the container liner route data, a bipartite network is used to describe the coupling relationship between routes and ports. In the bipartite network, there are two types of nodes: ports and routes. The edges between the two types of nodes reflect the docking relationship between routes and ports.

[0009] Step 2: Calculate the flow capacity of port nodes in the shipping network.

[0010] Step 3: Simulate the cascading failure of the port collection, including the redistribution of traffic within the shipping network and the update of the network structure.

[0011] Step 4: Take the network cascading failure scale as the fitness value, that is, the objective function F(U), and use equations (1) and (2) to construct the objective function:

[0012]

[0013] Constraint: |U|=k(2)

[0014] Where U is a set of ports of size k, i.e., the decision variable. m represents the total number of simulations, S x (U) represents the size of the cascading failure caused by set U in the xth simulation of the cascading failure model, that is, the number of other failure ports.

[0015] Step 5: Based on the improved multi-population genetic evolutionary algorithm, the key nodes in the shipping network are identified to obtain the optimal failure set, and the port nodes in the set are used as the key node set in the shipping network.

[0016] The step 1 is specifically as follows:

[0017] Step 1.1: Represent the shipping network as a bipartite network G = (R, V, E), where R and V represent the set of route nodes and port nodes respectively. E represents the edge set between the set R and the set V. If the edge between the route node and the port node exists in E, then the port is included in this route.

[0018] Step 1.2: The port network G′=(V,E′) is obtained by the unimodal projection of the network G. E′ represents the set of edges between ports. If two ports are included in at least one of the same routes, there is an undirected edge between the two ports. Route node j and port node i are connected by a link, and the weight of this edge is w ij represents the container flow that port i receives from route j. The total flow of the route is evenly distributed to all port pairs in the route, so w ij is defined as 2×t j / n j , t j is the total cargo volume on a route, n j is the number of ports in a route.

[0019] The step 2 is specifically as follows:

[0020] Step 2.1: Initial load L at port i i (0) is defined as the total flow that the port receives from all service routes calling the port.

[0021]

[0022] Where R represents all routes.

[0023] Step 2.1: Flow capacity C of port i i It represents the maximum traffic load that the port can handle and is defined as:

[0024] C i =(1+α)L i (0)

[0025] Where α>0 is the tolerance parameter, which represents the additional load that the port can accommodate beyond the initial load.

[0026] The step 3 is specifically as follows:

[0027] Step 3.1: Simulate the initial failure of the port set. Remove the port nodes in the key port set from the shipping network.

[0028] Step 3.2: Route adjustment behavior. When a port fails, each service route that originally calls the port will independently choose one of the following three possible behaviors with a certain probability: wait at the failed port with probability p1; call an alternative port that is still functioning normally with probability p2; skip the failed port with probability 1-p1-p2. If all alternative ports of the failed port fail, there are only two options: wait at the failed port with probability p1; skip the failed port with probability 1-p1.

[0029] Step 3.3: Load redistribution. If a service route is waiting at a failed port, the failed port load obtained from the service route will not be diverted to any other port. If a service route skips a failed port, the traffic of the route will be evenly distributed to the ports on the route that are still operating normally. If a route stops at an alternative port, one will be selected from all the alternative ports that are still in operation, and the cargo unloaded from the failed port on this route will be added to the selected alternative port. When a port fails, other ports in its location are usually used as alternative ports; among these alternative ports, ports that are geographically adjacent to the failed port and have a capacity not less than that of the failed port are usually given priority. Therefore, in the present invention, when determining the alternative port of a port, the port in its location is preferably selected as the alternative port. If a port is the only port in its location, it is considered that there is no alternative port for the port; secondly, when possible, an additional restriction is adopted: the alternative port should be located within a certain range from the port and its throughput capacity cannot be much lower than that of the original port.

[0030] Step 3.4: After each load redistribution run, the loads of the remaining ports are calculated. If the load of any port exceeds its capacity, the corresponding port will fail and another round of load redistribution will be triggered. The cascading process will terminate once the load of each remaining port is within its capacity or all ports in the initial shipping network fail.

[0031] The step 5 is specifically as follows:

[0032] Step 5.1: Problem Coding:

[0033] Define the population size as S, the evolutionary generation as Gen, and the maximum evolutionary generation as l max , the number of subpopulations is Z, and the probability of population crossover is P c , the population mutation rate is P m , the population migration generation number is M, and the population migration rate is P mr , the number of consecutive iterations without improvement is l, the simulated annealing cooling coefficient is q, the initial temperature is T1, and Gen, l=1 and Z are initialized.

[0034] Integer coding is used to set a fixed ID for each port in the shipping network. K port nodes are randomly or roulette-wheel-selected from the candidate set of port nodes in the shipping network as the genes of each individual in the population, and the Gen-th population set of the population is obtained.

[0035] in represents the Sth subpopulation of the Genth generation, represents the nth individual in the Sth subpopulation in the Genth generation, each of which represents a set of failed port nodes in the shipping network, and represents the kth gene in the nth individual and represents the kth failed port node.

[0036] The specific method of generating the port node candidate set is as follows:

[0037] Method 1: In each community, select the top-ranked ports according to the gateway index B and put them into the port node candidate set as candidate genes. The specific calculation method of B is as follows:

[0038]

[0039] Among them, port i is a member of community T, m iT Indicates the number of connections between port i and other ports outside T, m T and σ mT They represent the mean and standard deviation of the number of external connections of all ports in T, respectively.

[0040] Method 2: Select ports with B ≥ 1.5 as gateway hub ports and calculate the sum of the degrees D of all gateway hub ports in the region to which they belong. sum . D sum The larger the area, the easier it is to be selected, and the portal hub port node with a larger degree is also more likely to be selected as a candidate node.

[0041] Method 3: All ports in the shipping network are included as candidate genes into the port node candidate set.

[0042] Step 5.2: Use the elite-retaining binary tournament strategy to extract the subpopulation The parent is selected for subsequent reproduction. The offspring with the highest fitness in each sub-population will be retained. Then, a pair of offspring are randomly selected for comparison, and the offspring with higher fitness are added to the new sub-population. Until the number of individuals in the subpopulation reaches P n .

[0043] Step 5.3: For each subpopulation Perform a crossover operation, using a two-point crossover strategy with a crossover probability of P c Two crossover points are randomly generated on two pairs of parental chromosomes, and then the two chromosome segments at the crossover points are exchanged. After the chromosomes are crossed, there may be two identical gene values ​​on the chromosomes. The present invention is based on the replacement method of gene importance ranking, and randomly selects non-repeating genes from the genes with the highest gene importance values ​​to replace them, thereby obtaining a sub-population after crossing.

[0044] Step 5.4: According to P m Sure Whether each individual in the population mutates or not, if so, a node is randomly selected from the candidate set of port nodes of the subpopulation to replace it, so as to obtain a mutated subpopulation

[0045] Step 5.5: Count the number of times the gene appears in the chromosome in each sub-population and use this as the importance value of the gene.

[0046] Step 5.6: According to The corresponding shipping network node set is used to simulate the cascading failure of the shipping network.

[0047] Step 5.7: Calculate according to formula (1) The fitness value F(U) of .

[0048] Step 5.8: Calculate the mutated subpopulation The fitness value of the individuals in the subpopulation is calculated, and the average fitness value f of each subpopulation is calculated.avg .

[0049] Step 5.9: Set the fitness value f that is greater than the average fitness value of the population in which you are located avg The individuals are stored in the elite individual set Γ, Γ = {Γ1, Γ1, Γ1, …, Γ n}, where Γ n Represents the set of elite individuals of the nth subpopulation.

[0050] Step 5.10: Calculation The fitness value of the new individual is related to the f of the subpopulation to which it belongs. avg If it is greater than, keep the individual. If it is less than, remove it with probability p Gen Keep the offspring and with probability 1-p Gen A random selection is made from the elite individuals in the previous round to replace them, and finally the updated population A is formed. Gen+1 , and save the individual with the largest fitness value as where p Gen The calculation formula is as follows:

[0051] p Gen =exp(ΔE / T Gen )

[0052] In the formula, ΔE is the average fitness difference between the previous generation and the next generation, T Gen is the temperature of the Gen-th generation. Step 5.11: Update the temperature T. The update formula is as follows:

[0053] T Gen+1 =q×T Gen

[0054] Step 5.12: Update the number of iterations Gen = Gen + 1. Compare Is it greater than If it is greater than, then l=1; if it is less than, then l=l+1.

[0055] Step 5.13: Individual migration between subpopulations, calculate whether the remainder of Gen divided by M is 0. If it is 0, use the fully connected topology (FCT) to replace the inferior offspring and identify the excellent offspring in each subpopulation; when the predetermined number of iterations (M) is reached, the previous subpopulation will transfer its excellent offspring to the next subpopulation to replace the inferior offspring, so as to achieve the sharing of superior offspring between subpopulations and form a circular subpopulation migration pattern. If it is not 0, no individual migration will be performed.

[0056] Step 5.14: Termination condition: When the maximum number of iterations l is reached max Or when the solution has not been improved after l consecutive iterations, the algorithm will stop running and output the optimal individual as the key node set.

[0057] Beneficial effects of the present invention: Based on the improved multi-population genetic algorithm and in combination with the characteristics of the shipping network, the present invention proposes a new replacement method based on gene importance ranking and a simulated annealing strategy. When optimizing the current solution, a high-quality initial solution is generated by combining the network characteristics, and gene replacement and simulated annealing methods are used in the evolution process to prevent falling into the local optimum. Compared with the traditional genetic algorithm, this optimization method improves the diversity and stability of the solution, and solves the iterative redundancy problem caused by the initial solution dependency and gene duplication. In addition, the present invention introduces the fully connected topology (FCT) strategy to share dominant genes among subpopulations, thereby further improving the global search capability of the algorithm. In view of the possible convergence phenomenon of the population, the simulated annealing strategy is used to accept inferior solutions with a certain probability in the process of updating the population, thereby enhancing the diversity of the solution and the robustness of the algorithm, thereby improving the efficiency of the algorithm and the ability to solve complex network problems. The present invention effectively solves the difficult problem of identifying key port sets under cascading failures of the shipping network, and provides a new idea for improving the disaster resistance of shipping logistics. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 The present invention is a flowchart of the overall framework for identifying key nodes in a shipping network based on an improved multi-population genetic evolution algorithm in the method of the present invention. DETAILED DESCRIPTION

[0059] The specific implementation of the present invention is further described below in conjunction with the accompanying drawings and technical solutions.

[0060] The method for identifying key node sets under cascading failure of shipping network based on multi-population genetic algorithm of the present invention comprises the following steps:

[0061] Step 1: Shipping network modeling. Based on the container liner route data, a bipartite network is used to describe the coupling relationship between routes and ports. In this bipartite network, there are two types of nodes: ports and routes. The edges between the two types of nodes reflect the docking relationship between routes and ports.

[0062] Step 1.1: Represent the shipping network as a bipartite network G = (R, V, E), where R and V represent the sets of two types of nodes (i.e., routes and ports). E represents the edge set between the set R and the set V. If the edge between the route node and the port node exists in E, then the port is included in the route.

[0063] Step 1.2: The port network G′=(V,E′) is obtained by the unimodal projection of the network G. E′ represents the set of edges between ports. If two ports are included in at least one of the same routes, there is an undirected edge between the two ports. Route node j and port node i are connected by a link, and the weight of this edge is w ijrepresents the container flow that port i receives from route j. The total flow of the route is evenly distributed to all port pairs in the route, so w ij is defined as 2×t j / n j .

[0064] Step 2: Calculate the port node capacity in the shipping network.

[0065] Step 2.1: Initial load of port i (expressed by L i (0) indicates) is defined as the total flow obtained by the port from all service routes calling the port.

[0066]

[0067] Step 2.1: The flow capacity of port i (C i ) represents the maximum traffic load that the port can handle and is defined as:

[0068] C i =(1+α)L i (0)

[0069] Wherein, α>0 is a tolerance parameter, which indicates the additional load that the port can accommodate beyond the initial load. In this embodiment, α=0.4.

[0070] Step 3: Simulate the cascading failure of the port collection, including the redistribution of traffic within the shipping network and the update of the network structure.

[0071] Step 3.1: Simulate the initial failure of the port set. Remove the port nodes in the key port set from the shipping network.

[0072] Step 3.2: Route adjustment behavior. When a port fails, each service route that initially calls the port will independently choose one of the following three possible behaviors with a certain probability: wait at the failed port with a probability of p1; call an alternative port that is still functioning normally with a probability of p2; skip the failed port with a probability of 1-p1-p2. If all alternative ports of the failed port fail, there are only two options: wait at the failed port with a probability of p1; skip the failed port with a probability of 1-p1. This embodiment uses p1=0.2 and p2=0.25.

[0073] Step 3.3: Load redistribution. If a service route is waiting at a failed port, the failed port load obtained from the service route will not be diverted to any other port. If a service route skips a failed port, the traffic of the route will be evenly distributed to the ports on the route that are still functioning normally. If a route stops at an alternative port, one will be selected from all the alternative ports that are still functioning, and the cargo unloaded from the failed port on this route will be added to the selected alternative port. When a port fails, other ports in its country are usually used as alternative ports; among these alternative ports, ports that are geographically adjacent to the failed port and have a capacity not less than that of the failed port are usually given priority. Therefore, in the present invention, when determining the alternative port of a port, the domestic port is preferably selected as the alternative port. If a port is the only port in its country, it is considered that there is no alternative port for the port; secondly, when possible, an additional restriction is adopted: the alternative port should be located within 1,600KM of the port and its throughput capacity should reach 20% of the throughput capacity of the port.

[0074] Step 3.4: After each run of load redistribution, calculate the load of each port that survived the previous run. If the load of any port exceeds its capacity, the corresponding port will fail and trigger another round of load redistribution. The cascading process will terminate once the load of each remaining port is within its capacity or all ports in the initial shipping network have failed.

[0075] Step 4: Take the network cascading failure scale as the objective function and use equations (1) and (2) to construct the objective function:

[0076]

[0077] Constraint: |U|=k(2)

[0078] In the formula, U is a set of ports of size k, i.e., the decision variable, where k is set to k = 2, 3, 4, 5. x (U) represents the size of the cascading failure caused by set U in the x=10th simulation of the cascading failure model (i.e., the number of other failed ports).

[0079] Step 5: Based on the improved multi-population genetic evolutionary algorithm, the key nodes in the shipping network are identified to obtain the optimal failure set, and the port nodes in the set are used as the key node set in the shipping network; the details are as follows:

[0080] Step 5.1: Problem Coding:

[0081] Define the population size as S, the evolutionary generation as Gen, and the maximum evolutionary generation as l max=500, the number of subpopulations is Z=3, and the population crossover probability is P c =0.8, the population variation rate is P m =0.2, the population migration generation is M=30, and the population migration rate is P mr =0.2, the number of consecutive iterations without improvement is l=30, the simulated annealing cooling coefficient is q=0.98, the initial temperature is T1=100, and Gen=1, l=1 are initialized.

[0082] Definition: The present invention adopts integer coding to set a fixed ID for each port in the shipping network. The following three methods are used to obtain three initial subpopulations:

[0083] Subpopulation 1: In each community, the top 10% ports are selected according to the gateway index B and put into the gene pool as candidate genes; then each individual is randomly generated from the genes in the gene pool.

[0084] Subpopulation 2: Select ports with B ≥ 1.5 as gateway hub ports, group them according to their respective regions, and then calculate the sum of the degree of gateway hub ports in each region, D sum The method for generating each initial individual is as follows: First, use the roulette wheel selection method according to D sum The value selects a region, and then the same method is used to select different genes on individuals based on the degree of each port in the selected region.

[0085] Subpopulation three: All ports in the shipping network are included in the gene pool as candidate genes, and each initial chromosome is randomly generated from the gene pool.

[0086] The population of the generation in represents the Sth subpopulation of the Genth generation, represents the nth individual in the Sth subpopulation in the Genth generation, each of which represents a set of failed port nodes in the shipping network, and represents the kth gene in the nth individual and represents the kth failed port node.

[0087] Step 5.2: Use the elite-retaining binary tournament strategy to extract the subpopulation The parent is selected for subsequent reproduction. The offspring with the highest fitness in each sub-population will be retained. Then, a pair of offspring are randomly selected for comparison, and the offspring with higher fitness are added to the new sub-population. Until the number of individuals in the subpopulation reaches P n =150.

[0088] Step 5.3: For each subpopulation Perform a crossover operation, using a two-point crossover strategy with a crossover probability of P c Two crossover points are randomly generated on two pairs of parental chromosomes, and then the two chromosome segments at the crossover points are exchanged. After the chromosomes are crossed, there may be two identical gene values ​​on the chromosomes. The present invention is based on the replacement method of gene importance ranking, and randomly selects non-repeating genes from the genes with the highest gene importance values ​​to replace them, thereby obtaining a sub-population after crossing.

[0089] Step 5.4: According to P m Sure Whether each individual in the population mutates or not, if so, a node is randomly selected from the candidate set of port nodes of the subpopulation to replace it, so as to obtain a mutated subpopulation

[0090] Step 5.5: Count the number of times the gene appears in the chromosome in each sub-population and use this as the importance value of the gene.

[0091] Step 5.6: According to The corresponding shipping network node set is used to simulate the cascading failure of the shipping network.

[0092] Step 5.7: Calculate according to formula (1) The fitness value F(U) of .

[0093] Step 5.8: Calculate the mutated subpopulation The fitness value of the individuals in the subpopulation is calculated, and the average fitness value f of each subpopulation is calculated. avg .

[0094] Step 5.9: Set the fitness value f that is greater than the average fitness value of the population in which you are located avg The individuals are stored in the elite individual set Γ, Γ = {Γ1, Γ1, Γ1, …, Γ n}, where Γ n Represents the set of elite individuals of the nth subpopulation.

[0095] Step 5.10: Calculation The fitness value of the new individual is related to the f of the subpopulation to which it belongs. avg If it is greater than, keep the individual. If it is less than, remove it with probability p Gen Keep the offspring and with probability 1-p Gen A random replacement is selected from the elite individuals in the previous round, and finally A is formed. Gen+1 , and save the individual with the largest fitness value as where p Gen The calculation formula is as follows:

[0096] pGen =exp(ΔE / T Gen )

[0097] In the formula, ΔE is the average fitness difference between the previous generation and the next generation, T Gen is the temperature of the first generation.

[0098] Step 5.11: Update the temperature T. The update formula is as follows:

[0099] T Gen+1 =q×T Gen

[0100] Step 5.12: Update the number of iterations Gen = Gen + 1. Compare Is it greater than If it is greater than, then l=1; if it is less than, then l=l+1.

[0101] Step 5.13: Termination condition: When the maximum number of iterations (l max =500) or if there is no improvement in the solution after l = 30 consecutive iterations, the algorithm stops running.

[0102] In order to evaluate the effectiveness of the algorithm proposed in this invention in determining the most critical port set and the top 10 critical port sets, it is compared with a greedy method, four metric-based methods and an unimproved multi-population genetic algorithm. The specific comparison results are shown in Tables 1 and 2 below:

[0103] Table 1 - Comparison of cascading failure scales of the most critical port sets of each algorithm

[0104]

[0105]

[0106] Table 2- Comparison of cascading failure scales of top 10 key port sets of each algorithm

[0107]

[0108] As can be seen from Table 1, when k=2, the performance of the algorithm of the present invention is significantly better than other algorithms. Other algorithms ignore the importance of key ports in local areas and cannot obtain the key port combination under k=2 within the effective time. It can be seen that this algorithm has excellent performance under each k value. When k≥3, the two algorithms based on load and degree centrality are consistent with the performance of the algorithm of the present invention, and both return the same set of ports. In addition, as shown in Table 2, for the identification of the top 10 key port sets, at each k value, the algorithm of the present invention performs better than all compared algorithms. In summary, it can be seen that the algorithm proposed in the present invention is superior in identifying the key port combination of the shipping network.

Claims

1. A method for identifying key node sets under cascading failure of shipping networks based on multi-population genetic algorithm, characterized by: Here are the steps: Step 1: Modeling the shipping network. Based on the container liner route data, a bipartite network is used to describe the coupling relationship between routes and ports. In the bipartite network, there are two types of nodes: ports and routes. The edges between the two types of nodes reflect the relationship between routes and ports. Step 2: Calculate the flow capacity of port nodes in the shipping network; Step 3: Simulate the cascading failure of the port set, including redistribution of traffic within the shipping network and updating of the network structure; Step 4: Take the network cascading failure scale as the fitness value, that is, the objective function F(U), and use equations (1) and (2) to construct the objective function: Constraint: |U|=k(2) where U is a set of ports of size k, i.e., the decision variable; m represents the total number of simulations, S x (U) represents the size of the cascading failure caused by set U in the xth simulation of the cascading failure model, i.e., the number of other failure ports; Step 5: Based on the improved multi-population genetic evolutionary algorithm, the key nodes in the shipping network are identified to obtain the optimal failure set, and the port nodes in the set are used as the key node set in the shipping network; The step 1 is specifically as follows: Step 1.1: Represent the shipping network as a bipartite network G = (R, V, E), where R and V represent the set of route nodes and port nodes respectively; E represents the edge set between set R and set V. If the edge between the route node and the port node exists in E, then the port is included in this route; Step 1.2: The port network G′=(V,E′) is obtained by the unimodal projection of the network G; E′ represents the set of edges between ports. If two ports are included in at least one of the same routes, there is an undirected edge between the two ports; route node j and port node i are connected by a link, and the weight of this edge is w ij represents the container flow obtained by port i from route j; the total flow of the route is evenly distributed to all port pairs in the route, so w ij is defined as 2×t j / n j , t j is the total cargo volume on a route, n j is the number of ports in a route; The step 2 is specifically as follows: Step 2.1: Initial load L at port i i (0) is defined as the total traffic received by the port from all service routes calling the port; In the formula, R represents all routes; Step 2.1: Flow capacity C of port i i It represents the maximum traffic load that the port can handle and is defined as: C i =(1+α)L i (0) Among them, α>0 is the tolerance parameter, which indicates the additional load that the port can accommodate beyond the initial load; The step 3 is specifically as follows: Step 3.1: Simulate the initial failure of the port set; remove the port nodes in the key port set from the shipping network; Step 3.2: Route adjustment behavior; When a port fails, each service route that originally calls the port will independently choose one of the following three possible behaviors with a certain probability: wait at the failed port with probability p1; call an alternative port that is still functioning normally with probability p2; skip the failed port with probability 1-p1-p2; If all alternative ports of the failed port fail, there are only two options: wait at the failed port with probability p1; skip the failed port with probability 1-p1; Step 3.3: Load redistribution; if a service route is waiting at a failed port, the failed port load obtained from the service route will not be diverted to any other port; if a service route skips a failed port, the traffic of the route will be evenly distributed to the ports on the route that are still operating normally; if a route stops at an alternative port, one will be selected from all the alternative ports that are still in operation, and the cargo unloaded from the failed port on this route will be added to the selected alternative port; when a port fails, other ports in its location are usually used as alternative ports; among these alternative ports, ports that are geographically adjacent to the failed port and have a capacity not less than that of the failed port are usually given priority; therefore, when determining the alternative port of a port, the port within its location is preferably selected as the alternative port; if a port is the only port in its location, it is considered that there is no alternative port for the port; secondly, when possible, an additional restriction is adopted: the alternative port should be located within a certain range from the port and its throughput capacity cannot be much lower than that of the original port; Step 3.4: After each load redistribution run, the loads of the remaining ports are calculated; if the load of any port exceeds its capacity, the corresponding port will fail and trigger another round of load redistribution; once the load of each remaining port is within its capacity or all ports in the initial shipping network fail, the cascading process will terminate; The step 5 is specifically as follows: Step 5.1: Problem Coding: Define the population size as S, the evolutionary generation as Gen, and the maximum evolutionary generation as l max , the number of subpopulations is Z, and the probability of population crossover is P c , the population mutation rate is P m , the population migration generation number is M, and the population migration rate is P mr , the number of consecutive iterations without improvement is l, the simulated annealing cooling coefficient is q, the initial temperature is T1, and Gen, l=1 and Z are initialized; Integer coding is used to set a fixed ID for each port in the shipping network; k port nodes are randomly or roulette-wheel-selected from the candidate set of port nodes in the shipping network as the genes of each individual in the population, and the Gen-th population set of the population is obtained. in represents the Sth subpopulation of the Genth generation, represents the nth individual in the Sth subpopulation in the Genth generation, each of which represents a set of failed port nodes in the shipping network, and represents the kth gene in the nth individual, and represents the kth failed port node; The specific method of generating the port node candidate set is as follows: Method 1: In each community, select the top-ranked ports according to the gateway index B and put them into the port node candidate set as candidate genes; the specific calculation method of B is as follows: Among them, port i is a member of community T, m iT Indicates the number of connections between port i and other ports outside T, m T and σ mT They represent the mean and standard deviation of the number of external connections of all ports within T, respectively; Method 2: Select ports with B ≥ 1.5 as gateway hub ports and calculate the sum of the degrees D of all gateway hub ports in the region to which they belong. sum ;D sum The larger the area, the easier it is to be selected, and the portal hub port node with a larger degree is also more likely to be selected as a candidate node; Method 3: All ports in the shipping network are included as candidate genes into the port node candidate set; Step 5.2: Use the elite-retaining binary tournament strategy to extract the subpopulation The parents are selected for subsequent reproduction; the offspring with the highest fitness in each sub-population will be retained; then, a pair of offspring are randomly selected for comparison, and the offspring with higher fitness are added to the new sub-population Until the number of individuals in the subpopulation reaches P n ; Step 5.3: For each subpopulation Perform a crossover operation, using a two-point crossover strategy with a crossover probability of P c ; Two crossover points are randomly generated on the two pairs of parental chromosomes, and then the two chromosome segments at the crossover points are exchanged; after the chromosomes are crossed, there may be two identical gene values ​​on the chromosomes. Based on the replacement method of gene importance ranking, a non-repeating gene is randomly selected from the genes with the highest gene importance values ​​to replace them, thereby obtaining a sub-population after crossing Step 5.4: According to P m Sure Whether each individual in the population mutates or not, if so, a node is randomly selected from the candidate set of port nodes of the subpopulation to replace it, so as to obtain a mutated subpopulation Step 5.5: Count the number of times the gene appears in the chromosome in each subpopulation, and use this as the importance value of the gene; Step 5.6: According to The corresponding shipping network node set performs cascading failure simulation on the shipping network; Step 5.7: Calculate according to formula (1) The fitness value F(U); Step 5.8: Calculate the mutated subpopulation The fitness value of the individuals in the subpopulation is calculated, and the average fitness value f of each subpopulation is calculated. avg ; Step 5.9: Set the fitness value f that is greater than the average fitness value of the population in which you are located avg The individuals are stored in the elite individual set Γ, Γ = {Γ1, T1, Γ1, ..., Γ n }, where Γ n Represents the elite individual set of the nth subpopulation; Step 5.10: Calculation The fitness value of the new individual is related to the f of the subpopulation to which it belongs. avg If it is greater than, keep the individual; if it is less than, remove it with probability p Gen Keep the offspring and with probability 1-p Gen A random selection is made from the elite individuals in the previous round to replace them, and finally the updated population A is formed. Gen+1 , and save the individual with the largest fitness value as where p Gen The calculation formula is as follows: p Gen =exp(ΔE / T Gen ) In the formula, Δe is the average fitness difference between the previous generation and the next generation, T Gen is the temperature of the first generation; Step 5.11: Update the temperature T. The update formula is as follows: T Gen+1 =q×T Gen Step 5.12: Update the number of iterations Gen = Gen + 1; compare Is it greater than If it is greater than, then l = 1, if it is less than, then l = l + 1; Step 5.13: Individual migration between subpopulations. Calculate whether the remainder of Gen divided by M is 0. If it is 0, use the fully connected topology to replace the inferior offspring and identify the excellent offspring in each subpopulation. When the predetermined number of iterations M is reached, the previous subpopulation will transfer its excellent offspring to the next subpopulation to replace the inferior offspring, so as to achieve the sharing of the superior offspring between subpopulations and form a ring-shaped subpopulation migration pattern. If it is not 0, no individual migration will be performed. Step 5.14: Termination condition: When the maximum number of iterations l is reached max Or when the solution has not been improved after l consecutive iterations, the algorithm will stop running and output the optimal individual as the key node set.

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