Multi-objective optimization method for hydrogen refueling station based on multi-agent collaboration and risk quantification

Abstract

The invention relates to the field of hydrogen energy industry infrastructure planning, in particular to a hydrogen refueling station multi-objective optimization method based on multi-agent collaboration and risk quantification. The method can effectively solve the problems of economy, safety and multi-subject collaboration in hydrogen refueling station site selection, site selection optimization is realized through risk dynamic quantification and multi-objective decision, and the method comprises the following specific steps: integrating hydrogen source supply, transportation, construction operation and user demand data, and determining the site selection of the hydrogen refueling station on the basis of leakage scenes of hydrogen storage containers and transportation equipment; leakage diffusion is simulated, the risk radius is calculated, the risk weight is corrected through historical data to obtain the leakage radius, risk quantification is achieved in combination with regional resident coefficient innovation, a coupling economic cost and risk value objective function is constructed, and a multi-objective optimization model is established; and solving by adopting a multi-target whale optimization algorithm to obtain a site selection scheme balancing economical efficiency and safety. The method can significantly improve the planning rationality of the hydrogen refueling station, promotes the economic and safe layout of hydrogen energy facilities, and is suitable for urban low-carbon traffic development.

Description

Technical Field

[0001] The present invention relates to the field of hydrogen energy industry infrastructure planning, and specifically to a multi-objective optimization method for urban hydrogen refueling stations based on multi-agent collaboration and risk quantification. Background Art

[0002] With the rapid development of hydrogen fuel cell vehicles, the planning and layout of hydrogen refueling stations, as critical infrastructure, has become a core issue for the large-scale application of the hydrogen energy industry. Traditional hydrogen refueling station site selection methods often focus on optimizing a single objective, such as minimizing economic costs or maximizing geographic coverage. They lack systematic quantification of multi-dimensional risks and fail to fully integrate the collaborative needs of multiple stakeholders, including government regulation, operator profitability, and public safety demands. Due to the limitations of existing technologies, site selection plans often face an imbalance between economic efficiency, safety, and social acceptability, hindering the efficient deployment of hydrogen energy infrastructure.

[0003] At the risk quantification level, existing studies mostly use static risk assessment models to calculate safety distances based on fixed leakage scenarios and empirical parameters, which makes it difficult to reflect the impact of complex environmental variables (such as meteorological conditions and dynamic changes in population density) on risk propagation. For example, the risk scopes of hydrogen storage containers and transportation equipment under different leakage modes (such as jet fire and explosion) are significantly different, and traditional methods do not build a dynamic coupling model of leakage scenarios and risk diffusion, resulting in insufficient risk assessment accuracy. In addition, hydrogen energy infrastructure planning involves multivariate data such as hydrogen source supply, transportation routes, and user distribution. The existing models have weak processing capabilities for the fusion of multi-source heterogeneous data, which restricts the reliability of risk quantification results.

[0004] In terms of multi-objective collaborative optimization, current methods mostly use linear weighting or hierarchical optimization strategies, which make it difficult to effectively balance economic costs, risk control, and conflicts of interest among multiple subjects. There is a nonlinear contradiction between the safety threshold required by government regulations, the return on investment pursued by operators, and the convenience of hydrogen refueling that users care about. Traditional optimization models are prone to falling into local optimal solutions due to the lack of dynamic weight adjustment mechanisms and multi-criteria decision-making frameworks. At the same time, the coupling relationship between hydrogen station capacity constraints, hydrogen source production capacity limitations, and the spatial distribution of user demand has not been fully modeled, further weakening the engineering applicability of the planning scheme. Therefore, it is urgent to construct an optimization method that integrates dynamic risk quantification and multi-subject collaborative decision-making to improve the scientific nature and feasibility of urban hydrogen station planning. Summary of the Invention

[0005] In view of the problems of insufficient economy, safety and multi-agent interest coordination in the existing hydrogen refueling station site selection, a multi-objective optimization method for urban hydrogen refueling stations based on multi-agent collaboration and risk quantification is proposed, which is characterized by including the following steps:

[0006] S1: Determine the decision variables for optimizing the site selection of hydrogen refueling stations and obtain the basic data for the site selection of hydrogen refueling stations in the target area;

[0007] The basic data for hydrogen refueling station site selection in the target area includes the annual operating days of the hydrogen refueling station, daily hydrogen production capacity, planned number of hydrogen refueling stations, hydrogen risk data, hydrogen price data, hydrogen transportation data, hydrogen refueling station construction data, and user hydrogen refueling data;

[0008] The hydrogen risk data includes the storage pressure, storage volume and operating temperature of hydrogen storage containers and transportation equipment, wind speed, regional average temperature, regional average humidity, regional resident coefficient and regional support for hydrogen transportation equipment;

[0009] The hydrogen price data includes the price of hydrogen purchased from the hydrogen source, the cost of hydrogen production within the station, and the price of hydrogen sold at the hydrogen refueling station;

[0010] The hydrogen transportation data includes the distance from the hydrogen source to the hydrogen refueling station node, the transportation equipment rental price, the hydrogen transportation unit price, and the hydrogen transportation loss coefficient;

[0011] The construction and operation data of the hydrogen refueling station include the construction cost of the pipeline unit of the hydrogen refueling station purchased from outside the station, the construction cost of the booster unit of the hydrogen refueling station purchased from outside the station, the construction cost of the filling unit of the hydrogen refueling station purchased from outside the station, the infrastructure construction cost of the hydrogen refueling station purchased from outside the station, the construction cost of the pipeline unit of the hydrogen refueling station produced on the station, the construction cost of the booster unit of the hydrogen refueling station produced on the station, the construction cost of the filling unit of the hydrogen refueling station produced on the station, the infrastructure construction cost of the hydrogen refueling station produced on the station, the construction cost of the hydrogen storage bottle group, the construction cost of the high-pressure hydrogen storage tank, the depreciation rate of the hydrogen refueling station, the maximum capacity of the hydrogen refueling station produced on the station, the maximum capacity of the hydrogen storage bottle group and the maximum capacity of the high-pressure hydrogen storage tank;

[0012] The user hydrogen refueling data includes the unit hydrogen consumption of the user's vehicle, the maximum acceptable distance of the user and the user's per capita hydrogen refueling demand;

[0013] S2: Considering four types of leakage consequences of hydrogen storage containers and transportation equipment at hydrogen refueling stations, the Martinsen time-variable model is used to simulate the leakage diffusion process to obtain the maximum risk radius of each type of leakage consequence;

[0014] The hydrogen storage container of the hydrogen refueling station includes a hydrogen storage bottle group and a high-pressure hydrogen storage tank;

[0015] The transportation equipment includes a hydrogen long tube trailer and a liquid hydrogen tanker;

[0016] The four types of leakage consequences include jet fire, flash fire, fireball, and explosion;

[0017] S3: Construct a leakage radius weight optimization model, use historical leakage data to train a neural network model, and determine the leakage radius of hydrogen storage containers and hydrogen transportation equipment at hydrogen refueling stations through leakage radius weight correction;

[0018] S4: establishing a multi-objective collaborative optimization multi-objective function, wherein the multi-objective function includes a minimum total economic cost objective function and a minimum total risk quantization value objective function;

[0019] S5: Set constraints and, combined with the objective function, construct a multi-objective optimization model for urban hydrogen refueling stations based on multi-agent collaboration and risk quantification;

[0020] The constraints include hydrogen source capacity constraints, hydrogen refueling station type constraints, hydrogen refueling station quantity constraints, hydrogen refueling station capacity constraints, user distance constraints, user affiliation constraints, and hydrogen refueling station construction cost constraints;

[0021] S6: The model is solved using a multi-objective whale optimization algorithm to generate a Pareto optimal solution set, and a comprehensive optimal hydrogen station site selection plan is output based on preset priorities.

[0022] Furthermore, it is characterized in that the decision variables described in step S1 include hydrogen station establishment variables, hydrogen station type variables, the number of hydrogen storage bottle groups, the number of high-pressure hydrogen storage tanks, hydrogen source purchase variables for off-site hydrogen supply stations, hydrogen purchase volume for off-site hydrogen supply stations, and hydrogen production volume for on-site hydrogen production stations.

[0023] Furthermore, it is characterized in that the specific steps of step S3 are:

[0024] S301: Construct a risk radius weight optimization model. The objective function of the risk radius weight optimization model is shown as follows:

[0025]

[0026] Where, is the leakage radius error ratio; R h is the leakage radius of historical accidents; α is the leakage radius weight of jet fire consequences; R1 is the maximum risk radius of jet fire consequences; β is the leakage radius weight of flash fire consequences; R2 is the maximum risk radius of flash fire consequences; is the weight of the leakage radius of fireball consequences; R3 is the maximum risk radius of fireball consequences; θ is the weight of the leakage radius of explosion consequences; R4 is the maximum risk radius of explosion consequences;

[0027] The constraint conditions of the risk radius weight optimization model are as follows:

[0028]

[0029] α>0

[0030] β>0

[0031]

[0032] θ>0

[0033] S302: Importing historical accident data into the Martinsen time-variable model to simulate the leakage diffusion process and obtain the maximum risk radius of jet fire, flash fire, fireball and explosion leakage consequences;

[0034] S303: Dividing the historical leakage data into a training subset and a validation subset according to a preset ratio, iteratively optimizing the parameters of the neural network model using the training subset, and completing the training when the model prediction error reaches a preset convergence condition;

[0035] S304: Input the verification subset into a fully trained neural network model, and output the leakage radius weight for subsequent calculation of the leakage radius.

[0036] Furthermore, it is characterized in that the minimum total economic cost objective function in step S4 includes hydrogen purchase cost, hydrogen storage and transportation cost, hydrogen station construction and operation cost and user hydrogenation cost, and the objective function expression is as follows:

[0037] minF ec =F pr +F tr +F st +F user

[0038] Where, F ec is the total economic cost; F pr F is the purchase cost of hydrogen; tr is the storage and transportation cost of hydrogen; F st F is the construction cost of hydrogen refueling station; user Hydrogen refueling costs for users;

[0039] The hydrogen purchase cost is expressed as follows:

[0040]

[0041] Where, T is the annual operating days of the hydrogen refueling station; μ i is the hydrogen station construction variable. If a hydrogen station is built at node i, the variable value is 1, otherwise it is 0; i is the hydrogen station type variable. If the hydrogen station type at node i is an off-site hydrogen supply station, the variable value is 1, otherwise it is 0; Q i,j The amount of hydrogen purchased by the off-site hydrogen supply and refueling station; C j,pr The cost of purchasing hydrogen for the off-site hydrogen supply and refueling station; Q i C is the hydrogen production of the hydrogen production and refueling station; in-pr The cost of hydrogen production and refueling station on site;

[0042] The hydrogen storage and transportation cost expression is as follows:

[0043]

[0044] Where a is the rental fee of hydrogen transportation equipment; b is the unit price of hydrogen transportation equipment; L i,j is the distance between the hydrogen refueling station and the hydrogen source; c is the hydrogen storage loss coefficient;

[0045] The construction and operation cost of the hydrogen refueling station is expressed as follows:

[0046]

[0047] Where, τ is the average depreciation rate of the hydrogen refueling station; γ is the depreciation period of the hydrogen refueling station; The construction cost of hydrogen refueling stations for off-site hydrogen supply; The construction cost of the hydrogen production and refueling station on the station; The capacity of the hydrogen refueling station for off-site hydrogen supply; is the capacity of hydrogen production and refueling station in the station; P inj the cost of filling hydrogen refueling stations; The daily maintenance cost of the off-site hydrogen supply and refueling station; The daily maintenance cost of the hydrogen production and refueling station on site;

[0048] The user hydrogenation cost expression is as follows:

[0049]

[0050] Where, δ i,k User selection variable. If the user chooses to refuel at a hydrogen refueling station, the variable value is 1, otherwise it is 0. Q is the unit hydrogen consumption of user k’s vehicle; k is the per capita hydrogenation demand of regional users; C sal The price of hydrogen sold at hydrogen refueling stations;

[0051] The minimum total risk quantitative value objective function determines the leakage risk area of ​​the hydrogen storage container and transportation equipment through the leakage radius, and calculates the number of people exposed to the consequences as the quantitative value of the hydrogen station leakage risk by combining the regional resident coefficient. The objective function expression is as follows:

[0052]

[0053] Where, ψ l is the resident coefficient of area l; R st is the leakage radius of the hydrogen storage container; R tr is the leakage radius of the hydrogen storage container; π is the pi.

[0054] Furthermore, it is characterized in that the hydrogen source capacity constraint expression in step S5 is as follows:

[0055]

[0056] Where G j The daily production capacity of hydrogen source;

[0057] The hydrogen station type constraint expression is as follows:

[0058] φ i ≤μ i

[0059] β i,j ≤φ i

[0060] Where, β i,j Purchase variables for hydrogen sources for off-site hydrogen supply and refueling stations;

[0061] The hydrogen refueling station quantity constraint expression is as follows:

[0062]

[0063] Where, O l Plan the number of hydrogen refueling stations in area l;

[0064] The user selection constraint expression is as follows:

[0065]

[0066] The user membership constraint expression is as follows:

[0067] δ i,k ≤μ i

[0068]

[0069] The hydrogen station capacity constraint expression is as follows:

[0070]

[0071] Where, The maximum capacity of the hydrogen storage cylinder group; The number of hydrogen storage cylinders purchased from the station; is the maximum capacity of the high-pressure hydrogen storage tank; The number of high-pressure hydrogen storage tanks for hydrogen refueling stations purchased from outside the station; The maximum capacity of the hydrogen refueling station for off-site hydrogen purchases; The number of hydrogen storage cylinders in the hydrogen production and refueling station; The maximum capacity of the hydrogen production and refueling station within the station; The number of high-pressure hydrogen storage tanks in the hydrogen production and refueling station;

[0072] The construction cost constraint of the hydrogen refueling station includes the construction cost constraint of the hydrogen refueling station purchased from outside the station and the construction cost constraint of the hydrogen refueling station produced on the station. The construction cost constraint of the hydrogen refueling station purchased from outside the station is expressed as follows:

[0073]

[0074] Where, The construction cost of the pipeline unit for the hydrogen refueling station for purchasing hydrogen from outside the station; The construction cost of the booster unit for the hydrogen refueling station purchased from outside the station; The construction cost of the hydrogen filling unit for the hydrogen refueling station purchased from outside the station; The cost of building the infrastructure for the hydrogen refueling station for off-site hydrogen purchases;

[0075] The cost constraint expression of the on-site hydrogen production and refueling station construction is as follows:

[0076]

[0077] Where, The construction cost of the pipeline unit for hydrogen production and refueling station within the station; The construction cost of the hydrogen production and refueling station booster unit on the station; The construction cost of the hydrogen refueling unit for the on-site hydrogen production station; The construction cost of the hydrogen production unit of the hydrogen production and refueling station on the station; The cost of infrastructure construction for hydrogen production and refueling stations within the station.

[0078] Furthermore, it is characterized in that the specific steps of step S6 include:

[0079] S601: Set the parameters of the multi-objective whale optimization algorithm, which include the whale population size W, the number of iterations t, and the maximum number of iterations T. Generate an initial solution around the decision variables in the solution space as the population individual x t , and record the initial position X(t) of the whale population;

[0080] S602: Calculate the multi-objective function value (F ec ,F risk ), perform non-dominated sorting, calculate the crowding distance, and screen the best whale individuals in the population The calculation formula for congestion distance is as follows:

[0081]

[0082] Where, d x is the crowding distance of the xth individual; M is the number of objective functions; is the target value of the individual adjacent to the right of the x-th individual on the objective function m; is the target value of the adjacent individual to the left of the x-th individual on the objective function m; The maximum value of the objective function m; Minimum value of objective function m;

[0083] S603: Update the whale direction coefficient a1 and probability coefficient k, and calculate the whale linear coefficient variable A and the whale mutation coefficient variable C. The calculation formula is as follows:

[0084]

[0085] Where a1 is the whale direction coefficient; A is the whale iteration coefficient variable; C is the whale mutation coefficient variable; r1 and r2 are both random numbers in the range of (0,1);

[0086] S604: When the probability coefficient k is less than 0.5 and |A|<1, the random search behavior mechanism is used to update the population individuals. The update formula is as follows:

[0087] D r =|C×X r (t)-X(t)|

[0088] X(t+1)=X r (t)-A×D r

[0089] Where D r is the initial distance between the random whale individual and the prey; X(t) r is the position of the random whale population at the tth iteration; X(t+1) is the position of the whale population at the t+1th iteration;

[0090] S605: When the probability coefficient k is less than 0.5 and |A| ≥ 1, the prey encirclement behavior mechanism is used to update the population individuals. The update formula is as follows:

[0091] D1=|C×X(t) best -X(t)|

[0092] X(t+1)=X(t) best -A×D1

[0093] Where D1 is the initial distance between the whale and its prey; X(t) best is the optimal whale population position at the tth iteration;

[0094] S606: When the probability coefficient k is greater than 0.5, the spiral attack behavior mechanism is used to update the population individuals. The update formula is as follows:

[0095] D2=|X(t) best -X(t)|

[0096] X(t+1)=D2×e bl ×cos(2πl)+X(t) best

[0097] Where D2 is the updated distance between the individual whale and its prey; e bl is the spiral shape constant;

[0098] S607: Calculate and update the multi-objective function value (F ec ,F risk ), perform non-dominated sorting, calculate the crowding distance, and update the optimal whale individual in the population

[0099] S608: Determine whether the number of iterations reaches the maximum number of iterations. If so, exit the loop and output the optimal solution value and the location information of the optimal whale individual. Otherwise, return to S602. BRIEF DESCRIPTION OF THE DRAWINGS

[0100] Figure 1 Schematic diagram of the process of the multi-objective optimization method for urban hydrogen refueling stations based on multi-agent collaboration and risk quantification of the present invention;

[0101] Figure 2 A flowchart of the multi-objective whale optimization algorithm applicable to the present invention;

[0102] Figure 3 This is a node distribution map of a certain city in China according to a specific embodiment of the present invention;

[0103] Figure 4 This is a diagram of a site selection plan for a hydrogen refueling station in a certain city in China, which is a specific embodiment of the present invention. DETAILED DESCRIPTION

[0104] In order to enable those skilled in the art to better understand the technical solution of the present invention and to be able to implement it, the present invention is described in detail below with reference to the accompanying drawings and specific embodiments. The following embodiments are only used to more clearly illustrate the technical solution of the present invention and are not intended to limit the scope of protection of the present invention.

[0105] The present invention provides a multi-objective optimization method for urban hydrogen refueling stations based on multi-agent collaboration and risk quantification, specifically Figure 1 As shown, the following steps are included:

[0106] S1: Determine the decision variables for optimizing the site selection of hydrogen refueling stations and obtain the basic data for the site selection of hydrogen refueling stations in the target area;

[0107] The basic data for hydrogen refueling station site selection in the target area includes the annual operating days of the hydrogen refueling station, daily hydrogen production capacity, planned number of hydrogen refueling stations, hydrogen risk data, hydrogen price data, hydrogen transportation data, hydrogen refueling station construction data, and user hydrogen refueling data;

[0108] The hydrogen risk data includes the storage pressure, storage volume and operating temperature of hydrogen storage containers and transportation equipment, wind speed, regional average temperature, regional average humidity, regional resident coefficient and regional support for hydrogen transportation equipment;

[0109] The hydrogen price data includes the price of hydrogen purchased from the hydrogen source, the cost of hydrogen production within the station, and the price of hydrogen sold at the hydrogen refueling station;

[0110] The hydrogen transportation data includes the distance from the hydrogen source to the hydrogen refueling station node, the transportation equipment rental price, the hydrogen transportation unit price, and the hydrogen transportation loss coefficient;

[0111] The construction and operation data of the hydrogen refueling station include the construction cost of the pipeline unit of the hydrogen refueling station purchased from outside the station, the construction cost of the booster unit of the hydrogen refueling station purchased from outside the station, the construction cost of the filling unit of the hydrogen refueling station purchased from outside the station, the infrastructure construction cost of the hydrogen refueling station purchased from outside the station, the construction cost of the pipeline unit of the hydrogen refueling station produced on the station, the construction cost of the booster unit of the hydrogen refueling station produced on the station, the construction cost of the filling unit of the hydrogen refueling station produced on the station, the infrastructure construction cost of the hydrogen refueling station produced on the station, the construction cost of the hydrogen storage bottle group, the construction cost of the high-pressure hydrogen storage tank, the depreciation rate of the hydrogen refueling station, the maximum capacity of the hydrogen refueling station produced on the station, the maximum capacity of the hydrogen storage bottle group and the maximum capacity of the high-pressure hydrogen storage tank;

[0112] The user hydrogen refueling data includes the unit hydrogen consumption of the user's vehicle, the maximum acceptable distance of the user and the user's per capita hydrogen refueling demand;

[0113] S2: Considering four types of leakage consequences of hydrogen storage containers and transportation equipment at hydrogen refueling stations, the Martinsen time-variable model is used to simulate the leakage diffusion process to obtain the maximum risk radius of each type of leakage consequence;

[0114] The hydrogen storage container of the hydrogen refueling station includes a hydrogen storage bottle group and a high-pressure hydrogen storage tank;

[0115] The transportation equipment includes a hydrogen long tube trailer and a liquid hydrogen tanker;

[0116] The four types of leakage consequences include jet fire, flash fire, fireball, and explosion;

[0117] S3: Construct a leakage radius weight optimization model, use historical leakage data to train a neural network model, and determine the leakage radius of hydrogen storage containers and hydrogen transportation equipment at hydrogen refueling stations through leakage radius weight correction;

[0118] S4: establishing a multi-objective collaborative optimization multi-objective function, wherein the multi-objective function includes a minimum total economic cost objective function and a minimum total risk quantization value objective function;

[0119] S5: Set constraints and, combined with the objective function, construct a multi-objective optimization model for urban hydrogen refueling stations based on multi-agent collaboration and risk quantification;

[0120] The constraints include hydrogen source capacity constraints, hydrogen refueling station type constraints, hydrogen refueling station quantity constraints, hydrogen refueling station capacity constraints, user distance constraints, user affiliation constraints, and hydrogen refueling station construction cost constraints;

[0121] S6: The model is solved using a multi-objective whale optimization algorithm to generate a Pareto optimal solution set, and a comprehensive optimal hydrogen station site selection plan is output based on preset priorities.

[0122] In one embodiment, it is characterized in that the decision variables described in step S1 include hydrogen station establishment variables, hydrogen station type variables, the number of hydrogen storage bottle groups, the number of high-pressure hydrogen storage tanks, hydrogen source purchase variables for off-site hydrogen supply stations, hydrogen purchase volume for off-site hydrogen supply stations, and hydrogen production volume for on-site hydrogen production stations.

[0123] In one embodiment, it is characterized in that the specific steps of step S3 are:

[0124] S301: Construct a risk radius weight optimization model. The objective function of the risk radius weight optimization model is shown as follows:

[0125]

[0126] Where, is the leakage radius error ratio; R h is the leakage radius of historical accidents; α is the leakage radius weight of jet fire consequences; R1 is the maximum risk radius of jet fire consequences; β is the leakage radius weight of flash fire consequences; R2 is the maximum risk radius of flash fire consequences; is the weight of the leakage radius of fireball consequences; R3 is the maximum risk radius of fireball consequences; θ is the weight of the leakage radius of explosion consequences; R4 is the maximum risk radius of explosion consequences;

[0127] The constraint conditions of the risk radius weight optimization model are as follows:

[0128]

[0129] α>0

[0130] β>0

[0131]

[0132] θ>0

[0133] S302: Importing historical accident data into the Martinsen time-variable model to simulate the leakage diffusion process and obtain the maximum risk radius of jet fire, flash fire, fireball and explosion leakage consequences;

[0134] S303: Dividing the historical leakage data into a training subset and a validation subset according to a preset ratio, iteratively optimizing the parameters of the neural network model using the training subset, and completing the training when the model prediction error reaches a preset convergence condition;

[0135] S304: Input the verification subset into a fully trained neural network model, and output the leakage radius weight for subsequent calculation of the leakage radius.

[0136] In one embodiment, it is characterized in that the minimum total economic cost objective function in step S4 includes hydrogen purchase cost, hydrogen storage and transportation cost, hydrogen station construction and operation cost, and user hydrogenation cost, and the objective function expression is as follows:

[0137] minF ec =F pr +F tr +F st +F user

[0138] Where, F ec is the total economic cost; F pr F is the purchase cost of hydrogen; tr is the storage and transportation cost of hydrogen; F st F is the construction cost of hydrogen refueling station; user Hydrogen refueling costs for users;

[0139] The hydrogen purchase cost is expressed as follows:

[0140]

[0141] Where, T is the annual operating days of the hydrogen refueling station; μ i is the hydrogen station construction variable. If a hydrogen station is built at node i, the variable value is 1, otherwise it is 0; i is the hydrogen station type variable. If the hydrogen station type at node i is an off-site hydrogen supply station, the variable value is 1, otherwise it is 0; Q i,j The amount of hydrogen purchased by the off-site hydrogen supply and refueling station; C j,pr The cost of purchasing hydrogen for the off-site hydrogen supply and refueling station; Q i C is the hydrogen production of the hydrogen production and refueling station; in-pr The cost of hydrogen production and refueling station on site;

[0142] The hydrogen storage and transportation cost expression is as follows:

[0143]

[0144] Where a is the rental fee of hydrogen transportation equipment; b is the unit price of hydrogen transportation equipment; L i,j is the distance between the hydrogen refueling station and the hydrogen source; c is the hydrogen storage loss coefficient;

[0145] The construction and operation cost of the hydrogen refueling station is expressed as follows:

[0146]

[0147] Where, τ is the average depreciation rate of the hydrogen refueling station; γ is the depreciation period of the hydrogen refueling station; The construction cost of hydrogen refueling stations for off-site hydrogen supply; The construction cost of the hydrogen production and refueling station on the station; The capacity of the hydrogen refueling station for off-site hydrogen supply; is the capacity of hydrogen production and refueling station in the station; P inj the cost of filling hydrogen refueling stations; The daily maintenance cost of the off-site hydrogen supply and refueling station; The daily maintenance cost of the hydrogen production and refueling station on site;

[0148] The user hydrogenation cost expression is as follows:

[0149]

[0150] Where, δ i,k User selection variable. If the user chooses to refuel at a hydrogen refueling station, the variable value is 1, otherwise it is 0. Q is the unit hydrogen consumption of user k’s vehicle; k is the per capita hydrogenation demand of regional users; C sal The price of hydrogen sold at hydrogen refueling stations;

[0151] The minimum total risk quantitative value objective function determines the leakage risk area of ​​the hydrogen storage container and transportation equipment through the leakage radius, and calculates the number of people exposed to the consequences as the quantitative value of the hydrogen station leakage risk by combining the regional resident coefficient. The objective function expression is as follows:

[0152]

[0153] Where, ψ l is the resident coefficient of area l; R st is the leakage radius of the hydrogen storage container; R tr is the leakage radius of the hydrogen storage container; π is the pi.

[0154] In one embodiment, it is characterized in that the hydrogen source production capacity constraint expression in step S5 is as follows:

[0155]

[0156] Where G j The daily production capacity of hydrogen source;

[0157] The hydrogen station type constraint expression is as follows:

[0158] φ i ≤μ i

[0159] β i,j ≤φ i

[0160] Where, β i,j Purchase variables for hydrogen sources for off-site hydrogen supply and refueling stations;

[0161] The hydrogen refueling station quantity constraint expression is as follows:

[0162]

[0163] Where, O l Plan the number of hydrogen refueling stations in area l;

[0164] The user selection constraint expression is as follows:

[0165]

[0166] The user membership constraint expression is as follows:

[0167] δ i,k ≤μ i

[0168]

[0169] The hydrogen station capacity constraint expression is as follows:

[0170]

[0171] Where, The maximum capacity of the hydrogen storage cylinder group; The number of hydrogen storage cylinders purchased from the station; is the maximum capacity of the high-pressure hydrogen storage tank; The number of high-pressure hydrogen storage tanks for hydrogen refueling stations purchased from outside the station; The maximum capacity of the hydrogen refueling station for off-site hydrogen purchases; The number of hydrogen storage cylinders in the hydrogen production and refueling station; The maximum capacity of the hydrogen production and refueling station within the station; The number of high-pressure hydrogen storage tanks in the hydrogen production and refueling station;

[0172] The construction cost constraint of the hydrogen refueling station includes the construction cost constraint of the hydrogen refueling station purchased from outside the station and the construction cost constraint of the hydrogen refueling station produced on the station. The construction cost constraint of the hydrogen refueling station purchased from outside the station is expressed as follows:

[0173]

[0174] Where, The construction cost of the pipeline unit for the hydrogen refueling station for purchasing hydrogen from outside the station; The construction cost of the booster unit for the hydrogen refueling station purchased from outside the station; The construction cost of the hydrogen filling unit for the hydrogen refueling station purchased from outside the station; The cost of building the infrastructure for the hydrogen refueling station for off-site hydrogen purchases;

[0175] The cost constraint expression of the on-site hydrogen production and refueling station construction is as follows:

[0176]

[0177] Where, The construction cost of the pipeline unit for hydrogen production and refueling station within the station; The construction cost of the hydrogen production and refueling station booster unit on the station; The construction cost of the hydrogen refueling unit for the on-site hydrogen production station; The construction cost of the hydrogen production unit of the hydrogen production and refueling station on the station; The cost of infrastructure construction for hydrogen production and refueling stations within the station.

[0178] In one embodiment, it is characterized in that the specific steps of step S6 are as follows: Figure 2 As shown, including:

[0179] S601: Set the parameters of the multi-objective whale optimization algorithm, which include the whale population size W, the number of iterations t, and the maximum number of iterations T. Generate an initial solution around the decision variables in the solution space as the population individual x t , and record the initial position X(t) of the whale population;

[0180] S602: Calculate the multi-objective function value (F ec ,F risk ), perform non-dominated sorting, calculate the crowding distance, and screen the best whale individuals in the population The calculation formula for congestion distance is as follows:

[0181]

[0182] Where, d x is the crowding distance of the xth individual; M is the number of objective functions; is the target value of the individual adjacent to the right of the x-th individual on the objective function m; is the target value of the adjacent individual to the left of the x-th individual on the objective function m; The maximum value of the objective function m; Minimum value of objective function m;

[0183] S603: Update the whale direction coefficient a1 and probability coefficient k, and calculate the whale linear coefficient variable A and the whale mutation coefficient variable C. The calculation formula is as follows:

[0184]

[0185] A=2a1r1

[0186] C=2r2

[0187] Where a1 is the whale direction coefficient; A is the whale iteration coefficient variable; C is the whale mutation coefficient variable; r1 and r2 are both random numbers in the range of (0,1);

[0188] S604: When the probability coefficient k is less than 0.5 and |A|<1, the random search behavior mechanism is used to update the population individuals. The update formula is as follows:

[0189] D r =|C×X r (t)-X(t)|

[0190] X(t+1)=X r (t)-A×D r

[0191] Where D r is the initial distance between the random whale individual and the prey; X(t) r is the position of the random whale population at the tth iteration; X(t+1) is the position of the whale population at the t+1th iteration;

[0192] S605: When the probability coefficient k is less than 0.5 and |A| ≥ 1, the prey encirclement behavior mechanism is used to update the population individuals. The update formula is as follows:

[0193] D1=|C×X(t) best -X(t)|

[0194] X(t+1)=X(t) best -A×D1

[0195] Where D1 is the initial distance between the whale and its prey; X(t) best is the optimal whale population position at the tth iteration;

[0196] S606: When the probability coefficient k is greater than 0.5, the spiral attack behavior mechanism is used to update the population individuals. The update formula is as follows:

[0197] D2=|X(t) best -X(t)|

[0198] X(t+1)=D2×ebl ×cos(2πl)+X(t) best

[0199] Where D2 is the updated distance between the individual whale and its prey; e bl is the spiral shape constant;

[0200] S607: Calculate and update the multi-objective function value (F ec ,F risk ), perform non-dominated sorting, calculate the crowding distance, and update the optimal whale individual in the population

[0201] S608: Determine whether the number of iterations reaches the maximum number of iterations. If so, exit the loop and output the optimal solution value and the location information of the optimal whale individual. Otherwise, return to S602.

[0202] In a specific embodiment, the multi-objective optimization model of urban hydrogen refueling stations based on multi-agent collaboration and risk quantification described in the present invention is used to optimize the site selection of hydrogen refueling stations in a certain domestic city. The city includes 2 hydrogen source nodes, 15 candidate hydrogen refueling station nodes and 28 user nodes. It is planned to build 8 hydrogen refueling stations. The annual operating days of the hydrogen refueling station are 360 ​​days, and the daily hydrogen source production capacity is 5000kg / d. The capacity specifications of off-site hydrogen refueling stations and on-site hydrogen production stations are 500kg / d, 1000kg / d and 1500kg / d. The hydrogen selling price of the hydrogen source node is 26.5 yuan / kg, the cost of hydrogen production on the station is 24.5 yuan / kg, and the hydrogen selling price of the hydrogen refueling station is 40 yuan / kg. The wind speed in the area is 1.5m / s, the temperature is 25℃, the relative humidity is 50%, the hydrogen storage loss coefficient is 0.3%, and the hydrogen transportation equipment supported is a hydrogen long tube trailer. The specific coordinates of hydrogen sources, candidate nodes and demand nodes, the demand quantity of each demand node and the maximum acceptable distance are shown in Table 1.

[0203] Table 1 Specific coordinates of hydrogen sources, candidate nodes and demand nodes, demand node demand and maximum acceptable distance

[0204]

[0205]

[0206] The parameters of hydrogen refueling vehicles at demand nodes are shown in Table 2.

[0207] Table 2 Parameters of hydrogen refueling vehicles at demand nodes

[0208]

[0209] The construction cost parameters of hydrogen refueling stations of different capacities and types are shown in Table 3.

[0210] Table 3 Construction cost parameters of hydrogen refueling stations of different capacities and types

[0211]

[0212] The parameters of hydrogen storage container and transportation equipment are shown in Table 4.

[0213] Table 4 Hydrogen storage container and transportation equipment parameters

[0214]

[0215] Considering the four types of leakage consequences of hydrogen storage containers and transportation equipment at hydrogen refueling stations, the Martinsen time variable model is used to simulate the leakage diffusion process to obtain the maximum risk radius of each type of leakage consequence; a leakage radius weight optimization model is constructed, and the neural network model is trained using historical leakage data. The leakage radius of hydrogen storage containers and hydrogen transportation equipment at hydrogen refueling stations is determined by correcting the leakage radius weight; the regional resident coefficient is introduced to calculate the number of people exposed to the radiation. The calculation results of the number of people exposed to the leakage radius of candidate nodes of hydrogen refueling stations are shown in Table 5.

[0216] Table 5 Calculation results of the number of people exposed to the leakage radius of candidate hydrogen refueling station nodes (thousands of people)

[0217]

[0218] After inputting the above data into the model, the multi-objective whale optimization algorithm is used to solve the optimal hydrogen station site selection plan. The hydrogen station site selection plan is as follows: Figure 4 As shown. Figure 4 As shown, the plan builds a total of 8 hydrogen refueling stations, all of which are off-site hydrogen supply stations, and no on-site hydrogen production and refueling stations are built. The main reason for this is that the current construction cost of on-site hydrogen production and refueling stations is too high. The total risk value of the site selection plan (total number of people affected) is 55,000. The hydrogen refueling stations built at candidate points i1, i3, i4, and i5 purchase hydrogen from hydrogen source j1, with a total purchase of 2,955 kg / d; the hydrogen refueling stations built at candidate points i10, i12, i14, and i15 purchase hydrogen from hydrogen source j2, with a total purchase of 4,225 kg / d. There are two hydrogen refueling stations with a capacity of 500 kg / d, namely hydrogen refueling stations i3 and i5; there is only i14 hydrogen refueling station with a capacity of 1,500 kg / d; the remaining five hydrogen refueling stations all have a capacity of 1,000 kg / d. Two hydrogen refueling stations were built in densely populated areas of the city, at candidate points i3 and i10, with capacity specifications of 500kg / d and 1000kg / d respectively. The 1500kg / d hydrogen refueling station with greater risks was not built.

[0219] The cost distribution of this site selection plan is shown in Table 6. As can be seen, the total annual economic cost is 102.509 million yuan, of which the hydrogen purchase cost is 68.497 million yuan; the hydrogen transportation cost is 13.408 million yuan; the hydrogen refueling station construction cost is 18.656 million yuan; and the user hydrogen refueling cost is 1.948 million yuan. The total annual economic cost of the hydrogen refueling station is 100.561 million yuan. Of this, the hydrogen purchase cost is the highest, accounting for 66.82%.

[0220] Table 6 Cost distribution of site selection options

[0221]

[0222] To verify the effectiveness of the multi-objective optimization model, this study solved the single-objective optimization problems of minimizing total economic cost and minimizing total risk, respectively. The optimization results were compared with the multi-objective optimization scheme, as shown in Table 7. As can be seen from Table 7, the hydrogen purchase cost and the on-site construction cost of the hydrogen refueling station are consistent under the three schemes, but the hydrogen transportation cost and the user's hydrogen refueling cost show significant differences.

[0223] In the scenario with the optimal total economic cost, the cost of hydrogen transportation reached 13.621 million yuan, the highest among the three scenarios, while the cost of hydrogen refueling for users dropped to 1.504 million yuan, the lowest among the three. In contrast, the cost of hydrogen transportation in the scenario with the optimal total risk was reduced to 13.339 million yuan, a decrease of 2.07%, but the cost of hydrogen refueling for users increased to 3.089 million yuan, an increase of 105.3%. The reason for this is that the optimal risk scenario tends to select candidate sites with lower risk values. Most of these sites are close to hydrogen source distribution areas. Although this can reduce the cost of hydrogen transportation, the spatial distribution deviation from the demand center increases the cost of hydrogen refueling for users. The optimal economic scenario gives priority to the proximity of the demand side, but is limited by the geographical characteristics that most hydrogen sources are distributed outside the city, forming an inverse correlation between hydrogen transportation costs and user hydrogen refueling costs. It is worth noting that by balancing economy and safety, the multi-objective optimization scheme's storage and transportation costs (13.482 million yuan) and user costs (2.296 million yuan) are both between the two single-objective schemes, confirming the effectiveness of the multi-objective decision-making mechanism in balancing conflicting objectives.

[0224]

[0225]

[0226] The foregoing is merely an example of the embodiments of this specification and is not intended to limit the embodiments of this specification. For those skilled in the art, various modifications and variations of the embodiments of this specification are possible. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the embodiments of this specification shall be included within the scope of the claims of the embodiments of this specification.

Claims

1. A multi-objective optimization method for urban hydrogen refueling stations based on multi-agent collaboration and risk quantification, characterized by: The following steps are involved: S1: Determine the decision variables for optimizing the site selection of hydrogen refueling stations and obtain the basic data for the site selection of hydrogen refueling stations in the target area; The basic data for hydrogen refueling station site selection in the target area includes the annual operating days of the hydrogen refueling station, daily hydrogen source production capacity, the planned number of hydrogen refueling stations, hydrogen risk data, hydrogen price data, hydrogen transportation data, hydrogen refueling station construction data, and user hydrogen refueling data; The hydrogen risk data includes the storage pressure, storage volume and operating temperature of hydrogen storage containers and transportation equipment, wind speed, regional average temperature, regional average humidity, regional resident coefficient and regional support for hydrogen transportation equipment; The hydrogen price data includes the price of hydrogen purchased from the hydrogen source, the cost of hydrogen production within the station, and the price of hydrogen sold at the hydrogen refueling station; The hydrogen transportation data includes the distance from the hydrogen source to the hydrogen refueling station node, the transportation equipment rental price, the hydrogen transportation unit price, and the hydrogen storage loss coefficient; The construction and operation data of the hydrogen refueling station include the construction cost of the pipeline unit of the hydrogen refueling station purchased from outside the station, the construction cost of the booster unit of the hydrogen refueling station purchased from outside the station, the construction cost of the filling unit of the hydrogen refueling station purchased from outside the station, the infrastructure construction cost of the hydrogen refueling station purchased from outside the station, the construction cost of the pipeline unit of the hydrogen refueling station produced on the station, the construction cost of the booster unit of the hydrogen refueling station produced on the station, the construction cost of the filling unit of the hydrogen refueling station produced on the station, the infrastructure construction cost of the hydrogen refueling station produced on the station, the construction cost of the hydrogen storage bottle group, the construction cost of the high-pressure hydrogen storage tank, the depreciation rate of the hydrogen refueling station, the maximum capacity of the hydrogen refueling station produced on the station, the maximum capacity of the hydrogen storage bottle group and the maximum capacity of the high-pressure hydrogen storage tank; The user hydrogen refueling data includes the unit hydrogen consumption of the user's vehicle, the maximum acceptable distance of the user and the user's per capita hydrogen refueling demand; S2: Considering four types of leakage consequences of hydrogen storage containers and transportation equipment at hydrogen refueling stations, the Martinsen time-variable model is used to simulate the leakage diffusion process to obtain the maximum risk radius of each type of leakage consequence; The hydrogen storage container of the hydrogen refueling station includes a hydrogen storage bottle group and a high-pressure hydrogen storage tank; The transportation equipment includes a hydrogen long tube trailer and a liquid hydrogen tanker; The four types of leakage consequences include jet fire, flash fire, fireball, and explosion; S3: Construct a leakage radius weight optimization model, use historical leakage data to train a neural network model, and determine the leakage radius of hydrogen storage containers and hydrogen transportation equipment at hydrogen refueling stations through leakage radius weight correction; S4: establishing a multi-objective collaborative optimization multi-objective function, wherein the multi-objective function includes a minimum total economic cost objective function and a minimum total risk quantization value objective function; S5: Set constraints and, combined with the objective function, construct a multi-objective optimization model for urban hydrogen refueling stations based on multi-agent collaboration and risk quantification; The constraints include hydrogen source capacity constraints, hydrogen refueling station type constraints, hydrogen refueling station quantity constraints, hydrogen refueling station capacity constraints, user distance constraints, user affiliation constraints, and hydrogen refueling station construction cost constraints; S6: The model is solved using a multi-objective whale optimization algorithm to generate a Pareto optimal solution set, and a comprehensive optimal hydrogen station site selection plan is output based on preset priorities.

2. The multi-objective optimization method for urban hydrogen refueling stations based on multi-agent collaboration and risk quantification according to claim 1 is characterized in that: The decision variables described in step S1 include hydrogen station establishment variables, hydrogen station type variables, the number of hydrogen storage bottle groups, the number of high-pressure hydrogen storage tanks, hydrogen source purchase variables for off-site hydrogen supply stations, hydrogen purchase volume for off-site hydrogen supply stations, and hydrogen production volume for on-site hydrogen production stations.

3. The multi-objective optimization method for urban hydrogen refueling stations based on multi-agent collaboration and risk quantification according to claim 1 is characterized in that: The specific steps of step S3 are: S301: Construct a risk radius weight optimization model. The objective function of the risk radius weight optimization model is shown as follows: Where, is the leakage radius error ratio; R h is the leakage radius of historical accidents; α is the leakage radius weight of jet fire consequences; R1 is the maximum risk radius of jet fire consequences; β is the leakage radius weight of flash fire consequences; R2 is the maximum risk radius of flash fire consequences; is the weight of the leakage radius of fireball consequences; R3 is the maximum risk radius of fireball consequences; θ is the weight of the leakage radius of explosion consequences; R4 is the maximum risk radius of explosion consequences; The constraint conditions of the risk radius weight optimization model are as follows: α＞0 β＞0 θ>0 S302: Importing historical accident data into the Martinsen time-variable model to simulate the leakage diffusion process and obtain the maximum risk radius of jet fire, flash fire, fireball and explosion leakage consequences; S303: Dividing the historical leakage data into a training subset and a validation subset according to a preset ratio, iteratively optimizing the parameters of the neural network model using the training subset, and completing the training when the model prediction error reaches a preset convergence condition; S304: Input the verification subset into a fully trained neural network model, and output the leakage radius weight for subsequent calculation of the leakage radius.

4. The multi-objective optimization method for urban hydrogen refueling stations based on multi-agent collaboration and risk quantification according to claim 1 is characterized in that: The minimum total economic cost objective function in step S4 includes hydrogen purchase cost, hydrogen storage and transportation cost, hydrogen station construction and operation cost, and user hydrogenation cost. The objective function expression is as follows: min F ec =F pr +F tr +F st +F user Where, F ec is the total economic cost; F pr F is the purchase cost of hydrogen; tr is the storage and transportation cost of hydrogen; F st F is the construction cost of hydrogen refueling station; user Hydrogen refueling costs for users; The hydrogen purchase cost is expressed as follows: Where, T is the annual operating days of the hydrogen refueling station; μ i is the hydrogen station construction variable. If a hydrogen station is built at node i, the variable value is 1, otherwise it is 0; i is the hydrogen station type variable. If the hydrogen station type at node i is an off-site hydrogen supply station, the variable value is 1, otherwise it is 0; Q i,j The amount of hydrogen purchased by the off-site hydrogen supply and refueling station; C j,pr The cost of purchasing hydrogen for the off-site hydrogen supply and refueling station; Q i C is the hydrogen production of the hydrogen production and refueling station; in-pr The cost of hydrogen production and refueling station on site; The hydrogen storage and transportation cost expression is as follows: Where a is the rental fee of hydrogen transportation equipment; b is the unit price of hydrogen transportation equipment; L i,j is the distance between the hydrogen refueling station and the hydrogen source; c is the hydrogen storage loss coefficient; The construction and operation cost of the hydrogen refueling station is expressed as follows: Where, τ is the average depreciation rate of the hydrogen refueling station; γ is the depreciation period of the hydrogen refueling station; The construction cost of hydrogen refueling stations for off-site hydrogen supply; The construction cost of the hydrogen production and refueling station on the station; The capacity of the hydrogen refueling station for off-site hydrogen supply; The capacity of the hydrogen production and refueling station within the station; P inj the cost of filling hydrogen refueling stations; The daily maintenance cost of the off-site hydrogen supply and refueling station; The daily maintenance cost of the hydrogen production and refueling station on site; The user hydrogenation cost expression is as follows: Where, δ i,k User selection variable. If the user chooses to refuel at a hydrogen refueling station, the variable value is 1, otherwise it is 0. Q is the unit hydrogen consumption of user k’s vehicle; k is the per capita hydrogenation demand of regional users; C sal The price of hydrogen sold at hydrogen refueling stations; The minimum total risk quantitative value objective function determines the leakage risk area of ​​the hydrogen storage container and transportation equipment through the leakage radius, and calculates the number of people exposed to the consequences as the quantitative value of the hydrogen station leakage risk by combining the regional resident coefficient. The objective function expression is as follows: Where, ψ l is the resident coefficient of area l; R st is the leakage radius of the hydrogen storage container; R tr is the leakage radius of the hydrogen storage container; π is the pi.

5. The multi-objective optimization method for urban hydrogen refueling stations based on multi-agent collaboration and risk quantification according to claim 1 is characterized in that: The hydrogen source capacity constraint expression in step S5 is as follows: Where G j The daily production capacity of hydrogen source; The hydrogen station type constraint expression is as follows: f i ≤μ i b i,j ≤φ i Where, β i,j Purchase variables for hydrogen sources for off-site hydrogen supply and refueling stations; The hydrogen refueling station quantity constraint expression is as follows: Where, O l Plan the number of hydrogen refueling stations in area l; The user selection constraint expression is as follows: The user membership constraint expression is as follows: d i,k ≤μ i The hydrogen station capacity constraint expression is as follows: Where, The maximum capacity of the hydrogen storage cylinder group; The number of hydrogen storage cylinders purchased from the station; is the maximum capacity of the high-pressure hydrogen storage tank; The number of high-pressure hydrogen storage tanks for hydrogen refueling stations purchased from outside the station; The maximum capacity of the hydrogen refueling station for off-site hydrogen purchases; The number of hydrogen storage cylinders in the hydrogen production and refueling station; The maximum capacity of the hydrogen production and refueling station within the station; The number of high-pressure hydrogen storage tanks in the hydrogen production and refueling station; The construction cost constraint of the hydrogen refueling station includes the construction cost constraint of the hydrogen refueling station purchased from outside the station and the construction cost constraint of the hydrogen refueling station produced on the station. The construction cost constraint of the hydrogen refueling station purchased from outside the station is expressed as follows: Where, The construction cost of the pipeline unit for the hydrogen refueling station for purchasing hydrogen from outside the station; The construction cost of the booster unit for the hydrogen refueling station purchased from outside the station; The construction cost of the hydrogen filling unit for the hydrogen refueling station purchased from outside the station; The cost of building the infrastructure for the hydrogen refueling station for off-site hydrogen purchases; The construction cost constraint expression of the on-site hydrogen production and refueling station is as follows: Where, The construction cost of the pipeline unit for hydrogen production and refueling station within the station; The construction cost of the hydrogen production and refueling station booster unit on the station; The construction cost of the hydrogen production and refueling unit of the hydrogen station; The construction cost of the hydrogen production unit of the hydrogen production and refueling station on the station; The cost of infrastructure construction for the on-site hydrogen production and refueling station.

6. The multi-objective optimization method for urban hydrogen refueling stations based on multi-agent collaboration and risk quantification according to claim 1 is characterized in that: The specific steps of step S6 include: S601: Set the parameters of the multi-objective whale optimization algorithm, which include the whale population size W, the number of iterations t, and the maximum number of iterations T. Generate an initial solution around the decision variables in the solution space as the population individual x t , and record the initial position X(t) of the whale population; S602: Calculate the multi-objective function value (F ec ,F risk ), perform non-dominated sorting, calculate the crowding distance, and screen the best whale individuals in the population The calculation formula for congestion distance is as follows: Where, d x is the crowding distance of the xth individual; M is the number of objective functions; is the target value of the individual adjacent to the right of the x-th individual on the objective function m; is the target value of the adjacent individual to the left of the x-th individual on the objective function m; The maximum value of the objective function m; Minimum value of objective function m; S603: Update the whale direction coefficient a1 and probability coefficient k, and calculate the whale linear coefficient variable A and the whale mutation coefficient variable C. The calculation formula is as follows: A=2a1r1 C＝2r2 Where a1 is the whale direction coefficient; A is the whale iteration coefficient variable; C is the whale mutation coefficient variable; r1 and r2 are both random numbers in the range of (0,1); S604: When the probability coefficient k is less than 0.5 and |A|<1, the random search behavior mechanism is used to update the population individuals. The update formula is as follows: D r =|C×X r (t)-X(t)| X(t+1)=X r (t)-A×D r Where D r is the initial distance between the random whale individual and the prey; X(t) r is the position of the random whale population at the tth iteration; X(t+1) is the position of the whale population at the t+1th iteration; S605: When the probability coefficient k is less than 0.5 and |A| ≥ 1, the prey encirclement behavior mechanism is used to update the population individuals. The update formula is as follows: D1=|C×X(t) best -X(t)| X(t+1)=X(t) best -A×D1 Where D1 is the initial distance between the whale and its prey; X(t) best is the optimal whale population position at the tth iteration; S606: When the probability coefficient k is greater than 0.5, the spiral attack behavior mechanism is used to update the population individuals. The update formula is as follows: D2=|X(t) best -X(t)| X(t+1)=D2×e bl ×cos(2πl)+X(t) best Where D2 is the updated distance between the individual whale and its prey; e bl is the spiral shape constant; S607: Calculate and update the multi-objective function value (F ec ,F risk ), perform non-dominated sorting, calculate the crowding distance, and update the optimal whale individual in the population S608: Determine whether the number of iterations reaches the maximum number of iterations. If so, exit the loop and output the optimal solution value and the location information of the optimal whale individual. Otherwise, return to S602.

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