A disaster control strategy optimization method and system based on improved response surface and trust technology

Abstract

The application discloses a disaster control strategy optimization method and system based on an improved response surface and trust technology, relates to the technical field of disaster control, and comprises the following steps: taking the position coordinates of each boundary point of an isolation belt as decision variables, constructing a target function and constraint conditions after multidimensional evaluation; then, the target function and constraint conditions are converted into an unconstrained optimization problem, and the improved response surface method is used to solve the problem, so that the solving quality and speed of a local optimal solution are greatly improved; then, the trust technology is used to obtain a global optimal solution from a local optimal solution; finally, the global optimal solution is taken as an optimal disaster control strategy, and since the decision variables correspond to the position coordinates of each boundary point, the global optimal solution has certainty, that is, the optimal positions of each boundary point of the isolation belt. The application can efficiently obtain the global optimal solution of a forest fire control strategy, that is, the deterministic parameters of the forest fire prevention isolation belt, and effectively provides guiding suggestions for the development of disaster relief measures.

Description

Technical Field

[0001] This invention relates to the technical field of disaster control, and more specifically, to a method and system for optimizing disaster control strategies based on improved response surface and trust technologies. Background Technology

[0002] Large-scale forest fires are difficult to extinguish in a short time, so it is usually necessary to construct several firebreaks to prevent the spread of the affected area or protect important habitats and facilities. However, the construction of firebreaks often requires a trade-off between disaster losses and construction costs or efficiency: while completing firebreaks quickly may minimize the affected area, the required manpower and resources would be excessive; furthermore, the location of the firebreaks must be carefully considered to maximize disaster relief benefits. In summary, how to rationally design control strategies, i.e., deploying firebreaks, is a highly complex problem. Forest fire control strategy optimization is a large-scale nonlinear optimization problem involving geometric constraints. Its decision variables, such as the location and length of firebreak deployment points, are highly coupled and dependent, and its objective functions, such as the economic and casualty losses of the affected area, the total construction cost of the firebreaks, and the minimum construction speed of the firebreaks, do not have explicit functional expressions with the decision variables, making the optimization process extremely difficult.

[0003] Currently, computational methods for optimizing forest fire control strategies can be divided into two categories: traditional optimization algorithms and intelligent algorithms. Traditional optimization algorithms, such as gradient descent and Newton's method, have the following drawbacks in application scenarios: 1) They rely on derivative information, such as gradients and Hessian matrices, resulting in extremely slow solution speeds. In application scenarios, traditional optimization algorithms can only obtain derivative information through numerical differentiation. Given the specific nature of the application scenarios, especially when the number of decision variables is large, numerical differentiation of all variables requires a significant amount of computational resources and time, which cannot meet the requirements of real-time application scenarios; 2) The quality of local optimal solutions depends on the location of the initial feasible solution, and it is impossible to find the global optimum. Traditional optimization algorithms often start from the initial feasible solution, using derivative information to find a path that reduces the value of the objective function. In most cases, the final output is a local optimum near the initial feasible solution, which cannot meet the requirements of the application scenarios. Intelligent algorithms, such as genetic algorithms and particle swarm optimization, have the following drawbacks in application scenarios: 1) They rely on the selection of hyperparameters, and the iterative process requires a large amount of computational resources; 2) The final output results are random, which cannot meet the application requirements, and they also cannot guarantee finding the global optimal solution.

[0004] Existing technology provides a multi-objective optimization method for stiffened gearboxes based on response surface methodology, including: drawing a reducer model, the reducer model including an upper cover and a lower housing, with varying numbers of ribs distributed on the housing; initializing the design variables and parameters of the ribs; using the overall dimensional parameters of the gearbox as the objective function input and setting constraints; generating design points through experimental design, optimizing the model using the constructed response surface to generate a response surface model; establishing a mathematical model of the multi-objective optimization problem to obtain the Pareto optimal solution for the multi-objective optimization; setting constraints and multiple objective functions, setting an intelligent optimization algorithm, and optimizing the algorithm's parameters; and judging the optimization results and constraints. However, when the number of decision variables is large, this scheme requires a large amount of computational resources and time to obtain derivative information by numerically differentiating all variables, which cannot meet the needs of application scenarios. Summary of the Invention

[0005] To overcome the shortcomings of existing technologies in efficiently and accurately optimizing forest fire control strategies, this invention provides a disaster control strategy optimization method and system based on improved response surface methodology and trust technology. This method can efficiently find the global optimal solution of forest fire control strategies, and the values ​​in the global optimal solution are the deterministic parameters of forest firebreaks, effectively providing guidance for the formulation of disaster relief measures.

[0006] To solve the above-mentioned technical problems, the technical solution of the present invention is as follows: This invention provides a disaster control strategy optimization method based on improved response surface methodology and trust technology, comprising: S1: Obtain the coordinates of each boundary point of the isolation zone to construct the decision variables for disaster control strategies; S2: Conduct a multi-dimensional evaluation of the isolation zone corresponding to the decision variables of the disaster control strategy to obtain the corresponding evaluation parameters; S3: Construct the objective function by weighting all evaluation parameters and set constraints; S4: Rewrite the objective function and constraints to obtain the unconstrained optimization problem of disaster control strategy; S5: Solve the unconstrained optimization problem of disaster control strategy using the improved response surface method to obtain the local optimum solution of the unconstrained optimization problem; S6: Based on the local optimal solution of the unconstrained optimization problem, the global optimal solution of the unconstrained optimization problem is calculated using the trust technique; S7: Use the global optimal solution of the unconstrained optimization problem as the optimal strategy for disaster control to complete the construction planning of the isolation zone.

[0007] Preferably, the specific method of step S1 is as follows: Obtain the coordinates of each boundary point of the firebreak, arrange the coordinates of each boundary point in counterclockwise order, and form the decision variables for the disaster control strategy. In the formula, The decision variables representing disaster control strategies, and These represent the isolation zones. The x and y coordinates of the boundary points. Indicates the isolation zone number The ordinates of the boundary points. This indicates the floor function.

[0008] In particular, if we consider the isolation zone corresponding to the disaster control strategy as a multi-connected branch, i.e. a polygon group, then we can arbitrarily set the arrangement order of each connected branch, and then splice the variables contained in each connected branch in the set arrangement order to obtain the decision variables of the disaster control strategy.

[0009] Preferably, the specific method of step S2 is as follows: Using a forest fire spread and control framework based on discrete differential equations to determine the decision variables for disaster control strategies. Corresponding isolation zone Conduct multi-dimensional assessments to obtain parameters for assessing economic and casualty losses in the disaster-stricken areas. Total construction cost assessment parameters for the isolation zone Minimum construction speed assessment parameters for the isolation zone .

[0010] Preferably, the specific method of step S3 is as follows: The objective function is constructed by weighting the parameters for assessing economic and casualty losses in the disaster-stricken area, the total construction cost of the firebreak, and the minimum construction speed of the firebreak:

[0011] In the formula, Describe the objective function. Indicates the first One evaluation parameter, Indicates the first The relative importance coefficients corresponding to each evaluation parameter , , ; The constraints are set according to disaster relief needs. If the deployed firebreak needs to surround bounded habitats so that the final disaster-stricken area does not cover the habitats, then the constraints are:

[0012] If the isolation zone needs to surround the ultimately bounded disaster area so that the ultimately bounded disaster area does not cover the habitat, then the constraint is:

[0013] In the formula, Represents the area function. Indicates habitat, Indicates the final affected area. Indicates a separation zone on a plane. The isolated bounded connected component, and These represent the intersection and difference operations for two-dimensional geometric objects, respectively.

[0014] Preferably, the specific method of step S4 is as follows: Rewrite each constraint as follows:

[0015] Combining constraints to rewrite the set:

[0016] The constrained nonlinear optimization problem of disaster control strategy is as follows:

[0017] The constrained nonlinear optimization problem of the above disaster control strategy is transformed into an unconstrained optimization problem of the disaster control strategy:

[0018] In the formula, The augmented Lagrangian function represents the function of a constrained nonlinear optimization problem. This represents the optimized variable after transformation. Represents the Lagrange multiplier vector. , Indicates the rewritten first... The Lagrange multipliers corresponding to each constraint condition; Specifically, the augmented Lagrangian function for the constrained nonlinear optimization problem is:

[0019] In the formula, The Lagrangian function represents the constrained nonlinear optimization problem. Indicates the penalty coefficient. It is a 2-norm, and because:

[0020] Then we have:

[0021]

[0022]

[0023] In the formula, express exist gradient on, express exist The gradient on.

[0024] Preferably, the specific method of step S5 includes: S5.1: Initial feasible solution of the constrained nonlinear optimization problem for selecting a disaster control strategy Initialize the Lagrange multiplier vector The initial solution to the unconstrained optimization problem of disaster control strategy is obtained by piecing them together. Set error threshold ; S5.2: Set sampling radius In the For the center of the ball, radius Random sampling within a closed sphere There are points, and the set of sampling points is... And calculate the response value corresponding to each sampling point to obtain the response value set. ; S5.3: Construct an initial solution based on the set of sampling points and the set of response values. Improved response surface model at the location; S5.4: Based on the initial solution An improved response surface model is used to establish the optimization problem of the improved response surface. A nonlinear optimization algorithm is then used to solve the optimization problem of the improved response surface, obtaining the local optimum solution of the improved response surface at the initial solution. ; S5.5: If Then the local optimum of the improved response surface at the initial solution will be obtained. As a local optimum of the unconstrained optimization problem; otherwise, as a local optimum of the improved response surface at the initial solution. As a new initial solution, repeat steps S5.2-5.5.

[0025] Preferably, in step S5.3, an initial solution is constructed based on the set of sampling points and the set of response values. The specific method for improving the response surface model at this point is as follows: S5.3.1: Construct the initial first-order basis function set and calculate the initial first-order basis matrix corresponding to the sample point set; specifically: The initial set of first-order basis functions is denoted as ,in:

[0026] The initial first-order basis matrix is:

[0027] In the formula, Denotes the first in the initial set of first-order basis functions. One first-order basis function Indicates the floor function; initializes the first-order basis matrix. The Middle Liede row elements Recorded as ; S5.3.2: Based on the initial first-order basis matrix, construct an improved first-order basis function set and calculate the improved first-order basis matrix corresponding to the sample point set; specifically: Establish a mixed-integer programming problem:

[0028] in, These are the first and second parameter sets of the response surface model, respectively. , Indicates the positive penalty coefficient. Represents the second parameter set of the response surface model. Parameters Whether a value is non-zero is defined as follows: Solving the mixed-integer programming problem using the branch and bound method yields the specific values ​​of the first parameter of the response surface model. Specific values ​​of the second parameter set According to the above and Obtain the initial solution Improved first-order basis function set at the location And the improved first-order basis matrix corresponding to the set of sampling points. , Represents the second parameter set of the response surface model. The specific value of each element; 5.3.3: Based on the improved first-order basis function set, construct the initial second-order basis function set, and calculate the initial second-order basis matrix corresponding to the sampling point set; specifically: Improved first-order basis function set The initial set of second-order basis functions is obtained by multiplying and combining the basis functions pairwise:

[0029] Further calculate the initial second-order basis matrix corresponding to the set of sampling points:

[0030] In the formula, Denotes the initial set of second-order basis functions The number of elements in To make the set of sampling points the sampling points Substitute the basis functions into the initial second-order basis function set. The obtained value is denoted as . ; S5.3.4: Based on the initial second-order basis matrix, construct the improved second-order basis function set and calculate the improved second-order basis matrix corresponding to the sampling point set; specifically: Establish a mathematical programming problem:

[0031] In the formula, This represents the third parameter set of the response surface model. express The number of non-zero elements in the middle; The proximal gradient descent method is used to solve the mathematical programming problem, and the specific values ​​of the third parameter set of the response surface model are obtained. According to the above Obtain the initial solution Improved second-order basis function set at the location And the improved second-order basis matrix corresponding to the set of sampling points. In the formula, This represents the basis functions in the initial second-order basis function set corresponding to the third parameter set of the response surface model. The parameter values; S5.3.5: Construct the initial solution based on the improved first-order basis matrix and the improved second-order basis matrix corresponding to the sampling point set. Improved response surface model at the location:

[0032] In the formula, Indicates the initial solution An improved response surface model for [the location].

[0033] Preferably, the specific method of step S6 is as follows: S6.1: Establish a nonlinear dynamic system for the unconstrained optimization problem of disaster control strategies:

[0034] In the formula, Represents the optimized variables after transformation Regarding time variables The derivative, The augmented Lagrangian function represents the function of a constrained nonlinear optimization problem. express The transformed optimization variables gradient on; Each local optimum of the unconstrained optimization problem (1.2) of disaster control strategy corresponds to a stable equilibrium point of the nonlinear dynamic system (3.1). At each local optimum of the unconstrained optimization problem of disaster control strategy, by replacing the augmented Lagrangian function with the corresponding response surface model, the transformation form of the nonlinear dynamic system is as follows:

[0035] In the formula, Represents the optimized variables after transformation Regarding time variables The derivative, The response surface model represents the local optimum solution of the unconstrained optimization problem of disaster control strategy. express The transformed optimization variables gradient on; S6.2: The set of stable equilibrium points of the nonlinear dynamical system (3.1) is denoted as... Initialized to The set of tier-0 stable equilibrium points of the nonlinear dynamical system (3.1) is denoted as... Initialized to The set of tier-1 stable equilibrium points of the nonlinear dynamical system (3.1) is denoted as... Initialized to The set of response surface models is denoted as Initialized to ; S6.3: Randomly select an initial feasible solution to the unconstrained optimization problem of disaster control strategy, calculate a local optimum and its response surface model using the method in step S5, and add them to the tier-0 stable equilibrium point set. and response surface model set middle; S6.4: From the set of tier-0 stable equilibrium points Arbitrarily select a stable equilibrium point of the nonlinear dynamic system (3.1). From the set of response surface models Extract the corresponding response surface model Update the set of stable equilibrium points for tier-0, making The stable equilibrium point to be selected From the set Delete; update the set of stable equilibrium points, let The stable equilibrium point to be selected Add to collection In the middle; calculate the transformation form of a nonlinear dynamic system at the stable equilibrium point. Hessian matrix and its eigenvector set ,in:

[0036] in, Representing the response surface model The transformed optimization variables The Hessian matrix on, i.e. about The second-order partial derivative; according to Calculate the Hessian matrix eigenvalue set , Represents the Hessian matrix The Each feature value; then based on Calculate the Hessian matrix Feature vector set , Represents the Hessian matrix The eigenvalues eigenvectors; S6.5: From the set of eigenvectors Select a feature vector Update the feature vector set, let The feature vector to be selected From the set Delete from middle; with For the search direction, with step size Sampling yields point series , point column For a line far from a stable equilibrium point And it points to another stable equilibrium point. Stability region boundary The search path; S6.6: Determine the point sequence With the boundary of the stable region Do they intersect? If the point sequence If the objective function value consistently increases, it is determined that there are no intersection points, and the process returns to S6.5 to select a new feature vector; if the point sequence If the objective function value changes from increasing to decreasing, then an intersection point is determined to exist, and step S6.7 is executed; S6.7: Continue forward 0.1 The arrival point is defined as the escape point. From the escape point Starting from this point, we use the method in step S5 to calculate another stable equilibrium point of the nonlinear dynamic system. and its response surface model ; S6.8: Determining the Stable Equilibrium Point Is it in the set? In the middle; if Return to S6.5 and select a new feature vector; if Then the stable equilibrium point will be and its response surface model Add the tier-1 stable equilibrium point set respectively and response surface model set In the middle, proceed to step S6.9; S6.9: Repeat steps S6.5-S6.8 until the feature vector set is reached. ; S6.10: Repeat steps S6.4-S6.9 until the set of stable tier-0 equilibrium points is reached. ; S6.11: Determine the set of stable equilibrium points in Tier-1 Is it an empty set? If Let the set of stable equilibrium points of tier-1 be taken as the set of stable equilibrium points of tier-0, that is, let And clear the set of stable equilibrium points in tier-1, that is, let Return to S6.4 and select a stable equilibrium point; if Proceed to step S6.12; S6.12: From the set of stable equilibrium points Identify the global optimal solution to the unconstrained optimization problem. ,in, This represents the optimal variable after the transformation. These represent the decision variables for the optimal disaster control strategy. This represents the optimal Lagrange multiplier vector.

[0037] Preferably, the specific method of step S7 is as follows: By utilizing the dynamic simulation function of the forest fire spread and control framework based on discrete differential equations, the decision variables of the optimal disaster control strategy in the global optimal solution of the unconstrained optimization problem are transformed into the optimal disaster control strategy, thus completing the construction planning of firebreaks.

[0038] This invention also provides a disaster control strategy optimization system based on improved response surface and trust technologies, comprising: The decision variable construction module is used to obtain the location coordinates of each boundary point of the isolation zone and construct the decision variables for disaster control strategies. The decision variable evaluation module is used to evaluate the isolation zone corresponding to the decision variables of disaster control strategies from multiple dimensions and obtain the corresponding evaluation parameters. The objective function construction module is used to construct the objective function by weighting all evaluation parameters and setting constraints. The unconstrained optimization problem construction module is used to rewrite the objective function and constraints to obtain the unconstrained optimization problem of disaster control strategy; The local optimum solution module is used to solve the unconstrained optimization problem of disaster control strategy using the improved response surface method, and obtain the local optimum solution of the unconstrained optimization problem; The global optimal solution module is used to calculate the global optimal solution of an unconstrained optimization problem based on the local optimal solution of the unconstrained optimization problem, and uses trust techniques. The disaster control strategy planning module is used to take the global optimal solution of the unconstrained optimization problem as the optimal disaster control strategy and complete the construction planning of the isolation zone.

[0039] Compared with the prior art, the beneficial effects of the technical solution of the present invention are: This invention uses the coordinates of the boundary points of the firebreak as decision variables, constructs an objective function and constraints after multi-dimensional evaluation, transforms the objective function and constraints into an unconstrained optimization problem, and solves it using an improved response surface methodology, significantly improving the quality and speed of finding local optima. Then, using trust techniques, it starts from a local optimum to obtain the global optimum. Finally, the global optimum is used as the optimal disaster control strategy. Since the decision variables correspond to the coordinates of the boundary points, the global optimum is deterministic, representing the optimal positions of the boundary points of the firebreak. This invention can efficiently find the global optimum of forest fire control strategies, and the values ​​in the global optimum are the deterministic parameters of the forest firebreak, effectively providing guidance for the formulation of disaster relief measures. Attached Figure Description

[0040] Figure 1 This is a flowchart of the disaster control strategy optimization method based on improved response surface and trust technology described in Example 1.

[0041] Figure 2 This is a flowchart illustrating how the improved response surface methodology is used to solve the unconstrained optimization problem of disaster control strategy as described in Example 2, thereby obtaining a local optimum solution to the unconstrained optimization problem.

[0042] Figure 3 This is a flowchart illustrating the process of calculating the global optimal solution of an unconstrained optimization problem using trust techniques, as described in Example 2, which involves finding the local optimal solution to the unconstrained optimization problem.

[0043] Figure 4 This is a schematic diagram of the disaster control strategy optimization system based on improved response surface and trust technology in Example 3. Detailed Implementation

[0044] The accompanying drawings are for illustrative purposes only and should not be construed as limiting the scope of this patent. To better illustrate this embodiment, some parts in the accompanying drawings may be omitted, enlarged, or reduced, and do not represent the actual product dimensions; It will be understood by those skilled in the art that certain well-known structures and their descriptions may be omitted in the accompanying drawings.

[0045] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0046] Example 1 This embodiment provides a disaster control strategy optimization method based on improved response surface and trust technologies, such as Figure 1 As shown, it includes: S1: Obtain the coordinates of each boundary point of the isolation zone to construct the decision variables for disaster control strategies; S2: Conduct a multi-dimensional evaluation of the isolation zone corresponding to the decision variables of the disaster control strategy to obtain the corresponding evaluation parameters; S3: Construct the objective function by weighting all evaluation parameters and set constraints; S4: Rewrite the objective function and constraints to obtain the unconstrained optimization problem of disaster control strategy; S5: Solve the unconstrained optimization problem of disaster control strategy using the improved response surface method to obtain the local optimum solution of the unconstrained optimization problem; S6: Based on the local optimal solution of the unconstrained optimization problem, the global optimal solution of the unconstrained optimization problem is calculated using the trust technique; S7: Use the global optimal solution of the unconstrained optimization problem as the optimal strategy for disaster control to complete the construction planning of the isolation zone.

[0047] In its implementation, this embodiment uses the coordinates of each boundary point of the firebreak as decision variables, constructs an objective function and constraints after multi-dimensional evaluation, transforms the objective function and constraints into an unconstrained optimization problem, and solves it using an improved response surface methodology, significantly improving the quality and speed of finding local optima. Then, using trust techniques, it starts from a local optimum to obtain the global optimum. Finally, the global optimum is used as the optimal disaster control strategy. Since the decision variables correspond to the coordinates of each boundary point, the global optimum is deterministic, representing the optimal positions of each boundary point of the firebreak. This invention can efficiently find the global optimum of forest fire control strategies, and the values ​​in the global optimum are the deterministic parameters of the forest firebreak, effectively providing guidance for the formulation of disaster relief measures.

[0048] Example 2 This embodiment provides a disaster control strategy optimization method based on improved response surface and trust technologies, including: S1: Obtain the coordinates of each boundary point of the firebreak to construct the decision variables for the disaster control strategy; specifically: Obtain the coordinates of each boundary point of the firebreak, arrange the coordinates of each boundary point in counterclockwise order, and form the decision variables for the disaster control strategy. In the formula, The decision variables representing disaster control strategies, and These represent the isolation zones. The x and y coordinates of the boundary points. Indicates the isolation zone number The ordinates of the boundary points. Indicates the floor function; If we consider the isolation zone corresponding to the disaster control strategy as a multi-connected component, i.e. a polygon group, then we can arbitrarily set the arrangement order of each connected component, and then concatenate the variables contained in each connected component according to the set arrangement order to obtain the decision variables of the disaster control strategy.

[0049] S2: Conduct a multi-dimensional evaluation of the isolation zone corresponding to the decision variables of the disaster control strategy to obtain the corresponding evaluation parameters; specifically: Using a forest fire spread and control framework based on discrete differential equations to determine the decision variables for disaster control strategies. Corresponding isolation zone Conduct multi-dimensional assessments to obtain parameters for assessing economic and casualty losses in the disaster-stricken areas. Total construction cost assessment parameters for the isolation zone Minimum construction speed assessment parameters for the isolation zone .

[0050] S3: Construct the objective function by weighting all evaluation parameters and set constraints; The objective function is constructed by weighting the parameters for assessing economic and casualty losses in the disaster-stricken area, the total construction cost of the firebreak, and the minimum construction speed of the firebreak:

[0051] In the formula, Describe the objective function. Indicates the first One evaluation parameter, Indicates the first The relative importance coefficients corresponding to each evaluation parameter , , ; The constraints are set according to disaster relief needs. If the deployed firebreak needs to surround bounded habitats so that the final disaster-stricken area does not cover the habitats, then the constraints are:

[0052] If the isolation zone needs to surround the ultimately bounded disaster area so that the ultimately bounded disaster area does not cover the habitat, then the constraint is:

[0053] In the formula, Represents the area function. Indicates habitat, Indicates the final affected area. Indicates a separation zone on a plane. The isolated bounded connected component, and These represent the intersection and difference operations for two-dimensional geometric objects, respectively.

[0054] S4: Rewrite the objective function and constraints to obtain the unconstrained optimization problem of disaster control strategy; specifically: Rewrite each constraint as follows:

[0055] Combining constraints to rewrite the set:

[0056] The constrained nonlinear optimization problem of disaster control strategy is as follows:

[0057] The constrained nonlinear optimization problem of the above disaster control strategy is transformed into an unconstrained optimization problem of the disaster control strategy:

[0058] In the formula, The augmented Lagrangian function represents the function of a constrained nonlinear optimization problem. This represents the optimized variable after transformation. Represents the Lagrange multiplier vector. , Indicates the rewritten first... The Lagrange multipliers corresponding to each constraint condition; Specifically, the augmented Lagrangian function for the constrained nonlinear optimization problem is:

[0059] In the formula, The Lagrangian function represents the constrained nonlinear optimization problem. Indicates the penalty coefficient. It is a 2-norm, and because:

[0060] Then we have:

[0061]

[0062]

[0063] In the formula, express exist gradient on, express exist The gradient on.

[0064] S5: Solve the unconstrained optimization problem of disaster control strategy using the improved response surface methodology to obtain the local optimum solution of the unconstrained optimization problem; such as... Figure 2 As shown, the specific method is as follows: S5.1: Initial feasible solution of the constrained nonlinear optimization problem for selecting a disaster control strategy Initialize the Lagrange multiplier vector The initial solution to the unconstrained optimization problem of disaster control strategy is obtained by piecing them together. Set error threshold ; S5.2: Set sampling radius In the For the center of the ball, radius Random sampling within a closed sphere There are points, and the set of sampling points is... And calculate the response value corresponding to each sampling point to obtain the response value set. ; S5.3: Construct an initial solution based on the set of sampling points and the set of response values. An improved response surface model was developed; the specific method is as follows: S5.3.1: Construct the initial first-order basis function set and calculate the initial first-order basis matrix corresponding to the sample point set; specifically: The initial set of first-order basis functions is denoted as ,in:

[0065] The initial first-order basis matrix is:

[0066] In the formula, Denotes the first in the initial set of first-order basis functions. One first-order basis function Indicates the floor function; initializes the first-order basis matrix. The Middle Liede row elements Recorded as ; S5.3.2: Based on the initial first-order basis matrix, construct an improved first-order basis function set and calculate the improved first-order basis matrix corresponding to the sample point set; specifically: Establish a mixed-integer programming problem:

[0067] in, These are the first and second parameter sets of the response surface model, respectively. , Indicates the positive penalty coefficient. Represents the second parameter set of the response surface model. Parameters Whether a value is non-zero is defined as follows:

[0068] Solving the mixed-integer programming problem using the branch and bound method yields the specific values ​​of the first parameter of the response surface model. Specific values ​​of the second parameter set According to the above and Obtain the initial solution Improved first-order basis function set at the location And the improved first-order basis matrix corresponding to the set of sampling points. , Represents the second parameter set of the response surface model. The specific value of each element; S5.3.3: Based on the improved first-order basis function set, construct the initial second-order basis function set, and calculate the initial second-order basis matrix corresponding to the sampling point set; specifically: Improved first-order basis function set The initial set of second-order basis functions is obtained by multiplying and combining the basis functions pairwise:

[0069] Further calculate the initial second-order basis matrix corresponding to the set of sampling points:

[0070] In the formula, Denotes the initial set of second-order basis functions The number of elements in To make the set of sampling points the sampling points Substitute the basis functions into the initial second-order basis function set. The obtained value is denoted as . ; S5.3.4: Based on the initial second-order basis matrix, construct the improved second-order basis function set and calculate the improved second-order basis matrix corresponding to the sampling point set; specifically: Establish a mathematical programming problem:

[0071] In the formula, This represents the third parameter set of the response surface model. express The number of non-zero elements in the middle; The proximal gradient descent method is used to solve the mathematical programming problem, and the specific values ​​of the third parameter set of the response surface model are obtained. According to the above Obtain the initial solution Improved second-order basis function set at the location And the improved second-order basis matrix corresponding to the set of sampling points. In the formula, This represents the basis functions in the initial second-order basis function set corresponding to the third parameter set of the response surface model. The parameter values; S5.3.5: Construct the initial solution based on the improved first-order basis matrix and the improved second-order basis matrix corresponding to the sampling point set. Improved response surface model at the location:

[0072] In the formula, Indicates the initial solution An improved response surface model for [the location].

[0073] S5.4: Based on the initial solution An improved response surface model is used to establish the optimization problem of the improved response surface. A nonlinear optimization algorithm is then used to solve the optimization problem of the improved response surface, obtaining the local optimum solution of the improved response surface at the initial solution. ; S5.5: If Then the local optimum of the improved response surface at the initial solution will be obtained. As a local optimum of the unconstrained optimization problem; otherwise, as a local optimum of the improved response surface at the initial solution. As a new initial solution, repeat steps S5.2-5.5.

[0074] S6: Based on the local optimal solution of the unconstrained optimization problem, calculate the global optimal solution of the unconstrained optimization problem using the trust technique; for example... Figure 3 As shown, the specific method is as follows: S6.1: Establish a nonlinear dynamic system for the unconstrained optimization problem of disaster control strategies:

[0075] In the formula, Represents the optimized variables after transformation Regarding time variables The derivative, The augmented Lagrangian function represents the function of a constrained nonlinear optimization problem. express The transformed optimization variables gradient on; Each local optimum of the unconstrained optimization problem (1.2) of disaster control strategy corresponds to a stable equilibrium point of the nonlinear dynamic system (3.1). At each local optimum of the unconstrained optimization problem of disaster control strategy, by replacing the augmented Lagrangian function with the corresponding response surface model, the transformation form of the nonlinear dynamic system is as follows:

[0076] In the formula, Represents the optimized variables after transformation Regarding time variables The derivative, The response surface model represents the local optimum solution of the unconstrained optimization problem of disaster control strategy. express The transformed optimization variables gradient on; S6.2: The set of stable equilibrium points of the nonlinear dynamical system (3.1) is denoted as... Initialized to The set of tier-0 stable equilibrium points of the nonlinear dynamical system (3.1) is denoted as... Initialized to The set of tier-1 stable equilibrium points of the nonlinear dynamical system (3.1) is denoted as... Initialized to The set of response surface models is denoted as Initialized to ; S6.3: Randomly select an initial feasible solution to the unconstrained optimization problem of disaster control strategy, calculate a local optimum and its response surface model using the method in step S5, and add them to the tier-0 stable equilibrium point set. and response surface model set middle; S6.4: From the set of tier-0 stable equilibrium points Arbitrarily select a stable equilibrium point of the nonlinear dynamic system (3.1). From the set of response surface models Extract the corresponding response surface model Update the set of stable equilibrium points for tier-0, making The stable equilibrium point to be selected From the set Delete; update the set of stable equilibrium points, let The stable equilibrium point to be selected Add to collection In the middle; calculate the transformation form of a nonlinear dynamic system at the stable equilibrium point. Hessian matrix and its eigenvector set ,in:

[0077] in, Representing the response surface model The transformed optimization variables The Hessian matrix on, i.e. about The second-order partial derivative; according to Calculate the Hessian matrix eigenvalue set , Represents the Hessian matrix The Each feature value; then based on Calculate the Hessian matrix Feature vector set , Represents the Hessian matrix The eigenvalues eigenvectors; S6.5: From the set of eigenvectors Select a feature vector Update the feature vector set, let The feature vector to be selected From the set Delete from middle; with For the search direction, with step size Sampling yields point series , point column For a line far from a stable equilibrium point And it points to another stable equilibrium point. Stability region boundary The search path; S6.6: Determine the point sequence With the boundary of the stable region Do they intersect? If the point sequence If the objective function value consistently increases, it is determined that there are no intersection points, and the process returns to S6.5 to select a new feature vector; if the point sequence If the objective function value changes from increasing to decreasing, then an intersection point is determined to exist, and step S6.7 is executed; S6.7: Continue forward 0.1 The arrival point is defined as the escape point. From the escape point Starting from this point, we use the method in step S5 to calculate another stable equilibrium point of the nonlinear dynamic system. and its response surface model ; S6.8: Determining the Stable Equilibrium Point Is it in the set? In the middle; if Return to S6.5 and select a new feature vector; if Then the stable equilibrium point will be and its response surface model Add the tier-1 stable equilibrium point set respectively and response surface model set In the middle, proceed to step S6.9; S6.9: Repeat steps S6.5-S6.8 until the feature vector set is reached. ; S6.10: Repeat steps S6.4-S6.9 until the set of stable tier-0 equilibrium points is reached. ; S6.11: Determine the set of stable equilibrium points in Tier-1 Is it an empty set? If Let the set of stable equilibrium points of tier-1 be taken as the set of stable equilibrium points of tier-0, that is, let And clear the set of stable equilibrium points in tier-1, that is, let Return to S6.4 and select a stable equilibrium point; if Proceed to step S6.12; S6.12: From the set of stable equilibrium points Identify the global optimal solution to the unconstrained optimization problem. ,in, This represents the optimal variable after the transformation. These represent the decision variables for the optimal disaster control strategy. This represents the optimal Lagrange multiplier vector.

[0078] S7: Use the global optimal solution of the unconstrained optimization problem as the optimal strategy for disaster control to complete the construction planning of the firebreak; specifically: By utilizing the dynamic simulation function of the forest fire spread and control framework based on discrete differential equations, the decision variables of the optimal disaster control strategy in the global optimal solution of the unconstrained optimization problem are transformed into the optimal disaster control strategy, thus completing the construction planning of firebreaks.

[0079] Example 3 This embodiment provides a disaster control strategy optimization system based on improved response surface and trust technologies, such as Figure 4 As shown, it includes: The decision variable construction module is used to obtain the location coordinates of each boundary point of the isolation zone and construct the decision variables for disaster control strategies. The decision variable evaluation module is used to evaluate the isolation zone corresponding to the decision variables of disaster control strategies from multiple dimensions and obtain the corresponding evaluation parameters. The objective function construction module is used to construct the objective function by weighting all evaluation parameters and setting constraints. The unconstrained optimization problem construction module is used to rewrite the objective function and constraints to obtain the unconstrained optimization problem of disaster control strategy; The local optimum solution module is used to solve the unconstrained optimization problem of disaster control strategy using the improved response surface method, and obtain the local optimum solution of the unconstrained optimization problem; The global optimal solution module is used to calculate the global optimal solution of an unconstrained optimization problem based on the local optimal solution of the unconstrained optimization problem, and uses trust techniques. The disaster control strategy planning module is used to take the global optimal solution of the unconstrained optimization problem as the optimal disaster control strategy and complete the construction planning of the isolation zone.

[0080] The same or similar labels correspond to the same or similar parts; The terms used to describe positional relationships in the accompanying drawings are for illustrative purposes only and should not be construed as limiting this patent. Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the implementation of the present invention. Those skilled in the art can make other variations or modifications based on the above description. It is neither necessary nor possible to exhaustively describe all embodiments here. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the claims of the present invention.

Claims

1. A disaster control strategy optimization method based on improved response surface methodology and trust technology, characterized in that, include: S1: Obtain the coordinates of each boundary point of the isolation zone to construct the decision variables for disaster control strategies; S2: Conduct a multi-dimensional evaluation of the isolation zone corresponding to the decision variables of the disaster control strategy to obtain the corresponding evaluation parameters; S3: Construct the objective function by weighting all evaluation parameters and set constraints; S4: Rewrite the objective function and constraints to obtain the unconstrained optimization problem of disaster control strategy; S5: Solve the unconstrained optimization problem of disaster control strategy using the improved response surface methodology to obtain the local optimum solution of the unconstrained optimization problem. Specific methods include: S5.1: Initial feasible solution of the constrained nonlinear optimization problem for selecting a disaster control strategy Initialize the Lagrange multiplier vector The initial solution to the unconstrained optimization problem of disaster control strategy is obtained by piecing them together. Set error threshold ; S5.2: Set sampling radius In the For the center of the ball, radius Random sampling within a closed sphere There are points, and the set of sampling points is... And calculate the response value corresponding to each sampling point to obtain the response value set. ; S5.3: Construct an initial solution based on the set of sampling points and the set of response values. The improved response surface model is as follows: S5.3.1: Construct the initial first-order basis function set and calculate the initial first-order basis matrix corresponding to the sample point set; specifically: The initial set of first-order basis functions is denoted as ,in: The initial first-order basis matrix is: In the formula, Denotes the first in the initial set of first-order basis functions. One first-order basis function Indicates the floor function; initializes the first-order basis matrix. Middle Liede row elements Recorded as ; S5.3.2: Based on the initial first-order basis matrix, construct an improved first-order basis function set and calculate the improved first-order basis matrix corresponding to the sample point set; specifically: Establish a mixed-integer programming problem: in, These are the first and second parameter sets of the response surface model, respectively. , Indicates the positive penalty coefficient. Represents the second parameter set of the response surface model. Parameters Whether a value is non-zero is defined as follows: Solving the mixed-integer programming problem using the branch and bound method yields the specific values ​​of the first parameter of the response surface model. Specific values ​​of the second parameter set According to the above and Obtain the initial solution Improved first-order basis function set at the location And the improved first-order basis matrix corresponding to the set of sampling points. , Represents the second parameter set of the response surface model. The specific value of each element; S5.3.3: Based on the improved first-order basis function set, construct the initial second-order basis function set, and calculate the initial second-order basis matrix corresponding to the sampling point set; specifically: Improved first-order basis function set The initial set of second-order basis functions is obtained by multiplying and combining the basis functions pairwise: Further calculate the initial second-order basis matrix corresponding to the set of sampling points: In the formula, Denotes the initial set of second-order basis functions The number of elements in To make the set of sampling points the sampling points Substitute the basis functions into the initial second-order basis function set. The obtained value is denoted as . ; S5.3.4: Based on the initial second-order basis matrix, construct the improved second-order basis function set and calculate the improved second-order basis matrix corresponding to the sampling point set; specifically: Establish a mathematical programming problem: In the formula, This represents the third parameter set of the response surface model. express The number of non-zero elements in the neutron; The proximal gradient descent method is used to solve the mathematical programming problem, and the specific values ​​of the third parameter set of the response surface model are obtained. According to the above Obtain the initial solution Improved second-order basis function set at the location And the improved second-order basis matrix corresponding to the set of sampling points. In the formula, This represents the basis functions in the initial second-order basis function set corresponding to the third parameter set of the response surface model. The parameter values; S5.3.5: Construct the initial solution based on the improved first-order basis matrix and the improved second-order basis matrix corresponding to the sampling point set. Improved response surface model at the location: In the formula, Indicates the initial solution Improved response surface model at the location; S5.4: Based on the initial solution An improved response surface model is used to establish the optimization problem of the improved response surface. A nonlinear optimization algorithm is then used to solve the optimization problem of the improved response surface, obtaining the local optimum solution of the improved response surface at the initial solution. ; S5.5: If Then the local optimum of the improved response surface at the initial solution will be obtained. As a local optimum of the unconstrained optimization problem; otherwise, as a local optimum of the improved response surface at the initial solution. As a new initial solution, repeat steps S5.2-S5.5; S6: Based on the local optimal solution of the unconstrained optimization problem, the global optimal solution of the unconstrained optimization problem is calculated using the trust technique; S7: Use the global optimal solution of the unconstrained optimization problem as the optimal strategy for disaster control to complete the construction planning of the isolation zone.

2. The disaster control strategy optimization method based on improved response surface methodology and trust technology according to claim 1, characterized in that, The specific method for step S1 is as follows: Obtain the coordinates of each boundary point of the firebreak, arrange the coordinates of each boundary point in counterclockwise order, and form the decision variables for the disaster control strategy. In the formula, The decision variables representing disaster control strategies, and These represent the isolation zones. The x and y coordinates of the boundary points. Indicates the isolation zone number The ordinates of the boundary points. This indicates the floor function.

3. The disaster control strategy optimization method based on improved response surface methodology and trust technology according to claim 2, characterized in that, The specific method for step S2 is as follows: Using a forest fire spread and control framework based on discrete differential equations to determine the decision variables for disaster control strategies. Corresponding isolation zone Conduct multi-dimensional assessments to obtain parameters for assessing economic and casualty losses in the disaster-stricken areas. Total construction cost assessment parameters for the isolation zone Minimum construction speed assessment parameters for the isolation zone .

4. The disaster control strategy optimization method based on improved response surface methodology and trust technology according to claim 3, characterized in that, The specific method for step S3 is as follows: The objective function is constructed by weighting the parameters for assessing economic and casualty losses in the disaster-stricken area, the total construction cost of the firebreak, and the minimum construction speed of the firebreak: In the formula, Describe the objective function. Indicates the first One evaluation parameter, Indicates the first The relative importance coefficients corresponding to each evaluation parameter , , ; The constraints are set according to disaster relief needs. If the deployed firebreak needs to surround bounded habitats so that the final disaster-stricken area does not cover the habitats, then the constraints are: If the isolation zone needs to surround the ultimately bounded disaster area so that the ultimately bounded disaster area does not cover the habitat, then the constraint is: In the formula, Represents the area function. Indicates habitat, Indicates the final affected area. Indicates a separation zone on a plane. The isolated bounded connected component, and These represent the intersection and difference operations for two-dimensional geometric objects, respectively.

5. The disaster control strategy optimization method based on improved response surface methodology and trust technology according to claim 4, characterized in that, The specific method for step S4 is as follows: Rewrite each constraint as follows: Combining constraints to rewrite the set: The constrained nonlinear optimization problem of disaster control strategy is as follows: The constrained nonlinear optimization problem of the above disaster control strategy is transformed into an unconstrained optimization problem of the disaster control strategy: In the formula, The augmented Lagrangian function represents the function of a constrained nonlinear optimization problem. This represents the optimized variable after transformation. Represents the Lagrange multiplier vector. , Indicates the rewritten first... The Lagrange multipliers corresponding to each constraint condition; Specifically, the augmented Lagrangian function for the constrained nonlinear optimization problem is: In the formula, The Lagrangian function represents the constrained nonlinear optimization problem. Indicates the penalty coefficient. It is a 2-norm, and because: Then we have: In the formula, express exist gradient on, express exist The gradient on.

6. The disaster control strategy optimization method based on improved response surface methodology and trust technology according to claim 5, characterized in that, The specific method for step S6 is as follows: S6.1: Establish a nonlinear dynamic system for the unconstrained optimization problem of disaster control strategies: In the formula, Represents the optimized variables after transformation Regarding time variables The derivative of The augmented Lagrangian function represents the function of a constrained nonlinear optimization problem. express The transformed optimization variables gradient on; Each local optimum of the unconstrained optimization problem (1.2) of disaster control strategy corresponds to a stable equilibrium point of the nonlinear dynamic system (3.1). At each local optimum of the unconstrained optimization problem of disaster control strategy, by replacing the augmented Lagrangian function with the corresponding response surface model, the transformation form of the nonlinear dynamic system is as follows: In the formula, Represents the optimized variables after transformation Regarding time variables The derivative of The response surface model represents the local optimum solution of the unconstrained optimization problem of disaster control strategy. express The transformed optimization variables gradient on; S6.2: The set of stable equilibrium points of the nonlinear dynamical system (3.1) is denoted as... Initialized to The set of tier-0 stable equilibrium points of the nonlinear dynamical system (3.1) is denoted as... Initialized to The set of tier-1 stable equilibrium points of the nonlinear dynamical system (3.1) is denoted as... Initialized to The set of response surface models is denoted as Initialized to ; S6.3: Randomly select an initial feasible solution to the unconstrained optimization problem of disaster control strategy, calculate a local optimum and its response surface model using the method in step S5, and add them to the tier-0 stable equilibrium point set. and response surface model set middle; S6.4: From the set of tier-0 stable equilibrium points Arbitrarily select a stable equilibrium point of the nonlinear dynamic system (3.1). From the set of response surface models Extract the corresponding response surface model Update the set of stable equilibrium points for tier-0, making The stable equilibrium point to be selected From the set Delete; update the set of stable equilibrium points, let The stable equilibrium point to be selected Add to collection In the middle; calculate the transformation form of a nonlinear dynamic system at the stable equilibrium point. Hessian matrix and its eigenvector set ,in: in, Representing the response surface model The transformed optimization variables The Hessian matrix on, i.e. about The second-order partial derivative; according to Calculate the Hessian matrix eigenvalue set , Represents the Hessian matrix The Each feature value; then based on Calculate the Hessian matrix Feature vector set , Represents the Hessian matrix The eigenvalues eigenvectors; S6.5: From the set of eigenvectors Select a feature vector Update the feature vector set, let The feature vector to be selected From the set Delete from middle; with For the search direction, with step size Points were obtained by sampling , point column For a line far from a stable equilibrium point And it points to another stable equilibrium point. Stability region boundary The search path; S6.6: Determine the point sequence With the boundary of the stable region Do they intersect? If the point sequence If the objective function value consistently increases, it is determined that there are no intersection points, and the process returns to S6.5 to select a new feature vector; if the point sequence If the objective function value changes from increasing to decreasing, then an intersection point is determined to exist, and step S6.7 is executed; S6.7: Continue forward 0.1 The arrival point is defined as the escape point. From the escape point Starting from this point, we use the method in step S5 to calculate another stable equilibrium point of the nonlinear dynamic system. and its response surface model ; S6.8: Determining the Stable Equilibrium Point Is it in the set? In the middle; if Return to S6.5 and select a new feature vector; if Then the stable equilibrium point will be and its response surface model Add the tier-1 stable equilibrium point set respectively and response surface model set In the middle, proceed to step S6.9; S6.9: Repeat steps S6.5-S6.8 until the feature vector set is reached. ; S6.10: Repeat steps S6.4-S6.9 until the set of stable tier-0 equilibrium points is reached. ; S6.11: Determine the set of stable tier-1 equilibrium points Is it an empty set? If Let the set of stable equilibrium points of tier-1 be taken as the set of stable equilibrium points of tier-0, that is, let And clear the set of stable equilibrium points in tier-1, that is, let Return to S6.4 and select a stable equilibrium point; if Proceed to step S6.12; S6.12: From the set of stable equilibrium points Identify the global optimal solution to the unconstrained optimization problem. ,in, This represents the optimal variable after the transformation. These represent the decision variables for the optimal disaster control strategy. This represents the optimal Lagrange multiplier vector.

7. The disaster control strategy optimization method based on improved response surface methodology and trust technology according to claim 6, characterized in that, The specific method for step S7 is as follows: By utilizing the dynamic simulation function of the forest fire spread and control framework based on discrete differential equations, the decision variables of the optimal disaster control strategy in the global optimal solution of the unconstrained optimization problem are transformed into the optimal disaster control strategy, thus completing the construction planning of firebreaks.

8. A disaster control strategy optimization system based on improved response surface methodology and trust technology, implementing the method described in any one of claims 1-7, characterized in that, include: The decision variable construction module is used to obtain the location coordinates of each boundary point of the isolation zone and construct the decision variables for disaster control strategies. The decision variable evaluation module is used to evaluate the isolation zone corresponding to the decision variables of disaster control strategies from multiple dimensions and obtain the corresponding evaluation parameters. The objective function construction module is used to construct the objective function by weighting all evaluation parameters and setting constraints. The unconstrained optimization problem construction module is used to rewrite the objective function and constraints to obtain the unconstrained optimization problem of disaster control strategy; The local optimum solution module is used to solve the unconstrained optimization problem of disaster control strategy using the improved response surface method, and obtain the local optimum solution of the unconstrained optimization problem; The global optimal solution module is used to calculate the global optimal solution of an unconstrained optimization problem based on the local optimal solution of the unconstrained optimization problem, and uses trust techniques. The disaster control strategy planning module is used to take the global optimal solution of the unconstrained optimization problem as the optimal disaster control strategy and complete the construction planning of the isolation zone.

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