A drone-based emergency supplies delivery method considering thermal smoke risk and timeliness of rescue.

Abstract

This invention discloses a drone-based emergency supply delivery method that considers both dynamic thermal smoke risk and timely rescue effectiveness. The invention considers two factors: dynamic thermal smoke risk and timely rescue effectiveness. It constructs objective functions to minimize the cumulative dynamic thermal smoke risk and maximize the timely rescue effectiveness, respectively, and transforms the dual-objective model into a single-objective optimization model using marginal equilibrium theory. The single-objective optimization model is then solved, using Chebyshev chaotic mapping to generate the initial population positions; adaptive search coefficients are calculated; and the position of each individual is updated using the first-order gradient and Hessian matrix. Simultaneously, a sine-cosine perturbation mechanism is introduced to enhance the flexibility of the search direction; a trap avoidance operator is introduced, and random perturbations are introduced into the updated individual positions. Finally, the individual positions and the output optimal solution are updated. This invention offers lower delivery path risk, higher rescue effectiveness, and faster convergence speed, providing a reference for drone-based emergency supply delivery in mountainous fire areas.

Description

Technical Field

[0001] This invention belongs to the field of safety and emergency management technology, specifically relating to a drone-based emergency supplies delivery method that considers both thermal smoke risk and timeliness of rescue. Background Technology

[0002] Against the backdrop of global climate change, mountain fires are frequent and their spread is complex. The high mountains and deep valleys, along with the dynamic changes in fire intensity and weather, often lead to ground transportation disruptions, inefficient traditional material delivery methods, and extremely high personnel safety risks. The "last mile" delivery challenge of emergency supplies has become a key bottleneck restricting the effectiveness of mountain fire rescue. The rapid iteration of drone technology has provided a new solution for emergency material delivery in mountain fires. However, in actual firefield applications, it still faces challenges from complex environments such as high temperatures, dense smoke, and dynamic changes in fire intensity, as well as the shortcomings of traditional path planning algorithms in obstacle avoidance and target optimization, resulting in lagging delivery route planning and low delivery accuracy and safety. Therefore, research on drone-based emergency material delivery methods in mountain fire environments is of significant practical importance for improving the drone emergency rescue technology system and building an integrated air-ground mountain disaster emergency support system.

[0003] To address the path planning problem for drones in complex disaster environments, scholars both domestically and internationally have conducted extensive research at the model building and algorithm levels. Regarding model building, mountain fire scenarios are characterized by complex environments and dynamically changing obstacles, further increasing the difficulty of path planning. At the algorithm level, path planning algorithms can be broadly categorized into three types based on their principles: traditional search and sampling algorithms, intelligent optimization, and learning-driven algorithms. However, in three-dimensional complex, dynamically risky, and multi-constraint coupled scenarios such as mountain fires, these algorithms are prone to getting trapped in local optima, exhibiting slow convergence, and weak robustness.

[0004] To address the challenges of transporting supplies due to the complex terrain and dynamic spread of fires in mountainous areas, and to further improve the efficiency of emergency supply delivery, this invention optimizes the UAV emergency supply delivery method based on mountain fire model construction and route planning algorithm design. This invention effectively balances fire risk avoidance and emergency rescue timeliness, overcoming the limitations of traditional methods. First, a target model is constructed that minimizes the cumulative dynamic heat and smoke risk while maximizing the timeliness of rescue. Second, Newton-Raphson optimization (NRBO) is introduced into the UAV emergency supply route planning to solve the target model. Finally, a multi-strategy improved NRBO route planning algorithm is proposed based on NRBO, improving the model's solution accuracy and convergence speed through three major improvements: initial parameter solution, initial population optimization, and search direction. Compared to the traditional NRBO method, this invention offers lower delivery path risk, higher rescue efficiency, and faster convergence speed, providing a reference for UAV emergency supply delivery in mountainous fire areas. Summary of the Invention

[0005] To address the aforementioned problems and solve the difficulties in transporting supplies caused by the complex terrain and dynamic spread of fires in mountainous areas, this invention optimizes the UAV emergency supply delivery method based on mountainous fire model construction and route planning algorithm design. It proposes a UAV emergency supply delivery method that considers both thermal smoke risk and timely rescue effectiveness. This invention effectively balances fire risk avoidance and emergency rescue timeliness, overcoming the limitations of traditional methods. First, a target model is constructed that minimizes the cumulative dynamic thermal smoke risk and maximizes the timeliness of rescue effectiveness. Second, Newton-Raphson optimization (NRBO) is introduced into the UAV emergency supply route planning to solve the target model. Finally, based on NRBO, a multi-strategy improved NRBO route planning algorithm is proposed, improving the model's solution accuracy and convergence speed through three major improvements: initial parameter solution, initial population optimization, and search direction. Compared to the traditional NRBO method, this invention's method has lower delivery path risk, higher rescue effectiveness, and faster convergence speed, providing a reference for UAV emergency supply delivery in mountainous fires.

[0006] The above objectives are achieved through the following technical solutions:

[0007] The present invention provides a drone-based emergency supplies delivery method that considers both the risk of thermal smoke and the timeliness of rescue efforts. The method includes the following steps:

[0008] S1. Considering the two factors of dynamic hot smoke risk and timely rescue utility, we construct objective functions for minimizing the cumulative dynamic hot smoke risk and maximizing the timely rescue utility, respectively, and use the marginal equilibrium theory to transform the dual objective into a single objective optimization model.

[0009] S2. Solve the single-objective optimization model constructed in step S1, specifically including:

[0010] S2.1. The initial population position is generated using Chebyshev chaotic mapping;

[0011] S2.2. Calculate the adaptive search coefficients;

[0012] S2.3. Based on the current global best individual, update the position of each individual using the first-order gradient and Hessian matrix; at the same time, introduce a sine-cosine perturbation mechanism to enhance the flexibility of the search direction;

[0013] S2.4. A trap avoidance operator is introduced, which introduces random perturbation into the individual position updated in S2.3, thereby generating new individuals and enhancing population diversity;

[0014] S2.5. Update the individual and output the optimal solution.

[0015] Furthermore, the specific implementation method of step S1 is as follows:

[0016] S1.1 Construct the objective function for minimizing the cumulative dynamic thermal smoke risk:

[0017] The risk of hot smoke from mountain fires exhibits dynamic characteristics in time and space. The total path risk is a weighted cumulative sum of the risk density and length of each flight segment, directly reflecting the risk cost of the UAV's entire flight. The objective function is: in, This represents the drone's flight segment, where w is the current node and v is the next node; Indicates the entire path; Represents the flight segment at time t Dynamic thermal smoke risk density; Indicates flight segment The three-dimensional Euclidean flight distance; This represents the total cumulative cost of thermal smoke risk throughout the entire path;

[0018] S1.2 Construct the objective function to maximize the effectiveness of timely rescue:

[0019] Considering the short golden rescue window in mountain fires, an exponentially decaying rescue utility function is constructed, taking into account both material priority and delivery timeliness, and the following objective function is established: in, This represents the priority weight of the materials at demand point k. This represents the actual time it takes for the drone to arrive at the demand point k; This represents the attenuation coefficient of fire rescue effectiveness; This represents the total relief effectiveness of emergency supplies, where n represents the total number of supply demand points;

[0020] S1.3 Single-objective optimization model construction:

[0021] The two objective functions constructed in S1.1 and S1.2 have conflicting optimization directions and inconsistent dimensions. To avoid the subjective defects of fuzzy membership functions, marginal equilibrium theory is introduced, treating rescue utility as marginal benefit and thermal smoke risk as marginal cost. The two objective functions are merged and transformed by minimizing the equilibrium deviation. Marginal rescue utility is the increase in utility brought about by the reduction in unit time; marginal risk cost is the additional risk per unit delivery time. Unifying the dimensions facilitates equilibrium comparison. in, Indicates the total delivery time by drone; This represents the marginal cost of hot smoke risk;

[0022] Differentiate the objective function for maximizing the timeliness of rescue effectiveness constructed in S1.2: in, This indicates the marginal utility of seeking assistance;

[0023] The optimal path satisfies the equilibrium relationship between marginal utility and marginal risk. A single-objective model is constructed to minimize the sum of squared deviations from the equilibrium, eliminating the discrepancy between the units and the optimization direction. in, This is the risk aversion coefficient; the higher the value, the greater the emergency command department's preference for flight safety. Indicates the deviation from the single-objective equilibrium; This represents the final single-objective function after synthesis.

[0024] Furthermore, the specific implementation method of step S2.1 is as follows:

[0025] Chebyshev chaotic mapping is represented as: in, The number of chaotic iterations; It represents the i-th individual in the j-th dimension. Chaotic variables in the next chaotic iteration. It represents the i-th individual in the j-th dimension. The chaotic variables of the next chaotic iteration; after mapping the generated chaotic sequence to the search space, the initial position of the individual is obtained: in, and These represent the upper and lower limits of the search position, respectively. This represents the position of the i-th individual in the j-th dimension.

[0026] Furthermore, the specific implementation method of step S2.2 is as follows:

[0027] According to the Newton-Raphson optimization (NRBO) method, the current iteration number m and the maximum iteration number are... Dynamic adjustment The details are as follows: in, This represents the adaptive search coefficient value when the number of iterations is m in the Newton-Raphson optimization. This represents the maximum value of the adaptive search coefficient in Newton-Raphson optimization;

[0028] Next, an adaptive evolutionary strategy based on the covariance matrix is ​​introduced to improve the adaptive ability and convergence stability of the population optimization, resulting in the covariance matrix. The update is as follows: in, The learning rate represents the covariance matrix; This represents the position of the o-th elite individual in the m-th iteration; This represents the average position of elite individuals; Indicates elite weight, This indicates the number of elite individuals in the selection strategy. Let m be the population covariance matrix of the m-th iteration. Let the superscript represent the population covariance matrix of the (m-1)th iteration. This represents the transpose of a matrix.

[0029] Furthermore, the specific implementation method of step S2.3 is as follows:

[0030] The formula for updating the location of an individual is as follows: in, This indicates the individual's position after updating using the Newton-Raphson search rule. Let represent the position vector of the i-th individual in the m-th iteration. Indicates the first-order gradient; Represents the Hessian matrix; represents the inverse of the Hessian matrix; r represents the sine-cosine sway intensity coefficient; The disturbance angle is represented as follows: .

[0031] Furthermore, the specific implementation method of step S2.4 is as follows:

[0032] The perturbation formula is as follows: in, This represents a newly generated individual; Represents a randomly generated number between 0 and 1; This represents the disturbance coefficient. This represents the globally optimal individual position in the m-th iteration.

[0033] Furthermore, the specific implementation method of step S2.5 is as follows:

[0034] Calculate the original individuals separately Update individuals using Newton-Raphson search rules TAO updates individual The fitness value is calculated, and then the best individual is retained. The update formula is as follows: After the update is complete, re-select the globally optimal individual. Where N represents the population size.

[0035] The advantages of this invention compared to the prior art are:

[0036] 1. To address the issues of incomplete consideration of factors and subjective objective function in traditional models, this invention constructs a path planning model that integrates dynamic hot smoke risk field and timely rescue effectiveness. It adopts marginal equilibrium theory to transform the dual objective into a single objective optimization model, effectively avoiding the subjective defects of traditional fuzzy membership functions, while improving scenario adaptability.

[0037] 2. To address the problems of traditional algorithms being prone to getting trapped in local optima, slow convergence, and weak robustness, this invention introduces Newton-Raphson optimization (NRBO) into UAV emergency material route planning to solve the target model, thereby further improving the efficiency of path planning under three-dimensional complexity and dynamic risks.

[0038] 3. To address the shortcomings of Newton-Raphson optimization (NRBO) in terms of solution accuracy and convergence speed, this invention proposes a multi-strategy improved route planning algorithm for NRBO. Through three major improvements—initial parameter solution, initial population optimization, and search direction—the convergence performance and solution accuracy are enhanced. Attached Figure Description

[0039] Figure 1 Flowchart of the method of this invention.

[0040] Figure 2 Results of UAV emergency supply delivery route planning based on the BRBO method.

[0041] Figure 3 Results of UAV emergency supply delivery route planning based on the method of this invention.

[0042] Figure 4 Comparison of the fitness values ​​convergence curves of the two methods with the number of iterations. Detailed Implementation

[0043] The present invention will be further described below with reference to the accompanying drawings and specific examples.

[0044] S1. Model Building:

[0045] In terms of model construction, this invention considers two factors: dynamic thermal smoke risk and timely rescue utility, and constructs objective functions to minimize the cumulative dynamic thermal smoke risk and maximize the timely rescue utility, respectively. The marginal equilibrium theory is used to transform the dual-objective model into a single-objective optimization model, providing an accurate and reliable solution model for the route planning algorithm. The specific implementation is as follows:

[0046] S1.1 Construct the objective function for minimizing the cumulative dynamic thermal smoke risk:

[0047] The risk of hot smoke from mountain fires exhibits dynamic characteristics in time and space. The total path risk is a weighted cumulative sum of the risk density and length of each flight segment, directly reflecting the risk cost of the UAV's entire flight. The objective function is: in, This represents the drone's flight segment, where w is the current node and v is the next node; Indicates the entire path; Represents the flight segment at time t Dynamic thermal smoke risk density; Indicates flight segment The three-dimensional Euclidean flight distance; This represents the total cumulative cost of thermal smoke risk along the entire flight path. The objective function focuses on UAV flight safety, aiming to reduce the cumulative risk value of flight segments, avoid UAVs entering high-risk areas of the fire zone, and ensure the smooth execution of material delivery missions.

[0048] S1.2 Construct the objective function to maximize the effectiveness of timely rescue:

[0049] Considering the short golden rescue window in mountain fires, this invention constructs an exponentially decaying rescue utility function, taking into account both material priority and delivery timeliness, and establishes the following objective function: in, This represents the priority weight of the materials at demand point k; This represents the actual time it takes for the drone to arrive at the demand point k; This represents the attenuation coefficient of fire rescue effectiveness; This represents the total relief utility of emergency supplies, where n represents the total number of points of demand for supplies. The index term reflects the time-dependent decay of relief utility, and the priority weights distinguish the value difference between emergency supplies and general support supplies.

[0050] S1.3 Single-objective optimization model construction:

[0051] The two objective functions mentioned above suffer from conflicting optimization directions and inconsistent dimensions. To avoid the subjective defects of fuzzy membership functions, this invention introduces marginal equilibrium theory, treating rescue utility as marginal revenue and thermal smoke risk as marginal cost. The two objective functions are merged and transformed by minimizing equilibrium deviation. Marginal risk cost represents the additional risk per unit delivery time; a unified dimension facilitates equilibrium comparison. in, Indicates the total delivery time by drone; This represents the marginal cost of thermal smoke risk. Marginal relief utility is the increase in utility resulting from a reduction in time.

[0052] Differentiate the objective function for maximizing the effectiveness of timely rescue: in, This represents the marginal utility of seeking assistance. The optimal path satisfies the equilibrium relationship between marginal utility and marginal risk. A single-objective model is constructed to minimize the sum of squared deviations from the equilibrium, eliminating the discrepancy between the units and the optimization direction. in, This is the risk aversion coefficient; the higher the value, the greater the emergency command department's preference for flight safety. Indicates the deviation from the single-objective equilibrium; This represents the final single-objective function after synthesis. The above formula is the single-objective model to be solved.

[0053] S2. Solve the single-objective optimization model constructed in step S1, specifically including:

[0054] S2.1. Population Initialization

[0055] While traditional random initialization methods are simple to implement, they can easily lead to uneven distribution of individuals, thus affecting population diversity and global search capabilities. To address this issue, this invention employs Chebyshev chaotic mapping to generate initial population positions. Chaotic sequences possess good ergodicity and randomness, enabling them to more fully cover the search space, thereby improving the quality of population initialization.

[0056] Chebyshev chaotic mapping is represented as: in, The number of chaotic iterations; It represents the i-th individual in the j-th dimension. Chaotic variables in the next chaotic iteration. It represents the i-th individual in the j-th dimension. The chaotic variables of the next chaotic iteration; after mapping the generated chaotic sequence to the search space, the initial position of the individual is obtained: in, and These represent the upper and lower limits of the search position, respectively. This represents the position of the i-th individual in the j-th dimension. This method improves the uniformity of the initial population distribution, enhances the algorithm's global search capability, and provides better initial conditions for subsequent path optimization.

[0057] S2.2. Calculate the adaptive search coefficients;

[0058] According to the Newton-Raphson optimization (NRBO) method, the current iteration number m and the maximum iteration number are... Dynamic adjustment The details are as follows: in, This represents the adaptive search coefficient value when the number of iterations is m in the Newton-Raphson optimization. This represents the maximum value of the adaptive search coefficient in Newton-Raphson optimization;

[0059] Next, an adaptive evolutionary strategy based on the covariance matrix is ​​introduced to improve the adaptive ability and convergence stability of the population optimization, resulting in the covariance matrix. The update is as follows: in, The learning rate represents the covariance matrix; This represents the position of the o-th elite individual in the m-th iteration; This represents the average position of elite individuals; Indicates elite weight, This indicates the number of elite individuals in the selection strategy. Let m be the population covariance matrix of the m-th iteration. Let the superscript represent the population covariance matrix of the (m-1)th iteration. This represents the transpose of a matrix.

[0060] S2.3. Using the current globally optimal individual as a benchmark, update the position of each individual using the first-order gradient and the Hessian matrix; simultaneously, introduce a sine-cosine perturbation mechanism to enhance the flexibility of the search direction and avoid local optima caused by a single search direction. The formula for updating the individual's position is as follows: in, This indicates the individual's position after updating using the Newton-Raphson search rule. Let represent the position vector of the i-th individual in the m-th iteration. Indicates the first-order gradient; Represents the Hessian matrix; represents the inverse of the Hessian matrix; r represents the sine-cosine sway intensity coefficient; The disturbance angle is represented as follows: .

[0061] S2.4. To further avoid getting trapped in local optima, a trap avoidance operator is introduced. A random perturbation is introduced into the individual position updated in S2.3, thereby generating new individuals and enhancing population diversity. The perturbation formula is as follows: in, This represents a newly generated individual; Represents a randomly generated number between 0 and 1; This represents the disturbance coefficient. This represents the globally optimal individual position in the m-th iteration.

[0062] S2.5. Update the individual and output the optimal solution.

[0063] Calculate the original individuals separately Update individuals using Newton-Raphson search rules TAO updates individual The fitness value is calculated, and then the best individual is retained. The update formula is as follows: After the update is complete, re-select the globally optimal individual. Where N represents the population size.

[0064] Simulation experiment:

[0065] To verify the effectiveness of the proposed UAV emergency supply delivery method considering thermal smoke risk and timely rescue efficiency, a simulation experiment was designed. The simulation scenario was emergency supply delivery for a mountain fire, with a fixed emergency base as the take-off and landing point. Six supply demand points were set, with two priority categories: emergency rescue and logistical support. The scenario included a dynamic thermal smoke risk field. The UAV's cruising speed was set to 15 m / s, and the delivery flight time was constrained to 30 minutes. The flight altitude was set to a safety height difference of 50 m above the terrain elevation to avoid collisions. Table 1 lists the information for the six emergency supply demand points, including: number, three-dimensional coordinates, supply priority, risk coefficient, and safe flight altitude. Determining the specific location of each demand point in the three-dimensional space of the mountainous area is the core of UAV path planning. Supply priorities are divided into two categories: high and medium. High priority indicates the need for emergency rescue supplies, and medium priority indicates the need for logistical support supplies. Demand points R1, R2, and R3 are high priority, and demand points R4, R5, and R6 are medium priority. The larger the risk weight coefficient value, the higher the thermal smoke risk around the demand point.

[0066] Two methods are compared: the method of this invention and the traditional Newton-Raphson optimization algorithm (NBRO).

[0067] Table 1: Information on Emergency Supplies Demand Points R1 (500, 300, 320) high 0.9 370 R2 (700, 600, 450) high 0.85 500 R3 (900, 200, 380) high 0.80 540 R4 (1200, 500, 520) middle 0.70 550 R5 (1000, 800, 490) middle 0.75 600 R6 (1400, 300, 410) middle 0.65 460

[0068] Results analysis: Figure 2 The results of drone emergency supply delivery route planning based on the BRBO method are presented. Figure 3 The results of drone emergency supply delivery route planning based on the method of this invention are presented. It can be seen that both methods can successfully plan drone emergency supply delivery routes. Compared with Figure 2, Figure 3 The route is shorter and smoother. It can be seen that the method of this invention ( Figure 3 The planned route is more scientific and reasonable, and can achieve the shortest path.

[0069] Figure 4The convergence results of two algorithms are presented. The graph, with the number of iterations on the horizontal axis and fitness value on the vertical axis, shows the convergence speed and stable accuracy of the two algorithms after convergence. The red curve represents the method of this invention, and the green curve represents the NRBO method. The red curve (the method of this invention) decreases the fastest, reaching stable convergence around 80 iterations, with a final fitness value stabilizing at 0.18. The green curve (NRBO) decreases slowly in the early stages, with smaller fluctuations in the later stages, stabilizing after 140 iterations, and finally reaching a maximum convergence value of 2.97, indicating a tendency to get trapped in local optima. It can be seen that compared to NRBO, the method of this invention improves the convergence speed by 42.86%, possessing faster convergence speed and higher stable accuracy, and can quickly find the global optimum within a limited number of iterations, meeting the real-time requirements of emergency delivery.

Claims

1. A method for emergency material delivery using drones, considering both the risk of thermal smoke and the timeliness of rescue efforts, characterized in that... The method includes the following steps: S1. Considering the two factors of dynamic hot smoke risk and timely rescue utility, we construct objective functions for minimizing the cumulative dynamic hot smoke risk and maximizing the timely rescue utility, respectively, and use the marginal equilibrium theory to transform the dual objective into a single objective optimization model. S2. Solve the single-objective optimization model constructed in step S1, specifically including: S2.

1. The initial population position is generated using Chebyshev chaotic mapping; S2.

2. Calculate the adaptive search coefficients; S2.

3. Based on the current global best individual, update the position of each individual using the first-order gradient and Hessian matrix; at the same time, introduce a sine-cosine perturbation mechanism to enhance the flexibility of the search direction; S2.

4. A trap avoidance operator is introduced, which introduces random perturbation into the individual position updated in S2.3, thereby generating new individuals and enhancing population diversity; S2.

5. Update the individual and output the optimal solution; the specific implementation method of step S1 is as follows: S1.1 Construct the objective function for minimizing the cumulative dynamic thermal smoke risk: The risk of hot smoke from mountain fires exhibits dynamic characteristics in time and space. The total path risk is a weighted cumulative sum of the risk density and length of each flight segment, directly reflecting the risk cost of the UAV's entire flight. The objective function is: in, This represents the drone's flight segment, where w is the current node and v is the next node; Indicates the entire path; Represents the flight segment at time t Dynamic thermal smoke risk density; Indicates flight segment The three-dimensional Euclidean flight distance; This represents the total cumulative cost of thermal smoke risk throughout the entire path; S1.2 Construct the objective function to maximize the effectiveness of timely rescue: Considering the short golden rescue window in mountain fires, an exponentially decaying rescue utility function is constructed, taking into account both material priority and delivery timeliness, and the following objective function is established: in, This represents the priority weight of the materials at demand point k. This represents the actual time it takes for the drone to arrive at the demand point k; This represents the attenuation coefficient of fire rescue effectiveness; This represents the total relief effectiveness of emergency supplies, where n represents the total number of supply demand points; S1.3 Single-objective optimization model construction: The two objective functions constructed in S1.1 and S1.2 have conflicting optimization directions and inconsistent dimensions. To avoid the subjective defects of fuzzy membership functions, marginal equilibrium theory is introduced, treating rescue utility as marginal benefit and thermal smoke risk as marginal cost. The two objective functions are merged and transformed by minimizing the equilibrium deviation. Marginal rescue utility is the increase in utility brought about by the reduction in unit time; marginal risk cost is the additional risk per unit delivery time. Unifying the dimensions facilitates equilibrium comparison. in, Indicates the total delivery time by drone; This represents the marginal cost of hot smoke risk; Differentiate the objective function for maximizing the timeliness of rescue effectiveness constructed in S1.2: in, This indicates the marginal utility of seeking assistance; The optimal path satisfies the equilibrium relationship between marginal utility and marginal risk. A single-objective model is constructed to minimize the sum of squared deviations from the equilibrium, eliminating the discrepancy between the units and the optimization direction. in, This is the risk aversion coefficient; the higher the value, the greater the emergency command department's preference for flight safety. Indicates the deviation from the single-objective equilibrium; This represents the final single-objective function after synthesis.

2. The drone-based emergency supplies delivery method considering thermal smoke risk and timeliness of rescue as described in claim 1, characterized in that, The specific implementation method of step S2.1 is as follows: Chebyshev chaotic mapping is represented as: in, The number of chaotic iterations; It represents the i-th individual in the j-th dimension. Chaotic variables in the next chaotic iteration. It represents the i-th individual in the j-th dimension. The chaotic variables of the next chaotic iteration; after mapping the generated chaotic sequence to the search space, the initial position of the individual is obtained: in, and These represent the upper and lower limits of the search position, respectively. This represents the position of the i-th individual in the j-th dimension.

3. The drone-based emergency supplies delivery method considering thermal smoke risk and timeliness of rescue as described in claim 1, characterized in that, The specific implementation method of step S2.2 is as follows: Based on the Newton-Raphson optimization method, the current iteration number m and the maximum iteration number are... Dynamic adjustment The details are as follows: in, This represents the adaptive search coefficient value when the number of iterations is m in the Newton-Raphson optimization. This represents the maximum value of the adaptive search coefficient in Newton-Raphson optimization; Next, an adaptive evolutionary strategy based on the covariance matrix is ​​introduced to improve the adaptive ability and convergence stability of the population optimization, resulting in the covariance matrix. The update is as follows: in, The learning rate represents the covariance matrix; This represents the position of the o-th elite individual in the m-th iteration; This represents the average position of elite individuals; Indicates elite weight, This indicates the number of elite individuals in the selection strategy. Let m be the population covariance matrix of the m-th iteration. Let the superscript represent the population covariance matrix of the (m-1)th iteration. This represents the transpose of a matrix.

4. The drone-based emergency supplies delivery method considering thermal smoke risk and timeliness of rescue as described in claim 1, characterized in that, The specific implementation method of step S2.3 is as follows: The formula for updating the location of an individual is as follows: in, This indicates the individual's position after updating using the Newton-Raphson search rule. Let represent the position vector of the i-th individual in the m-th iteration. Indicates the first-order gradient; Represents the Hessian matrix; represents the inverse of the Hessian matrix; r represents the sine-cosine sway intensity coefficient; The disturbance angle is represented as follows: 。 5. The drone-based emergency supplies delivery method considering thermal smoke risk and timeliness of rescue effectiveness according to claim 1, characterized in that, The specific implementation method of step S2.4 is as follows: The perturbation formula is as follows: in, This represents a newly generated individual; Represents a randomly generated number between 0 and 1; This represents the disturbance coefficient. This represents the globally optimal individual position in the m-th iteration.

6. The drone-based emergency supplies delivery method considering thermal smoke risk and timeliness of rescue as described in claim 1, characterized in that, The specific implementation method of step S2.5 is as follows: Calculate the original individuals separately Update individuals using Newton-Raphson search rules TAO updates individual The fitness value is calculated, and then the best individual is retained. The update formula is as follows: After the update is complete, re-select the globally optimal individual. Where N represents the population size.

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