Optimal Collaborative Scheduling of Multi-Aircraft Types for Forest Fires General Aviation Rescue

Abstract

The scheduling of rescue aircraft needs to be studied in depth because of its criticality for the general aviation rescue of forest fires. This paper constructs a collaborative schedule optimization model for general aviation rescue under the condition of multiple aircraft, from multiple rally points to multiple fire points, targeting the shortest rescue time and the lowest rescue cost in the context of forest fires based on the simulation verification of a forest fire that broke out simultaneously in multiple locations in Liangshan Prefecture, Sichuan Province, China. The Non-dominated Sorting Genetic Algorithm II (NSGA-II) algorithm was used to find the optimal set of solutions satisfying the objective function: four feasible solutions. Then, the optimal solution was solved based on the weighted TOPSIS method, which was the optimal solution for this rescue task. The simulation results show that unnecessary flight times can be reduced by optimizing the schedule plan. Under the premise of ensuring rescue timeliness, the utilization rate of rescue aircraft was improved, and rescue costs were further reduced. The presented work provides a theoretical reference for the efficient development of general aviation rescue.

1. Introduction

As the global climate environment continues to deteriorate, forest fire risk increases. It poses a significant threat to the environment and economy and warns us to prioritize forest fire prevention and control in China, home to abundant forest resources [1]. In the past, forest fire fighting in China was mainly based on the tactic of using numerous people. However, due to the high oil content of trees in the southwest region, which is prone to fire, and the ever-changing wind direction in the mountains, rescue personnel may be swallowed up by the sea of fire if they are not careful. For instance, during the Xichang forest fire in 2020, 19 individuals who were involved in firefighting lost their lives, and 3 were injured. This occurred due to unexpected wind shifts, a sudden surge in wind speed, fire spreading through the air, and unsuccessful self-rescue attempts during the rescue operation. The southwestern mountainous areas of China have rugged terrain, steep slopes, and deep valleys, making it challenging for rescue personnel to reach the location. General aviation aircraft have become increasingly popular for forest fire rescue due to their maneuverability, minor terrain restrictions, and rapid response speed [2].

This general aviation rescue issue has attracted widespread attention from domestic and foreign researchers, mainly focusing on the research on the location of emergency facilities [3], scheduling of emergency rescue resources, and optimization of rescue routes [4]. Scholars from various countries have conducted extensive research on scheduling emergency rescue resources in general aviation rescue. Zhou [5] divided the aviation rescue scheduling problem into two levels: strategic and tactical. At the strategic level, he built a combined scheduling model of multiple rescue and disaster points according to the different characteristics of different emergency relief supplies. At the tactical level, he determined each disaster point’s priority and built a real-time scheduling planning model algorithm. Shao et al. [6] established an optimal scheduling model for aviation emergency supplies coordinated by multiple airports, with aircraft performance and material quantity as constraints and transportation time and disaster relief effect as optimization objectives. Li et al. [7] used multiple supply and demand points of civil aviation emergency relief materials and a variety of emergency relief material scheduling resources to establish a multi-objective programming model. They applied a genetic algorithm to solve the optimal material scheduling scheme. Tang et al. [8] established a civil aviation emergency material scheduling model with limited support capacity, considering the limitation of the affected airport’s support capacity on the aircraft’s material carrying capacity. Wu [9] analyzed the operation environment of ground vehicles and airside aircraft under air-to-ground coordination scheduling and then established an air-to-ground coordination emergency scheduling model considering the aircraft’s performance differences in the air-to-ground coordination scheduling process. Zhang et al. [10] proposed the concept of helicopter collaborative rescue from multiple rescue points to multiple resource demand points. They constructed an optimized scheduling model for helicopter collaborative rescue to minimize helicopter configuration time, maximize utility, and maximize demand satisfaction. Liu et al. [11] constructed a many-to-many aircraft scheduling model for navigation rescue scheduling in significant disasters and proposed a genetically simulated annealing hybrid algorithm for the solution. Liu et al. [12] revealed the influence mechanism of uncertainty factors based on the Multi-Agent method and analyzed the task flow based on Discrete Event System (DEVS) method, and they proposed a helicopter maritime search and rescue (MSAR) response plan evaluation framework called UMAD. Zhang et al. [13] considered helicopter performance constraints and meteorological factors, divided the target rescue airspace, combined the speed advantage of helicopters and the convenience of ground vehicles, and proposed an emergency dispatch mode for air-to-ground transportation. Xue [14] proposed a conceptual model of helicopter emergency response dispatch for evaluating the effectiveness of helicopter emergency response dispatch for flood disasters and developed a multi-agent helicopter emergency response dispatch simulation system. Liu [15] constructed a mathematical optimization model for the departure scheduling of a mixed fleet of fixed-wing naval aircraft and naval helicopters, taking the maximum departure time of the fleet and the maximum taxiing time of the fixed-wing aircraft fleet as the optimization objectives and considering the process constraints, space constraints, and resource constraints. Yu et al. [16] proposed a hierarchical optimization method for a hybrid helicopter fleet scheduling scheme (HOMHFSS) for the problem of helicopter fleet scheduling after natural disasters. The scheduling scheme consists of two parts: task allocation and route planning. Song et al. [17] considered earthquakes as a scenario to minimize the total rescue time and rescue cost as the scheduling optimization objective. They constructed a mathematical model with a single rescue point and multiple disaster points, introduced a time window penalty function to measure the urgency of not being in the disaster area, and constructed an optimization model for scheduling emergency material aviation deployment forces.

On 6 August 2023, a wildfire broke out in California, USA. A Riverside County Fire Department helicopter went to the fire scene to deal with the situation. At the same time, another helicopter from the California Fire Department was also dispatched to help extinguish the fire. Two aircraft collided in the air, resulting in the death of three crew members. Therefore, how to make better scheduling decisions for rescue aircraft during forest fire rescue, improve the efficiency of aviation emergency rescue, reduce losses in disaster areas, and ensure people’s safety while ensuring flight safety have become the most critical issues in emergency rescue.

To sum up, most of the existing studies have focused on the scheduling of aviation emergency rescue supplies. Although general aviation rescue aircraft has been recognized as the most advanced and efficient rescue means, more research on rescue aircraft scheduling still needs to be conducted. Among them, there is more research on rescue aircraft scheduling for flood disasters, maritime search and rescue, and other emergencies. At the same time, there is relatively little research on general aviation rescue scheduling for forest fires. Therefore, efficiently scheduling rescue aircraft to extinguish a fire from multiple rally points to multiple fire points is an essential problem to be studied and broken through.

Due to its early stages of development, China’s aviation emergency rescue system has numerous challenges that need to be addressed. These include a weak foundation, technical difficulties, high safety standards, and complex support conditions [18,19]. Aiming at general aviation scheduling, which is a crucial link in forest fire general aviation emergency rescue, this paper focuses on improving the ability of general aviation to fight forest fires. Specifically, this paper provides an in-depth study of the scheduling of emergency rescue operations under multi-aircraft conditions and analyzes the differences in performance of different aircraft types. The innovation of this paper is to propose a collaborative scheduling optimization method for forest fire general aviation rescue under the condition of multi-aircraft types. The contributions of this paper include the following: First, a complex rescue scenario was established, from dispatching rescue aircraft at multiple rally points to participating in multi-cycle fire extinguishing tasks at multiple fire points until the forest fire was extinguished. Then, with the objective of minimizing the total time and total cost spent on the rescue mission when fighting forest fires, a multi-objective optimization model with multiple rally points to multiple fire points was constructed using different aircraft performances as constraints. Taking a forest fire with multiple ignition points in Liangshan Prefecture of Sichuan Province as an example, the NSGA-II algorithm was used to solve the model. Unlike general scheduling optimization studies that only compute the Pareto-optimal solution set [20], this paper used the weighted TOPSIS method to filter the optimal solution from the Pareto-optimal solution set derived by the NSGA-II algorithm. It avoided the situation that the optimal scheduling plan can only be selected by experience in the past. This paper’s work can assist rescuers in quickly selecting the most suitable scheduling plan to carry out complex multi-aircraft collaborative scheduling decisions. It can save significant amounts of time and cost, improve fleet scheduling efficiency, and provide theoretical support and a scientific basis for the development of general aviation rescue strategy.

This paper is structured as follows. First, the existing literature is reviewed in Section 1. The proposed modeling approach is discussed in Section 2, followed by the explanation of the meta-heuristic used in this paper in Section 3. A case study is presented in Section 4. Conclusions and discussions are presented in Section 5.

2. Optimization Model of General Aviation Collaborative Scheduling in Forest Fires under Multi-Aircraft Types Conditions

2.1. Model Description and Assumptions

General aviation rescue flights in forest fires are divided into dispatch flights and firefighting flights [21]. Dispatch flights refer to the process of flying from the home airport to the designated rally point for assembly. Firefighting flights refer to the process of performing firefighting task flights under unified command and schedule after arriving at the rally point [19]. This paper considered several different types of rescue aircraft used during firefighting flights, as well as the different rally points, fire points, and water points available for rescue operations. The rescue aircraft were stationed at different rally points.

In preparation for the firefighting flight, it is essential to have a collaborative scheduling plan for scheduling the rescue aircraft ahead of time. The aim is to organize rescue aircraft to participate in multi-cycle firefighting tasks from the rally point while ensuring that practical constraints are met. This plan will help minimize the total time and cost of the rescue tasks until the forest fire is extinguished.

This paper made the following assumptions before constructing the model to facilitate understanding and improve the operability of calculations:

• When coordinating the scheduling of general aviation rescue aircraft, a multi-to-one approach is used. This means that several rescue aircraft can be sent to the same fire point at the same time to extinguish the fire.
• When carrying out the tasks, the rescue aircraft maintains a constant flight speed through direct flight mode.
• The number and location of aircraft rally, fire, and water points can be determined in advance.
• The number and type of rescue aircraft that can be scheduled at each rally point are determined.
• The amount of water required to extinguish the fire at the fire point can be determined in advance.
• Each rescue aircraft can only rescue one fire point in a cycle.

2.2. Model Description and Assumptions

The definition of the model parameters designed in this paper is shown in

Table 1. Model parameter significance.

Parameters	Significance
$A$	The set of rally points, $a\in A$.
$F$	The set of fire points, $f,f^{\prime }\in F$.
$K$	The set of rescue aircraft, $k\in K$.
$N$	the set of task execution cycles, $n\in N$, $n=1,2\cdot \cdot \cdot \cdot \cdot \cdot ,n_{\max }$.
$Q$	The set of water point, $q\in Q$.
$W$	the set of water required $w_f$ to extinguish all fires.
$T$	The time it takes for the aircraft with the longest task time to complete the task among all rescue aircraft.
$T_k$	The time for aircraft $k$ to execute the entire firefighting task
$t_k^n$	The time for aircraft $k$ to execute the nth cycle of tasks.
$C$	The cost for all aircraft to execute the entire firefighting task.
$c_k^n$	The cost for aircraft $k$ to execute the nth round of tasks.
$x_{{}_{k,a}}^n$	Sub-task 1, a 0-1 variable, where 1 means that aircraft $k$ did not execute a flight task in the nth round, and 0 otherwise.
$x_{{}_{k,a,f}}^n$	Sub-task 2, a 0-1 variable, where 1 means that aircraft $k$ flew from rally point $a$ to fire point $f$ to execute a fire extinguishing task in the nth round, and 0 otherwise.
$x_{{}_{k,f,a}}^n$	Sub-task 3, a 0-1 variable, where 1 means that aircraft $k$ flew from fire point $f$ to rally point $a$ to execute a fire extinguishing task in the nth round, and 0 otherwise.
$x_{{}_{k,f,f}}^n$	Sub-task 4, a 0-1 variable. Aircraft $k$ flies from fire point $f$ to water point $w$ to fetch water after completing the fire extinguishing task in the nth round and then flies back to fire point $f$ to execute the fire extinguishing task, which is 1, otherwise 0.
$x_{{}_{k,f,f^{\prime }}}^n$	Sub-task 5, a 0-1 variable. Aircraft $k$ flies from fire point $f$ to water point $w$ to fetch water after completing the fire extinguishing task in the nth round and then flies back to fire point $f^{\prime }$ to execute the fire extinguishing task, which is 1, otherwise 0.
$d_{a,f}$	The distance from rally point $a$ to fire point $f$.
$d_{f,w}$	The distance from fire point $f$ to water point $w$.
$t_{zb}$	The preparation time for aircraft $k$ to execute tasks from the rally point each time.
$t_w$	The additional time required for aircraft $k$ to fetch and spray water each time.
$r_k$	The flight cost per minute of aircraft $k$ flight.
$m_k$	The fixed cost of aircraft $k$ to execute tasks from the rally point.
$v_k$	The flight speed of aircraft $k$.
$w_k$	The water capacity of aircraft $k$.
$y_k$	The flight fuel consumes per minute of aircraft $k$.
$Y_k$	The maximum fuel capacity of aircraft $k$.

, and the diagram of the five sub-tasks in firefighting flights is shown in Figure 1.

2.3. Model Building

In recent years, general aviation aircraft bucket water spraying has become increasingly popular in China as a crucial method of fighting forest fires. However, relying on a single aircraft is no longer effective in extinguishing large fires. As a result, more efficient fleet bucket firefighting strategies are being implemented in China’s forests. The key to successful firefighting is developing efficient fleet scheduling strategies to minimize the damage caused by fires.

Therefore, this paper analyzed the characteristics of collaborative scheduling of general aviation rescue for forest fires under multi-aircraft types. According to the rules of aircraft bucket firefighting operations, the rescue process was divided into multiple cycles, and the rescue task is divided into five sub-tasks. A multi-aircraft collaborative scheduling optimization model from multiple rally points to multiple fire points was established, with the following objective function:

(1) The total time spent on rescue tasks is minimal. The most important goal of forest fire rescue is to extinguish the fire at the first time, minimizing the threat of fire to forest resources and people’s lives. The key is to optimize the scheduling plan and arrange the optimal rescue target for each rescue aircraft, minimizing the total time of the entire fire extinguishing task while meeting the needs of the fire points.

In this paper, $O_1$ is used to denote the objective function 1, as shown in Equations (1)–(5):

$$O_1=\min T$$

(1)

$$T=\max T_k$$

(2)

$$T_k={\displaystyle \sum _{n=1}^{n_{\max }}{t}_k^n}$$

(3)

$$t_k^n=\left(\frac{d_{a,f}}{v_k}+t_{zb}\right)x_{{}_{k,a,f}}^n+\frac{d_{a,f}}{v_k}{x}_{{}_{k,f,a}}^n+\left(\frac{d_{f,q}+d_{f^{\prime },q}}{v_k}+t_{qm}\right)x_{{}_{k,f,f^{\prime }}}^n+\left(\frac{2d_{f,q}}{v_k}+t_{qm}\right)x_{{}_{k,f,f}}^n$$

(4)

$$n_{\max }=\lceil \frac{The required amount of water for extinguishing the fire}{The maximum total water carrying capacity of a single helicopter in a single cycle}\rceil$$

(5)

(2) The total cost of the rescue mission is minimized. In response to China’s call for energy conservation and emission reduction, the key to reducing rescue costs as much as possible while meeting rescue efficiency is to reduce the number of unnecessary flights. That is, scheduling the minimum number of rescue aircraft from each rally point to extinguish fires at all fire points.

In this paper, $O_2$ is used to denote the objective function 2, as shown in Equations (6)–(8):

$$O_2=\min C$$

(6)

$$C={\displaystyle \sum _{k=1}^K{\displaystyle \sum _{n=1}^{n_{\max }}{C}_k^n}}$$

(7)

$$c_k^n=\left(\frac{d_{a,f}}{v_k}{r}_k+m_k\right)x_{{}_{k,a,f}}^n+\left(\frac{d_{a,f}}{v_k}{x}_{{}_{k,f,a}}^n+\left(\frac{d_{f,q}+d_{f^{\prime },q}}{v_k}+t_{qm}\right)x_{{}_{k,f,f^{\prime }}}^n+\left(\frac{2d_{f,q}}{v_k}+t_{qm}\right)x_{{}_{k,f,f}}^n\right)r_k$$

(8)

And the constraint conditions of the objective function are represented by Equations (9)–(11):

$$x_{{}_{k,a}}^n+x_{{}_{k,a,f}}^n+x_{{}_{k,f,a}}^n+x_{{}_{k,f,f}}^n+x_{{}_{k,f,f^{\prime }}}^n=1$$

(9)

$${\displaystyle \sum _{n=1}^{n_{\max }}{\displaystyle \sum _{k=1}^K\left(x_{{}_{k,a,f}}^n+x_{{}_{k,f,f}}^n\right)}}\ge w_f$$

(10)

$$\frac{d_{a,f}}{v_k}{x}_{{}_{k,a,f}}^1{y}_k+{\displaystyle \sum _{n=2}^{n_{\max }}\left(\frac{d_{a,f}}{v_k}{x}_{{}_{k,a,f}}^n+\frac{d_{a,f}}{v_k}{x}_{{}_{k,f,a}}^n+\left(\frac{d_{f,q}+d_{f^{\prime },q}}{v_k}+t_{qm}\right)x_{{}_{k,f,f^{\prime }}}^n+\left(\frac{2d_{f,q}}{v_k}+t_{qm}\right)x_{{}_{k,f,f}}^n\right)}{y}_k\le Y_k$$

(11)

Equation (9) is a task constraint, indicating that the rescue aircraft can only perform one sub-task per cycle. Equation (10) is a water constraint, indicating that the amount of water transported to each fire point must be greater than the amount of water required by the fire point, ensuring that there is sufficient water to extinguish fires at all fire points. Equation (11) is a maximum fuel constraint that ensures that the fuel consumption of each aircraft for the entire firefighting tasks does not exceed the maximum fuel capacity of that aircraft.

3. Multi-Aircraft Collaborative Scheduling Optimization Model Solving

3.1. NSGA-II Algorithm for Solving the Optimal Solution Set

3.1.1. NSGA-II Algorithm Solution Idea

Existing optimization studies are mainly classified into single-objective optimization and multi-objective optimization. For the problem of scheduling emergency resources under large-scale disasters, time minimization is usually the goal because of the time constraints and heavy tasks [9]. However, the costs incurred by the emergency rescue operation cannot be ignored. Forest fire general aviation rescue should be a multi-objective optimization problem.

There are a variety of algorithms that can be utilized for multi-objective evolution. Some commonly used ones include NSGA-II [22,23], which is based on fast non-dominated sorting, and the Adaptive Weighted sum Genetic Algorithm (AWGA) [24,25], which is based on aggregation. The NSGA-II algorithm has the properties of both fast dominated sorting and elite strategy [26], which increases the sampling space, reduces the algorithm’s complexity, and eliminates the need to manually formulate any more shared parameters [27]. It is one of the most widely used algorithms for multi-objective evolution and is widely used in aviation, logistics, management, and other industries [23,28,29].

Compared with the original NSGA algorithm, the NSGA-II algorithm uses the fast non-dominated sorting method, reducing computational complexity and dramatically reducing computational time. It adopts the elite retention strategy to merge the offspring and parent individuals before non-dominated sorting, which ensures that excellent individuals have a higher probability of being retained. It uses a crowding degree instead of the original fitness sharing strategy to ensure the diversity of individuals in the population. Compared with other metaheuristics, the NSGA-II algorithm possesses better performance and results in solving multi-objective optimization problems. It can explore the search space efficiently, quickly converge to the Pareto-optimal frontier, and provide more high-quality solution sets for decision-makers.

The multi-aircraft collaborative scheduling optimization model established in this paper has two objective functions, which have the characteristics of the multi-objective optimization problem. Therefore, the NSGA-Ⅱ algorithm was selected to solve the above mathematical model and calculate a series of Pareto optimal solution sets.

The specific process of the NSGA-II algorithm is shown in Figure 2.

3.1.2. NSGA-II Algorithm Design

In this paper, the chromosomes were encoded by means of real-number encoding. The specific encoding method was as follows: all the fire points were numbered sequentially to represent chromosome segments. Then, the fire point numbers of each rescue aircraft scheduled to extinguish the fire were concatenated together, which was a chromosome fragment representing a task cycle. Finally, splicing chromosome fragments from multiple task cycles together determined the chromosome representing the entire rescue plan.

The diagram of the chromosome structure is shown in Figure 3.

As shown in Figure 3, it is an example chromosome fragment constructed with a structure of $\left\{1,1,1,1,2,2,0,1,1,3,3,0\right\}$, representing a scheduling plan for one task cycle. In this example, the length of the chromosome segment was 12, indicating a total of 12 rescue aircraft. This paper distinguished the rally point and aircraft type where the aircraft was located through the sequence of gene loci. In this example, gene loci 1–4 represent aircraft belonging to rally point 1, gene loci 5–9 represent aircraft belonging to rally point 2, and gene loci 10–12 represent aircraft belonging to rally point 3.

Among them, aircraft 5, 6, and 10 are heavy aircraft, while the rest are light. Each gene locus value indicates whether aircraft was involved in a rescue mission during n cycle. In this example, 1, 2, 3 means that aircraft went to the fire point to execute a firefighting task during the cycle, and 0 means that aircraft did not execute a rescue task during this cycle. And the encoding structure of the chromosome can be adjusted according to the actual situation.

In this paper, the fitness function is the objective function itself, and the crossover method used is simulated binary crossover. The mutation method is polynomial mutation, and the selection method is tournament selection.

3.2. Weight TOPIS Method for Solving the Optimal Solution

The NSGA-II algorithm usually calculates a series of Pareto optimal solution sets, but it often needs an optimal scheme in forest fire general aviation rescue. It now needs a comprehensive evaluation method to select the optimal solution. The TOPSIS method (technology for order preference by similarity to an ideal solution method) is a method commonly used in system engineering to perform decision analysis on multiple objectives in a finite program [30]. It is used to evaluate the samples with quantitative indexes according to the degree of superiority and inferiority of solutions in a comprehensive, objective, and scientific way for selecting the best solution from the set of alternatives [31,32]. Compared with traditional evaluation methods such as the analytic hierarchy process (AHP), the TOPSIS method avoids the subjective evaluation of data, does not require an objective function, does not need to pass the test, and can well portray the comprehensive impact strength of multiple impact indicators. The shortcoming of this method is that it does not assign weights to each evaluation criterion. Two commonly used assignment methods are the AHP method and the entropy weight method (EWM) [33]. In this paper, because there are only two evaluation indexes and they are both data, the AHP method cannot transform these data into the basis for constructing the judgment matrix, and the number of evaluation indexes is not enough to establish a hierarchical structure of a multi-level ladder. It is often challenging for the weights determined by the EWM method to meet the importance of the influencing factors considered in the actual rescue. Therefore, this paper combined the needs of the actual rescue situation and used the expert scoring method to assign weights to the indexes. Through the combination of subjective and objective secondary evaluation of the Pareto set solution, this paper determined with the optimal program suitable for this rescue mission so that the evaluation results were more accurate and reasonable.

The specific steps of weight TOPIS are as follows:

Step 1. The total time and total cost of the rescue task designed in the objective function are included as evaluation index, and since the total time and total cost are both inverse indexes (the smaller the value, the better), the inverse processing makes them positive and dimensionless, as shown in Equations (12) and (13):

$$\overline{T}=\frac{T_{\max }-T}{T_{\max }-T_{\min }}$$

(12)

$$\overline{C}=\frac{C_{\max }-C}{C_{\max }-C_{\min }}$$

(13)

where $\overline{T}$ and $\overline{C}$ are positive indexes; $T_{\max }$ and $T_{\min }$ denote the maximum and minimum values of the total time spent on rescue tasks, respectively; $C_{\max }$ and $C_{\min }$ denote the maximum and minimum values of the total cost spent on rescue tasks, respectively; and $T$ and $C$ are the actual values of each scheduling plan.

Step 2. We calculated the weighted Euclidean distance between each scheduling plan and the optimal and worst plans, denoted as $D_i^{+}$ and $D_i^{-}$, respectively, as shown in Equations (14) and (15):

$$D_i^{+}=\sqrt{{\displaystyle \sum _{j=1}^m{\left[w_j\left(a_{ij}-a_{ij}^{+}\right)\right]}^2}}$$

(14)

$$D_i^{-}=\sqrt{{\displaystyle \sum _{j=1}^m{\left[w_j\left(a_{ij}-a_{ij}^{-}\right)\right]}^2}}$$

(15)

where $D_i^{+}$ and $D_i^{-}$ denote the positive and negative ideal solution distances of solution $i$, respectively; $j$ denotes the two evaluation indexes, $j=1,2$; $m$ denotes the number of evaluation indexes, $m=1,2,\dots ,4$; $w_j$ denotes the weight of the jth index; $a_{ij}^{+}$ denotes the optimal solution in the ideal state; $a_{ij}^{-}$ denotes the worst solution in the ideal state; and $a_{ij}$ denotes the data corresponding to the jth index of solution $i$.

Step 3. We calculated the relative closeness $E_i$ between each scheduling solution and the optimal solution, as shown in Equation (16):

$$E_i=\frac{D_i^{-}}{D_i^{+}+D_i^{-}}$$

(16)

where $E_i$ denotes the relative proximity, and the larger the value of $E_i$, the closer it is to 1, which proves the better the fit, and the solution obtained based on the weight TOPSIS method is the most superior.

To sum up, the specific flowchart of the NSGA II-Weight TOPSIS model proposed in this paper is as follows (Figure 4).

4. Simulation Verification

In this paper, we considered Xichang-Liangshan Prefecture as an example to construct a multi-aircraft collaborative schedule scenario from multiple rally points to multiple fire points. Assuming that forest fires occur simultaneously in Lier Village, Yalongjiang Township, Muli County, Lawo Village, Lawo Township, Coronation County, and Ruiyuan Village, then the Dahua Township, Yuexi County, Xichang Qingshan Airport, Yangyuan Airport, and Muli Airport can send rescue aircraft to execute firefighting tasks, and the rescue aircraft take Qionghai as the water point to extract water for firefighting.

We set Lier Village, Lawo Village, and Ruiyuan Village as fire point 1, 2, and 3, respectively, and Xichang Qingshan Airport, Yangyuan Airport, and Muli Airport as rally point 1, 2, and 3, respectively. We used Google Maps to measure the distance between different points. The information of each fire point is shown in

Table 2. Information of each fire point.

Information	Fire Point 1	Fire Point 2	Fire Point 3
Distance from Rally Point 1/km	111.22	36.22	237.06
Distance from Rally Point 2/km	124.72	83.82	158.20
Distance from Rally Point 3/km	63.73	73.44	140.59
Distance from Water Point/km	133.85	59.04	90.22
Required Fire Extinguishing Water Volume/tons	24	18	18

.

In this paper, two types of rescue aircraft were selected for firefighting tasks, and the performance parameters of rescue aircraft and the cost parameters during the execution of the tasks are shown in

Table 3. Parameters of different types.

Aircraft Type	Performance Parameters				Cost Parameters
	Flight Speed/(km/h)	Water-Carrying Capacity/Tons	Take-Off Preparation Time/min	Fuel Capacity/L	Take-Off Cost/CNY	Flight Cost/(CNY/km)
Heavy Aircraft	150	3	30	2450	1500	15
Light Aircraft	200	1.5	20	1530	1000	10

.

In this example, it is assumed that there are a total of 12 rescue aircraft available for firefighting tasks, among which Qingshan Airport can schedule five rescue aircraft, including two heavy aircraft and three light aircraft; Yanyuan Airport can schedule three rescue aircraft, including one heavy aircraft and two light aircraft; Muli Airport can schedule four rescue aircraft, all of which are light. All rescue aircraft can carry a total of 22.5 tons of water in a single cycle, and the required extinguishing water for this fire is 60 tons. Therefore, this firefighting task requires three cycles to complete. Based on the above data, this paper established a multi-aircraft collaborative scheduling optimization model based on Python and used the NSGA-II algorithm to obtain the optimal solution set. We set the chromosome length to 36, the initial population size to 100, the crossover probability to 0.5, and the mutation probability to 0.5. The Pareto non-inferiority solution set was obtained after 100 iterations. This paper compared NSGA-II with the AWGA algorithm, another common multi-objective evolutionary algorithm. The results are shown in

Table 4. Algorithm comparison result.

Parameter	NSGA-II	AWGA
T	1.1629	1.1499
hv	0.01984	0.01568
S	0	636.4562
NPS	4	3

. There were four evaluation indicators, respectively: (1) t refers to elapsed time. The shorter the time, the better. (2) HV is hypervolume. The larger the HV, the better the comprehensive performance of the algorithm. (3) S is spacing, and the smaller the S, the more homogeneous the solution set. (4) NPS are the numbers of Pareto solutions. The more NPS, the better.

According to Table 4, the HV, S, and NPS of the NSGA-II algorithm were better than the AWGA algorithm, and the T of the NSGA-II algorithm was 0.0129s slower than the AWGA algorithm. Therefore, a multi-objective optimization model was constructed in this paper. After comparing the performance of the NSGA-II algorithm and the AWGA algorithm, the NSGA-II algorithm was adopted as the final solution, and the results are shown in Figure 5. The relationship between the two objective functions can be seen in Figure 5, where the lower the total rescue cost, the longer the total rescue time. The total rescue time and total cost for the four feasible scheduling plans included in the derived optimal solution set are shown in

Table 5. Calculation results of each feasible scheduling plan.

Objective Function	Plan 1	Plan 2	Plan 3	Plan 4
Total Rescue Time/min	243.7536	248.3136	247.8112	272.756
Total Rescue Cost/yuan	39,240.702	38,735.806	39,139.494	38,373.226

, and the specific rescue aircraft schedule method for each plan is shown in

Table 6. Specific rescue aircraft schedule method for each plan.

Plan 1
Rally Point	Rally Point 1					Rally Point 2			Rally Point 3
Aircraft Type	H	H	L	L	L	H	L	L	L	L	L	L
Cycle 1	2	2	0	1	1	3	3	0	1	1	1	1
Cycle 2	3	3	0	3	3	2	1	1	3	3	1	1
Cycle 3	2	2	0	1	1	2	2	1	1	3	1	1
Plan 2
Rally Point	Rally Point 1					Rally Point 2			Rally Point 3
Aircraft Type	H	H	L	L	L	H	L	L	L	L	L	L
Cycle 1	1	2	0	2	1	1	3	0	1	1	1	3
Cycle 2	3	3	0	3	3	2	1	1	3	3	3	1
Cycle 3	2	2	0	1	1	2	2	0	1	3	1	1
Plan 3
Rally Point	Rally Point 1					Rally Point 2			Rally Point 3
Aircraft Type	H	H	L	L	L	H	L	L	L	L	L	L
Cycle 1	2	2	0	1	1	1	3	0	1	1	1	3
Cycle 2	3	3	0	3	3	2	1	1	3	3	3	1
Cycle 3	2	2	0	1	1	2	2	1	1	3	1	1
Plan 4
Rally Point	Rally Point 1					Rally Point 2			Rally Point 3
Aircraft Type	H	H	L	L	L	H	L	L	L	L	L	L
Cycle 1	2	2	0	1	1	1	3	0	1	1	1	1
Cycle 2	3	3	0	3	3	3	1	1	3	3	1	1
Cycle 3	2	2	0	1	2	2	2	0	1	3	1	1

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As shown in Figure 6, the diagram of the collaborative scheduling method for the first cycle of rescue aircraft in Plan 1, the solid blue line in the diagram represents the scheduling heavy aircraft, and the green dashed line represents the scheduling light aircraft. That is, schedule 2 heavy aircraft from rally point 1 to fire point 2, and schedule 2 light aircraft to fire point 1; schedule 1 heavy aircraft from rally point 2 to fire point 3, and schedule 1 light aircraft to fire point 3; and schedule 4 light aircraft from rally point 3 to fire point 1.

Taking the total time and total cost of rescue tasks in each plan as evaluation indexes, nine industry experts were invited to score by the Delphi method, including four experts from the Ministry of Emergency Management of the People’s Republic of China Southern General Station of Aerial Forest Protection, two experts from the general aviation Company, and three experts from universities with the research direction of general aviation emergency rescue. The experts of the general aviation company considered that each rescue task should minimize the cost of rescue while ensuring the efficiency of rescue and improving the economics of the company’s operations. College teachers pointed out that forest fires differ from other natural disasters and are greatly affected by the speed of forest fire spread. According to experts from the China Southern General Station of Aerial Forest Protection, it is crucial to respond swiftly and extinguish a fire immediately after it occurs. Failure to do so can result in the fire spreading rapidly, making it difficult to control and potentially putting the lives and property of the public at risk. For this reason, rescue time should always be a top priority. Nine experts carefully evaluated the urgency and cost-effectiveness of rescuing forests from fires. We summed the scoring results of the experts, taking the weight of the average value to the total tasks time as 0.75 and the weight of the total tasks cost as 0.25 to give weight to the evaluation indexes. The weight TOPSIS method was used for plan evaluation, and the results are shown in

Table 7. Weight TOPSIS method evaluation results.

Plan	${\mathit{D}}_{\mathit{i}}^{+}$	${\mathit{D}}_{\mathit{i}}^{-}$	${\mathit{E}}_{\mathit{i}}$	Rank
Plan 1	0.500	0.866	0.634	2
Plan 2	0.249	0.786	0.759	1
Plan 3	0.458	0.747	0.620	3
Plan 4	0.866	0.500	0.366	4

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From Table 6, we can obtain that the relative proximity $E_i$ of plan 2 was the largest and the closest to the positive ideal solution distance $D_i^{+}$, so we chose Plan 2 as the optimal scheduling option from four feasible scheduling plan, in which the total rescue time was 248.3136 min and the total rescue cost was CNY 38,735.806.

Although the total rescue time was the shortest for Plan 1, the total rescue cost for Plan 1 increased by 1.28% compared to Plan 2. Although the total rescue time of Plan 1 was the shortest, the total rescue cost of Plan 1 increased by 1.28% compared to Plan 2. Compared to Plan 3, the total rescue time of Plan 2 increased slightly, only by 0.2%, but the total rescue cost decreased by 1.04%. Although Plan 4 had the lowest total rescue cost, its rescue time increased by 8.96% compared to Plan 2. Therefore, it was verified that Plan 2 was the best scheduling plan that balanced rescue timeliness and economy.

5. Conclusions

Due to the large operating radius of general aviation, aircraft can play an essential role in disaster investigation, on-site command, personnel, and material delivery. However, it also exposes the lack of coordination ability. Therefore, this paper aimed to address the critical issue of aircraft scheduling in general aviation rescue during a forest fire. This paper’s innovativeness lies in facing the increasing complexity of rescue scheduling under the condition of multiple rally points, multiple fire points, and multiple aircraft types and proposing a collaborative scheduling optimization method for forest fire general aviation rescue.

To begin, we analyzed the current disaster relief flight scenario and considered the rescue aircraft’s capabilities and the various rescue operations required. As a result, we identified five sub-tasks that the aircraft needs to undertake during disaster relief missions. These sub-tasks involve performing rescue operations at the rally, water, and fire points, respectively. Then, with the objective function of minimizing the total time and total cost spent on the rescue mission when fighting forest fires, task constraints, water quantity constraints, and maximum fuel quantity constraints were set. An innovative optimization model for forest fire general aviation rescue coordination scheduling was constructed under multi-aircraft conditions from multiple rally points to multiple fire points. An optimal solution is often needed in forest fire rescue. Therefore, this paper differs from general scheduling optimization studies that only calculate the Pareto optimal solution set. Instead, this paper combined the urgency and economy of actual forest fire rescue situations, used the Delphi method to invite experts to score and assign weights to the indexes, and used the weight TOPSIS method to select the optimal solution from the Pareto optimal solution set obtained from the NSGA-II algorithm. This method makes the evaluation results more accurate and reasonable, better conducts the complex multi-aircraft coordinated scheduling decisions, and improves the fleet scheduling efficiency. Finally, this paper considered a multiple fire point in Liangshan Prefecture as the scenario for simulation verification. Since the model constructed in this paper had two objective functions, the NSGA-II algorithm based on fast non-dominated sorting was used to solve the model, and four feasible plans that met the objective function were obtained. Furthermore, the NSGA-II algorithm was compared with the AWGA algorithm, another standard multi-objective evolutionary algorithm, to verify the feasibility and effectiveness of the model and algorithm. Then, based on the weight TOPSIS method, the optimal scheduling plan was selected from the four feasible plans; the total time spent on executing the plan was 248.3136 s, and the total cost was CNY 38,735.806.

The results prove that this method avoids the past situation where the optimal scheduling plan can only be selected empirically and can help rescuers quickly select the relatively optimal one. The optimized scheduling plan can effectively reduce the number of unnecessary flights. Under the premise of guaranteeing the timeliness of rescue, it improves the utilization rate of rescue aircraft, further reduces the rescue cost, and makes the rescue both timely and economical. Therefore, the research results of this paper can improve the ability of general aviation to fight forest fires, provide suggestions for efficient decision-making in coordinated scheduling of multi-aircraft from multiple rally points to multiple fire points in forest fire rescue, and provide theoretical support and scientific basis for the development of general aviation rescue strategies in the future.

There are some limitations in this paper. The actual factors considered in the multi-aircraft coordinative scheduling model constructed in this paper are limited. In addition, the algorithm used in this paper is an existing algorithm. In future research, more influencing factors can be considered, such as the change of fire situation, airspace limitation, and variable weather conditions during the rescue process, to make the scheduling model more in line with reality and to improve the reasonableness and accuracy of the scheduling decision. The innovation of the algorithm can also improve its efficiency in solving more objective functions and more complex scheduling models.