A Resource-Constrained Medical Event Scheduling Method Based on Serial Scheduling Ant Colony System

Abstract

This invention discloses a resource-constrained medical event scheduling method based on a serial scheduling-generated ant colony system. First, the resource-constrained medical event scheduling problem is modeled. Then, a baseline sequence is generated to determine the execution order of activities in the resource-constrained medical event scheduling problem. Next, a serial scheduling generation method is used to construct an initial scheduling scheme that satisfies the medical event scheduling problem based on the baseline sequence. Finally, an ant colony algorithm is used to optimize the scheduling scheme, resulting in an optimized scheduling scheme. This invention can efficiently obtain feasible solutions that simultaneously satisfy priority constraints and resource constraints.

Description

Technical Field

[0001] This invention belongs to the field of operations research technology, specifically relating to a resource-constrained medical event scheduling method. Background Technology

[0002] With the development of technology, the scale of various events in the era of big data is becoming increasingly larger, and resource constraints are becoming more and more important. How to comprehensively consider the duration, cost, benefits, and resource allocation of event tasks and schedule them reasonably is a huge challenge in operations research. The medical event scheduling problem refers to, given a series of resource constraints, rationally arranging the execution order and resource allocation of a series of medical events that must be completed, and finding the optimal solution for a given objective.

[0003] In recent years, scheduling medical events under the uncertain environment caused by the pandemic has become a hot research topic. Since medical resources are limited in most hospitals and medical institutions, scheduling medical events with resource constraints has greater practical application value. Furthermore, since medical activities rarely involve a single mode, scheduling medical events with multiple modes better reflects the realities of medical events. With the impact of the pandemic, the execution time and cost of each mode in a medical event are uncertain. In particular, the execution time of each mode not only affects the event's duration but may even cause changes to the entire scheduling plan.

[0004] Generally, the three key elements of the medical event scheduling problem include the event's resources, activities, and objectives. Based on these elements, medical event scheduling problems can be categorized. According to whether there are resource constraints, medical event scheduling problems can be divided into unconstrained scheduling problems and resource-constrained scheduling problems. Unconstrained scheduling problems assume that event execution is not limited by resources; these problems are relatively rare in reality and have few applications. Resource-constrained problems, on the other hand, are constrained by resources, which may include renewable and non-renewable resources, requiring the finding of feasible scheduling solutions while satisfying resource constraints. Medical event scheduling problems can also be classified according to the characteristics of the activities. Based on the different execution modes of the activities, they can be divided into unimodal and multimodal medical event scheduling problems. In unimodal problems, each activity has only one execution mode, while in multimodal problems, each activity has several candidate modes, each with different execution times and costs, resulting in an exponentially expanding solution space. Based on whether activities have time windows, medical event scheduling problems can be divided into medical event scheduling problems with time windows and those without. In medical event scheduling problems with time windows, the start time range for each activity is given, and activities can only begin execution within the given time range. Based on whether activities have preemption, medical event scheduling problems can be divided into preemptive medical event scheduling problems and non-preemptive medical event scheduling problems. In preemptive medical event scheduling problems, some activities have preemption and priority execution rights. As for the objectives of medical event scheduling problems, they generally include shortest duration, lowest cost, and maximum net present value, etc. Depending on the objectives, medical event scheduling problems can be divided into single-objective medical event scheduling problems and multi-objective medical event scheduling problems. In single-objective medical event scheduling problems, the optimal scheduling solution that meets a given single objective needs to be found. In multi-objective medical event scheduling problems, the optimization yields a set of Pareto solutions that are not dominated by other solutions. For different objectives, different optimal scheduling solutions will be obtained through optimization. Summary of the Invention

[0005] To overcome the shortcomings of existing technologies, this invention provides a resource-constrained medical event scheduling method based on a serial scheduling-generated ant colony system. First, the resource-constrained medical event scheduling problem is modeled. Then, a baseline sequence is generated to satisfy the execution order of activities in the resource-constrained medical event scheduling problem. Next, a serial scheduling generation method is used to construct an initial scheduling scheme that satisfies the medical event scheduling problem based on the baseline sequence. Finally, an ant colony algorithm is used to optimize the scheduling scheme, resulting in an optimized scheduling scheme. This invention can efficiently obtain feasible solutions that simultaneously satisfy priority constraints and resource constraints.

[0006] The technical solution adopted by this invention to solve its technical problem includes the following steps:

[0007] Step 1: Model the resource-constrained medical event scheduling problem;

[0008] Step 1-1: Construct the medical event scheduling problem based on the double-symbol network graph G=(E,A);

[0009] Assume there are n nodes in the network, and node E = {e1, e2, ..., e}. n} represents a medical event in the medical event scheduling; assuming there are m edges in the network, edge A = {a1, a2, ..., a...} m} represents the specific activities in the medical event schedule;

[0010] Each activity corresponds to several execution modes, and each execution mode corresponds to different uncertain costs and uncertain execution times;

[0011] In order to satisfy the priority constraints in network G, for each medical event, all preceding events must be completed before subsequent events can proceed;

[0012] Step 1-2: The goal of the optimization problem is to maximize the benefit f(S) of the scheduling scheme S:

[0013] f(S)=I(S)-O(S)+B(S) (1)

[0014] Where I(S) and O(S) are the total revenue and total expenditure of the scheduling program, respectively, and B(S) is the additional allowance for the scheduling program; revenue f(S) is the net present value of the discounted cash flow, which is also the total fitness value.

[0015] The total revenue of the scheduling scheme is the sum of the revenues of each medical event in the network:

[0016]

[0017] Steps 1-3: At the beginning of the scheduling process, the revenue of the first medical event is proportional to the total value U of the medical events. Assuming the proportion is λ, then:

[0018] I1(S)=λU (3)

[0019] Starting from the second event, the value of the event gradually depreciates. Assuming the depreciation rate is α, then for the period from the second event to the (n-1)th event, we have:

[0020] I i (S)=θW i ×exp(-α×T i (S)) (4)

[0021] Where θ is the payout rate for the event, and W i T is the net value of event i. i (S) represents the occurrence time of event i in scheduling scheme S;

[0022] For the last medical event n, the revenue is the payment of the remaining value, which is...

[0023]

[0024] The project expenditures are:

[0025]

[0026] in, Let d be the expected cost of the i-th event in the selected execution mode of the scheduling scheme S. i ′ is the execution time of the i-th event obtained through Monte Carlo simulation in the selected execution mode;

[0027] Steps 1-4: There will be a reward for completing the medical event ahead of schedule, and a penalty if it is not completed within the agreed time. The specific reward or penalty is calculated by formula (7):

[0028]

[0029] Where T L and T U These are the earliest and latest expected times, respectively. When the actual time used is less than the earliest time, a reward is obtained, with a reward factor of γ. When the actual time used is longer than the latest expected time, a certain fitness value is deducted as a penalty, with a penalty factor of δ.

[0030] Step 2: Generate a baseline sequence that satisfies the order of activity execution in the resource-constrained medical event scheduling problem to be solved;

[0031] Given a preceding event for each activity, the activities are ordered according to the order constraints of the events. After each activity is completed, the state of all activities is updated. The state of all activities whose preceding events have been completed is updated to be selectable. An equally likely random selection is made among all selectable activities, and the selected selectable activity becomes the next activity to be performed. Then, the state of all activities is updated again until all activities are ordered. An execution mode is randomly selected for each activity. Finally, the ordered activities and the selected execution modes form the baseline sequence.

[0032] Step 3: Using a serial scheduling generation method, construct an initial scheduling scheme that satisfies the medical event scheduling problem based on the baseline sequence;

[0033] Select the first unselected activity and its execution mode from the baseline sequence, and add it to the double-code network composed of the already selected activities. Under the conditions of satisfying the order of activities and resource constraints, this forms the shortest thread of the double-code network. Repeat this process to continuously expand the double-code network until all activities in the baseline sequence have been selected.

[0034] Step 4: Optimize the scheduling scheme using the ant colony algorithm;

[0035] The optimization path of ants in the ant colony algorithm is updated using heuristic information, with the optimization objective being the net present value of discounted cash flow. The update of pheromone h simultaneously considers the cost and execution time of the medical event.

[0036]

[0037] in, and Let γ be the expected cost and expected execution time of the medical event, respectively; γ be the resources required for the event; and κ be the calculation parameter.

[0038] Step 5: Perform scheduling simulation based on the cost and execution time characteristics of each medical event;

[0039] The cost of each medical event follows a normal distribution, and the cost is directly set as the expected value. The execution time of each medical event is simulated and scheduled using the Monte Carlo method, randomly selecting from possible execution times. The number of scheduling simulations required for fitness value evaluation in the next generation during the ant colony algorithm iteration process is set according to the correlation between scheduling schemes.

[0040] The correlation r between the two scheduling schemes is calculated using formula (9):

[0041]

[0042] Where X represents the fitness value obtained in each simulation of scheduling scheme 1, EX represents the mean fitness value in scheduling scheme 1, Y represents the fitness value obtained in each simulation of scheduling scheme 2, and EY represents the mean fitness value in scheduling scheme 2.

[0043] Step 6: Simulate the next generation based on the correlations between the scheduling schemes optimized in the previous generation;

[0044] The specific calculation of the number of scheduling simulations f is given by formula (10):

[0045]

[0046] Step 7: Repeat steps 4 to 6 to obtain the optimized scheduling scheme.

[0047] The beneficial effects of this invention are as follows:

[0048] 1. The method of the present invention ensures the feasibility of randomly generated solutions in a double-symbol network graph through a serial scheduling generation method, breaks through the constraint on the order of events in the resource-constrained medical event scheduling problem, ensures that the solutions optimized in the ant colony system are all feasible solutions, and avoids the situation where infeasible solutions are obtained through optimization.

[0049] 2. The method of the present invention applies the ant colony system generated based on serial scheduling to the resource-constrained medical event scheduling problem. By performing scheduling simulation based on the characteristics of the parameters, it can efficiently obtain feasible solutions that simultaneously satisfy priority constraints and resource constraints. Attached Figure Description

[0050] Figure 1 This is a dual-code network diagram of an embodiment of the present invention.

[0051] Figure 2 This is a scheduling scheme generated by serial scheduling in an embodiment of the present invention. Detailed Implementation

[0052] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0053] This invention designs an ant colony system based on serial scheduling to address the multi-modal medical event scheduling problem with resource constraints under the pandemic environment. In order to more comprehensively consider various objectives such as schedule and cost in the medical event scheduling problem, the optimization objective in this invention considers the net present value of discounted cash flow.

[0054] A resource-constrained medical event scheduling method based on a serial scheduling ant colony generation system includes the following steps:

[0055] Step 1: Model the resource-constrained medical event scheduling problem and generate a baseline sequence that satisfies the execution order of activities in the resource-constrained medical event scheduling problem to be solved;

[0056] Step 1-1: Construct the medical event scheduling problem based on the double-symbol network graph G=(E,A);

[0057] Assume there are n nodes in the network, and node E = {e1, e2, ..., e}. n} represents a medical event in the medical event scheduling; assuming there are m edges in the network, edge A = {a1, a2, ..., a...} m} represents the specific activities in the medical event schedule;

[0058] Each activity corresponds to several execution modes, and each execution mode corresponds to different uncertain costs and uncertain execution times;

[0059] In order to satisfy the priority constraints in network G, for each medical event, all preceding events must be completed before subsequent events can proceed;

[0060] Step 1-2: The goal of the optimization problem is to maximize the benefit f(S) of the scheduling scheme S:

[0061] f(S)=I(S)-O(S)+B(S) (1)

[0062] Where I(S) and O(S) are the total revenue and total expenditure of the scheduling plan execution, respectively, and B(S) is the additional allowance for the scheduling plan execution;

[0063] The total revenue of the scheduling scheme is the sum of the revenues of each medical event in the network:

[0064]

[0065] Steps 1-3: At the beginning of the scheduling process, the revenue of the first medical event is proportional to the total value U of the medical events. Assuming the proportion is λ, then:

[0066] I1(S)=λU (3)

[0067] Starting from the second event, the value of the event gradually depreciates. Assuming the depreciation rate is α, then for the period from the second event to the (n-1)th event, we have:

[0068] I i (S)=θW i ×exp(-α×T i (S)) (4)

[0069] Where θ is the payout rate for the event, and W i T is the net value of event i. i (S) represents the occurrence time of event i in scheduling scheme S;

[0070] For the last medical event n, the revenue is the payment of the remaining value, which is...

[0071]

[0072] The project expenditures are:

[0073]

[0074] in, Let d be the expected cost of the i-th event in the selected execution mode of the scheduling scheme S. i′ is the execution time of the i-th event obtained through Monte Carlo simulation in the selected execution mode;

[0075] Steps 1-4: There will be a reward for completing the medical event ahead of schedule, and a penalty if it is not completed within the agreed time. The specific reward or penalty is calculated by formula (7):

[0076]

[0077] Where T L and T U These are the earliest and latest expected times, respectively. When the actual time used is less than the earliest time, a reward is obtained, with a reward factor of γ. When the actual time used is longer than the latest expected time, a certain fitness value is deducted as a penalty, with a penalty factor of δ.

[0078] Step 2: Generate a baseline sequence that satisfies the order of activity execution in the resource-constrained medical event scheduling problem to be solved;

[0079] Given a preceding event for each activity, the activities are ordered according to the order constraints of the events. After each activity is completed, the state of all activities is updated. The state of all activities whose preceding events have been completed is updated to be selectable. An equally likely random selection is made among all selectable activities, and the selected selectable activity becomes the next activity to be performed. Then, the state of all activities is updated again until all activities are ordered. An execution mode is randomly selected for each activity. Finally, the ordered activities and the selected execution modes form the baseline sequence.

[0080] Step 3: Using a serial scheduling generation method, construct a scheduling scheme that satisfies the medical event scheduling problem based on the baseline sequence;

[0081] Select the first unselected activity and its execution mode from the baseline sequence, and add it to the double-code network composed of the already selected activities. Under the conditions of satisfying the order of activities and resource constraints, this forms the shortest thread of the double-code network. Repeat this process to continuously expand the double-code network until all activities in the baseline sequence have been selected.

[0082] Step 4: Optimize the scheduling scheme using the ant colony algorithm;

[0083] The optimization path of ants in the ant colony algorithm is updated using heuristic information, with the optimization objective being the net present value of discounted cash flow. The update of pheromone h simultaneously considers the cost and execution time of the medical event.

[0084]

[0085] in, and Let γ be the expected cost and expected execution time of the medical event, respectively; γ be the resources required for the event; and κ be the calculation parameter.

[0086] Step 5: Based on the cost and execution time characteristics of each medical event, perform scheduling simulation processing;

[0087] The cost of each medical event follows a normal distribution, and the cost is directly set as the expected value. The execution time of each medical event is simulated and scheduled using the Monte Carlo method, randomly selecting from possible execution times. The number of scheduling simulations required for fitness value evaluation in the next generation is set according to the correlation between scheduling schemes.

[0088] The direct correlation r between the scheduling schemes is calculated using formula (9):

[0089]

[0090] Step 6: Simulate the next generation based on the correlations between the scheduling schemes optimized in the previous generation;

[0091] The specific calculation of the number of scheduling simulations f is given by formula (10):

[0092]

[0093] Step 7: Repeat steps 4 to 6 to obtain the optimized scheduling scheme. Specific implementation examples:

[0095] 1. Modeling the resource-constrained medical event scheduling problem. This embodiment considers a medical event scheduling problem constructed based on a double-symbol network graph G=(E,A). For example... Figure 1 As shown, assume there are n nodes in the network, and node E = {e1, e2, ..., e}. n} represents a medical event in the medical event scheduling. Assume the network has m edges, where edge A = {a1, a2, ..., a...} n} represents a specific activity in the medical event scheduling. Each activity has several corresponding execution modes, each with m... i Corresponding to different uncertain costs c i and uncertain execution time d i To satisfy the priority constraints in network G, for each medical event, all preceding events must be completed before subsequent events can proceed.

[0096] The goal of the optimization problem is to maximize the benefit f(S) of the scheduling scheme S:

[0097] f(S)=I(S)-O(S)+B(S) (1)

[0098] Where I(S) and O(S) represent the project's revenue and expenses, respectively, and B(S) represents the project's additional allowance. The total project revenue is the sum of the revenues from each medical event within the network.

[0099]

[0100] At the beginning of implementation, the revenue from the first medical event is directly proportional to the total value of the event; assuming the proportion is λ, then...

[0101] I1(S)=λU (3)

[0102] Starting from the second event, the value of the events gradually depreciates over time. Assuming a depreciation rate of α, then for the period from the second event to the (n-1)th event, we have:

[0103] I i (S)=θW i ×exp(-α×T i (S)) (4)

[0104] Where θ is the payout rate for the event, and W i T is the net value of event i. i (S) represents the occurrence time of event i in the scheduling scheme S. The last event n is the payment of the remaining value.

[0105]

[0106] Regarding project expenditures, there are

[0107]

[0108] in, Let be the expected cost of the i-th event in the scheduling scheme S under the selected execution mode, and d i ′ is the execution time of the i-th event obtained through Monte Carlo simulation under the selected execution mode. Furthermore, since medical events are often urgent, there is a reward for completing the event ahead of schedule, and a penalty for failing to complete it within the agreed time. The specific allowance is calculated using formula (7):

[0109]

[0110] Where T L and T UThese are the earliest and latest expected times, respectively. When the actual time used is less than the earliest time, a reward is obtained, with a reward factor of γ. When the actual time used is longer than the latest expected time, a certain fitness value is deducted, with a penalty factor of δ.

[0111] Given a preceding event for each activity, the activities are ordered according to the order constraints of the events. After each activity is completed, the state of all activities is updated. The state of all activities whose preceding events have been completed is updated to be selectable. An equally likely random selection is made among all selectable activities, and the selected selectable activity becomes the next activity to be performed. Then, the state of all activities is updated again until all activities are ordered. An execution mode is randomly selected for each activity. Finally, the ordered activities and the selected execution modes form the baseline sequence.

[0112] 2. Construct a scheduling scheme that satisfies priority event constraints using a serial scheduling generation method. First, schedule a1 into the first thread. Then schedule a2. Since a2 can only be executed after activity a1 finishes, it is scheduled into the second thread starting from the time a1 finishes. Next, schedule a4. Due to resource constraints, a4 can only be executed after a2 finishes, so it is scheduled into the first thread starting from the time a2 finishes. For activity a3, from a priority constraint perspective, it only needs to finish after activity a1. Since executing a3 and a4 together satisfies resource constraints, a3 is scheduled into the second thread after a2 finishes, minimizing the total time. Finally, schedule activity a5. It needs to be executed after activities a1, a2, and a3. Since executing a5 and a4 together satisfies resource constraints, a5 is scheduled into the second thread after a3 finishes, minimizing the total time. This completes the construction of the entire scheduling scheme. Figure 2 The information is provided in the text.

[0113] 3. An ant colony optimization algorithm is used to update the ants' optimal path using heuristic information. Since the optimization objective in this embodiment considers the net present value of discounted cash flow, the update of pheromones simultaneously considers the cost and execution time of the medical event.

[0114]

[0115] in, and Let γ represent the expected cost and expected execution time of the event, γ represent the resources required for the event, and κ represent a parameter set according to the actual situation of the problem. By providing mixed heuristic information, the ant's search ability can be enhanced, helping it to find superior scheduling solutions with lower costs, shorter execution times, and fewer resource consumption more quickly.

[0116] 4. Based on the characteristics of the two uncertain parameters—the cost and execution time of each medical event—different scheduling simulations are performed on each parameter. The cost of each medical event, since it follows a normal distribution, can be directly set as its expected value. However, the execution time of each medical event, since it does not follow a normal distribution, needs to be simulated and scheduled using the Monte Carlo method, randomly generated from possible execution times. The number of scheduling simulations required for fitness value evaluation in the next generation is set according to the correlation between scheduling schemes. The direct correlation between scheduling schemes is calculated using formula (9):

[0117]

[0118] 5. Simulate the next generation based on the correlation between the scheduling schemes optimized in the previous generation. For scheduling schemes with weak correlation, perform a large number of simulations. For scheduling schemes with strong correlation, perform only a small number of scheduling simulations. According to the definition of correlation, it is generally believed that when the coefficient r is greater than or equal to 0.7, the correlation between scheduling schemes is relatively strong. At this time, only a small number of simulations are needed to accurately judge the quality of the scheduling scheme. Therefore, the number of scheduling simulations f is set to 1. When the coefficient r is less than 0.7, since the correlation is weaker, more simulations are needed to compare the scheduling schemes. Therefore, the number of scheduling simulations n is made to be related to the reciprocal of r. The specific calculation rule is given by formula (10):

[0119]

Claims

1. A method for generating resource-constrained medical event scheduling based on serial scheduling for ant colony system, characterized in that, Includes the following steps: Step 1: Model the resource-constrained medical event scheduling problem; Step 1-1: Construct the medical event scheduling problem based on the double-symbol network graph G=(E,A); Assume there are n nodes in the network, and node E = {e1, e2, ..., e}. n } represents a medical event in the medical event scheduling; assuming there are m edges in the network, edge A = {a1, a2, ..., a...} m } represents the specific activities in the medical event schedule; Each activity corresponds to several execution modes, and each execution mode corresponds to different uncertain costs and uncertain execution times; In order to satisfy the priority constraints in network G, for each medical event, all preceding events must be completed before subsequent events can proceed; Step 1-2: The goal of the optimization problem is to maximize the benefit f(S) of the scheduling scheme S: f(S)=I(S)-O(S)+B(S) (1) Where I(S) and O(S) are the total revenue and total expenditure of the scheduling program, respectively, and B(S) is the additional allowance for the scheduling program; revenue f(S) is the net present value of the discounted cash flow, which is also the total fitness value. The total revenue of the scheduling scheme is the sum of the revenues of each medical event in the network: Steps 1-3: At the beginning of the scheduling process, the revenue of the first medical event is proportional to the total value U of the medical events. Assuming the proportion is λ, then: I1(S)=λU (3) Starting from the second event, the value of the event gradually depreciates. Assuming the depreciation rate is α, then for the period from the second event to the (n-1)th event, we have: I i (S) = θw i × exp(-α × T i (S)) (4) where θ is the payout rate of the event, W i is the net value of event i, T i (S) is the occurrence time of event i in schedule S; For the last medical event n, the revenue is the payment of the remaining value, which is... The project expenditures are: wherein, di is the expected cost of the i-th event of the schedule S in the selected mode of execution, i di is the expected cost of the i-th event of the schedule S in the selected mode of execution, Steps 1-4: There will be a reward for completing the medical event ahead of schedule, and a penalty if it is not completed within the agreed time. The specific reward or penalty is calculated by formula (7): Where T L and T U These are the earliest and latest expected times, respectively. When the actual time used is less than the earliest time, a reward is obtained, with a reward factor of γ. When the actual time used is longer than the latest expected time, a certain fitness value is deducted as a penalty, with a penalty factor of δ. Step 2: Generate a baseline sequence that satisfies the order of activity execution in the resource-constrained medical event scheduling problem to be solved; Given a preceding event for each activity, the activities are ordered according to the order constraints of the events. After each activity is completed, the state of all activities is updated. The state of all activities whose preceding events have been completed is updated to be selectable. An equally likely random selection is made among all selectable activities, and the selected selectable activity becomes the next activity to be performed. Then, the state of all activities is updated again until all activities are ordered. An execution mode is randomly selected for each activity. Finally, the ordered activities and the selected execution modes form the baseline sequence. Step 3: Using a serial scheduling generation method, construct an initial scheduling scheme that satisfies the medical event scheduling problem based on the baseline sequence; Select the first unselected activity and its execution mode from the baseline sequence, and add it to the double-code network composed of the already selected activities. Under the conditions of satisfying the order of activities and resource constraints, this forms the shortest thread of the double-code network. Repeat this process to continuously expand the double-code network until all activities in the baseline sequence have been selected. Step 4: Optimize the scheduling scheme using the ant colony algorithm; The optimization path of ants in the ant colony algorithm is updated using heuristic information, with the optimization objective being the net present value of discounted cash flow. The update of pheromone h simultaneously considers the cost and execution time of the medical event. where, and are the expected cost and expected execution time of the medical event, respectively, γ is the resource required by the event, and κ is a computation parameter; Step 5: Perform scheduling simulation based on the cost and execution time characteristics of each medical event; The cost of each medical event follows a normal distribution, and the cost is directly set as the expected value. The execution time of each medical event is simulated and scheduled using the Monte Carlo method, randomly selecting from possible execution times. The number of scheduling simulations required for fitness value evaluation in the next generation during the ant colony algorithm iteration process is set according to the correlation between scheduling schemes. The correlation r between the two scheduling schemes is calculated using formula (9): Where X represents the fitness value obtained in each simulation of scheduling scheme 1, EX represents the mean fitness value in scheduling scheme 1, Y represents the fitness value obtained in each simulation of scheduling scheme 2, and EY represents the mean fitness value in scheduling scheme 2. Step 6: Simulate the next generation based on the correlations between the scheduling schemes optimized in the previous generation; The specific calculation of the number of scheduling simulations f is given by formula (10): Step 7: Repeat steps 4 to 6 to obtain the optimized scheduling scheme.

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