Distributed blocking flow shop batch scheduling multi-objective optimization method with workpiece arrival

Abstract

The invention discloses a distributed blocking flow shop batch scheduling multi-objective optimization method with workpiece arrival, which relates to the technical field of data processing and comprises the following implementation steps of: setting a model index by combining two objectives of minimizing maximum completion time and total energy consumption; two problem attributes are provided for DBFSPCSDJA, and detailed construction methods of encoding, initialization, intersection, variation and local search strategies are provided respectively; designing a complete solution composed of factory distribution of the workpieces, the machining sequence of the workpieces in each factory, the size and number of sub-batches and the machining speed of the workpieces; different initialization methods are provided; carrying out local search on evolution of the workpiece sequence; and performing experimental design and performance analysis verification. According to the distributed blocking flow shop batch scheduling multi-objective optimization method with workpiece arrival, the minimum total energy consumption can be realized under the condition that the flow shop can be completed within the shortest time.

Description

Technical Field

[0001] The present invention relates to the field of data processing technology, and in particular to a multi-objective optimization method for batch scheduling in a distributed blocked flow shop with arriving workpieces. Background Art

[0002] A distributed blocking flow shop with workpiece arrivals is a highly complex and realistic production scheduling model. It requires solving the problems of machine allocation and process sequencing in a distributed environment, and dealing with the blocking effect caused by the lack of a buffer zone and the dynamic nature of workpiece arrival over time. Researching effective scheduling algorithms is of great significance for optimizing the performance of such manufacturing systems, including shortening delivery times and improving equipment utilization.

[0003] Currently, when scheduling distributed blocking flow shops with consistent sub-batches and dynamic workpiece insertion, it is impossible to achieve the lowest total energy consumption while ensuring the shortest completion time. At the same time, workpieces cannot be transferred to another factory before completion. Each machine can only process one sub-batch at a time, which reduces the workpiece processing efficiency. In addition, the buffer space between adjacent machines is limited, and the transportation time and switching time of the workpiece are easily ignored.

[0004] Therefore, a new multi-objective optimization method for batch scheduling in a distributed blocked flow shop with workpiece arrival is proposed to solve the above problems. Summary of the Invention

[0005] The main purpose of the present invention is to provide a multi-objective optimization method for batch scheduling in a distributed blocked flow shop with workpiece arrival, so as to solve the problems raised in the above background.

[0006] To achieve the above objectives, the present invention adopts a technical solution: a multi-objective optimization method for batch scheduling in a distributed blocked flow shop with workpiece arrival, the method comprising the following implementation steps:

[0007] Step 1: Establish the problem model, combine DBFSP_CSDJA to consider the two objectives of minimizing the maximum completion time and total energy consumption, set the model index, and obtain the optimization objectives and constraints of DBFSP_CSDJA;

[0008] Step 2: Propose two problem attributes for DBFSP_CSDJA. The problem attributes are used to design knowledge for effective search operators.

[0009] Step 3: Through the improved second-generation non-dominated genetic algorithm, the detailed construction methods of encoding, initialization, crossover, mutation, and local search strategies are given, as well as the main differences between INSGAII and NSGAII;

[0010] Step 4: Design a complete solution through coding regarding the factory allocation of workpieces, the processing sequence of workpieces within each factory, the size and number of sub-batches, and the processing speed of workpieces;

[0011] Step 5: Propose different initialization methods for workpiece population initialization, speed initialization and sub-batch population initialization;

[0012] Step 6: Design crossover and mutation strategies for the workpiece sequence, sub-batch sequence, and machine speed, and perform local search on the evolution of the workpiece sequence;

[0013] Step 7: Experimental design and performance analysis verification.

[0014] The specific steps of establishing the problem model are as follows:

[0015] The problem model is set to solve the main tasks of batch scheduling in a distributed blocked flow shop with job arrivals. The main tasks include determining the factory allocation of jobs, determining the job processing sequence, determining the number and size of sub-batches, and assigning speeds to operations.

[0016] The model index, model parameters and model decision variables are constructed, and the objectives and constraints are optimized according to the model index, model parameters and model decision variables to obtain the problem model of batch scheduling in a distributed blocked flow shop with workpiece arrival.

[0017] The encoding steps in step 3 are specifically as follows:

[0018] In DBFSP_CSDJA, the complete solution contains the following information: the factory allocation of workpieces, the processing order of workpieces in each factory, the size and number of sub-batches, and the processing speed of workpieces. A one-dimensional vector is designed to represent the complete solution, which is denoted as (π, v, Z);

[0019] π=(π1,π2,...,π n+f-1 ) represents the artifact sequence, where f-1 virtual artifacts act as factory separators;

[0020] v=(v1,v2,...,v n×m ) is a speed sequence that specifies the processing speed of each workpiece on each machine;

[0021] Z=(z1,z2,...,z n×L ) is the sub-batch sequence, providing information about how the workpieces are divided into sub-batches.

[0022] The initialization includes workpiece population initialization, sub-batch population initialization and speed initialization;

[0023] The workpiece population initialization is used to integrate a heuristic algorithm that combines a maximum processing time rule and a greedy iteration rule. The heuristic algorithm is represented as LPT IG. First, LPT is used to generate a workpiece sequence. The workpiece sequence is generated according to the descending processing time of all workpieces. Then, a destruction and reconstruction operation is performed on the workpiece sequence. In the destruction phase, for each processing plant, half of the workpieces are randomly removed. Then, the removed workpieces are reinserted into the remaining workpiece sequence, and the workpieces are inserted at the position with the best target value.

[0024] The sub-batch population initialization algorithm includes three strategies: uniform initialization, random initialization and mixed initialization.

[0025] The speed initialization adopts SAS rules to set an appropriate processing speed for each workpiece to reduce total energy consumption.

[0026] The crossover strategy in step 6 is to design multiple crossover strategies for workpiece sequences, speed sequences, and sub-batch sequences, and enhance population diversity and improve global search capabilities through different gene recombination methods;

[0027] The mutation strategy in step six is ​​to keep the speed sequence unchanged and design multiple mutation strategies for the workpiece sequence and sub-batch sequence to improve the diversity of the algorithm search space and the quality of the optimization solution.

[0028] The local search strategy in step 3 is to design a set of neighborhood structures N for the evolution of the workpiece sequence. K , where k∈{1,...,k max}, and k max It is set to the maximum value of 5, and the neighborhood structures include single-plant two-point insertion, single-plant two-point exchange, double-plant two-point insertion, single-plant subsequence insertion, and single-plant overall backward movement.

[0029] The main differences between INSGAII and NSGAII are as follows:

[0030] Difference 1: Fusion of three different strategies to generate workpiece population, sub-batch population and speed setting respectively;

[0031] Difference 2: Introducing multiple crossover and mutation operations to perturb the workpiece population and sub-batch sequence to explore potential non-dominated solutions;

[0032] Difference 3: The speed sequence remains unchanged, the workpiece population executes VNS and CFLS, and the sub-batch sequence executes exchange and insertion of local search operators.

[0033] The experimental design and performance analysis verification are used to propose three initialization strategies. A random variant of NSGAII (denoted as N1) is designed for comparison. A total of 675 instances are used to calculate the HV value. At the same time, variance analysis is performed to evaluate the differences between the algorithms. If the RPI value of NSGAII is always lower than that of N1, it indicates that the initialization strategy significantly enriches the diversity of the population and improves the quality of the population. If the p-value is less than 0.05, it indicates that there is a statistically significant difference between NSGAII and N1.

[0034] The experimental design and performance analysis verification are carried out to analyze the influence of the designed crossover and mutation operations. INSGAII is also compared with the INSGAII algorithm without the fusion of the three initialization strategies. The INSGAII without crossover and mutation is called N2. The crossover probability P is calculated by c and mutation probability P m Set it to 0 while keeping the population size PS and the proportion of the population performing local search unchanged. If the p value is less than 0.05, it indicates that there is a significant difference between KDNSGAII and N2;

[0035] The experimental design and performance analysis verification are conducted to verify the effectiveness of the local search strategy. INSGAII with the local search strategy and N3 without the local search strategy are integrated. If the p-value is 0.0132, which is less than 0.05, it indicates that there is a significant difference between the two algorithms, and INSGAII is better than N3. It is judged that the proposed local search operator can not only improve the convergence speed of the solution, but also enhance the exploration and exploration capabilities at the same time.

[0036] The present invention has the following beneficial effects:

[0037] The present invention sets a distributed blocked flow shop batch scheduling multi-objective problem model and sets constraints on the problem model. It integrates heuristic initialization, enhanced crossover and mutation operations, and local search strategies for the workshop in real time according to the constraints of the flow shop scheduling. It can effectively improve the completion time and total energy consumption of the workshop batch scheduling multi-objective optimization and achieve diversity and stability. At the same time, through the improved second-generation non-dominated genetic algorithm, it provides important theoretical support and practical guidance for the green production scheduling of the flow shop, can achieve better solution quality and convergence efficiency, highlight the broad application prospects in solving the complex scheduling problems of distributed blocked flow shops, and enable the flow shop to achieve the lowest total energy consumption while ensuring the shortest completion time. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 This is an overall flow chart of a multi-objective optimization method for batch scheduling in a distributed blocked flow shop with workpiece arrival according to the present invention;

[0039] Figure 2The figure is a basic flow chart of the INSGAII algorithm of a multi-objective optimization method for batch scheduling in a distributed blocking flow shop with workpiece arrival according to the present invention. DETAILED DESCRIPTION

[0040] In order to make the technical means, creative features, objectives and effects achieved by the present invention easier to understand, the present invention is further described below in conjunction with specific implementation methods.

[0041] Please refer to Figures 1 to 2 A multi-objective optimization method for batch scheduling in a distributed blocked flow shop with workpiece arrival is shown in FIG. The method includes the following implementation steps:

[0042] Step 1: Establish the problem model, combine DBFSP_CSDJA to consider the two objectives of minimizing the maximum completion time and total energy consumption, set the model index, and obtain the optimization objectives and constraints of DBFSP_CSDJA;

[0043] Step 2: Two problem attributes are proposed for DBFSP_CSDJA. The problem attributes are used as knowledge for designing effective search operators. DBFSP_CSDJA proposes two problem attributes as knowledge for designing effective search operators. The two problem attributes are as follows:

[0044] Property 1: If two scheduling schemes x1 = (π1, v, Z) and x2 = (π2, v, Z), satisfy C max (x1)<C max (x2) or TEC(x1)<TEC(x2), then x1 dominates x2, that is, x1>x2;

[0045] Property 2: If two schedules x1 = (π1, v, Z) and x2 = (π2, v, Z) satisfy:

[0046] (a) CF(d,x1)=CF(d,x2);

[0047] (b) j∈{1,...,M},v i,j (x1)<v i,j (x2);

[0048] (c) j∈{1,...,M},v i,j (x1)<v i,j (x2); then TEC(x1)<TEC(x2) and x1>x2

[0049] Step 3: Through the improved second-generation non-dominated genetic algorithm, the detailed construction methods of encoding, initialization, crossover, mutation, and local search strategies are given, as well as the main differences between INSGAII and NSGAII;

[0050] Step 4: Design a complete solution through coding regarding the factory allocation of workpieces, the processing sequence of workpieces within each factory, the size and number of sub-batches, and the processing speed of workpieces;

[0051] Step 5: Propose different initialization methods for workpiece population initialization, speed initialization and sub-batch population initialization;

[0052] Step 6: Design crossover and mutation strategies for the workpiece sequence, sub-batch sequence, and machine speed, and perform local search on the evolution of the workpiece sequence;

[0053] Step 7: Experimental design and performance analysis verification.

[0054] The specific steps to build the problem model are as follows:

[0055] The problem model is set to solve the main tasks of batch scheduling in a distributed blocked flow shop with job arrivals. The main tasks include determining the factory allocation of jobs, determining the job processing sequence, determining the number and size of sub-batches, and assigning speeds to operations.

[0056] Construct model index, model parameters and model decision variables. Based on the model index, model parameters and model decision variables, optimize the objectives and constraints to obtain the problem model of batch scheduling in a distributed blocking flow shop with workpiece arrival. The model index is shown in the following table:

[0057]

[0058] The model parameters are shown in the following table:

[0059]

[0060]

[0061] The model decision variables are shown in the following table:

[0062]

[0063]

[0064] The optimization objectives and constraints of the distributed blocking flow shop batch scheduling problem model with workpiece arrival are shown in the following table:

[0065]

[0066]

[0067] By substituting the above constraint formula into the parameters, the multi-objective optimization and constraint effect can be achieved for the batch scheduling of distributed blocking flow shop.

[0068] The encoding steps in step 3 are as follows:

[0069] In DBFSP_CSDJA, the complete solution contains the following information: the factory allocation of workpieces, the processing order of workpieces in each factory, the size and number of sub-batches, and the processing speed of workpieces. A one-dimensional vector is designed to represent the complete solution, which is denoted as (π, v, Z);

[0070] π=(π1,π2,...,π n+f-1 ) represents the artifact sequence, where f-1 virtual artifacts act as factory separators;

[0071] v=(v1,v2,...,v n×m ) is a speed sequence that specifies the processing speed of each workpiece on each machine;

[0072] Z=(z1,z2,...,z n×L ) is the sub-batch sequence, providing information about how the workpieces are divided into sub-batches.

[0073] Initialization includes workpiece population initialization, sub-batch population initialization and speed initialization;

[0074] The workpiece population is initialized using a heuristic algorithm that integrates the maximum processing time rule and the greedy iteration rule. This heuristic algorithm is represented as LPT IG. First, LPT is used to generate a workpiece sequence. The workpiece sequence is generated according to the descending processing time of all workpieces. Then, a destruction and reconstruction operation is performed on the workpiece sequence. In the destruction phase, for each processing plant, half of the workpieces are randomly removed. Then, the obtained workpieces are reinserted into the remaining workpiece sequence, and the workpieces are inserted at the position with the best target value.

[0075] The sub-batch population initialization algorithm includes three strategies: uniform initialization, random initialization and mixed initialization. The specific details are as follows:

[0076] The uniform initialization step is: set the number of sub-batches to the maximum number of sub-batches, for job J j , the size of each sub-batch is initialized to in Represents the floor function, that is, returns a value less than or equal to T j / L's maximum integer, then calculate the remaining size And the remaining size r jRandomly added to a subbatch.

[0077] The steps for random initialization are:

[0078] Step 1: For each artifact, initialize the remaining size r j =T j , for the number of sub-batches, initialized sequentially from 1 to L;

[0079] Step 2: If l∈[1,L-1], then in the range [0, r j ] Randomly generate job J j The size of the lth sub-batch;

[0080] Step 3: If l = L, set the size of the lth subbatch to the remaining size r j .

[0081] The steps for hybrid initialization are:

[0082] Step 1: Divide the workpiece in an even manner;

[0083] Step 1.1: Divide the workpieces into sub-batches evenly. For the j-th workpiece, the size of each sub-batch is initialized to in Returns a value less than or equal to T j / L's maximum integer;

[0084] Step 1.2: Calculate the remaining size And the remaining size r j Randomly add to a sub-batch;

[0085] Step 2: Perform randomization process on each artifact, iterating over sub-batches

[0086] Step 2.1: In the range [0,S j,l ] randomly select an integer R and set S j,l =S j,l +R or S j,l =S j,l -R;

[0087] Step 2.2: For sub-batch L+1-l, set S j,L+1-l =S j,L+1-l -R or S j,L+1-l =S j,L+1-l +R.

[0088] Speed ​​initialization uses SAS rules to set the appropriate processing speed for each workpiece to reduce total energy consumption.

[0089] The crossover strategy in step 6 is to design multiple crossover strategies for workpiece sequences, speed sequences, and sub-batch sequences, and enhance population diversity and improve global search capabilities through different gene recombination methods;

[0090] The mutation strategy in step six is ​​to keep the speed sequence unchanged and design multiple mutation strategies for the workpiece sequence and sub-batch sequence to improve the diversity of the algorithm search space and the quality of the optimization solution.

[0091] The local search strategy in step 3 is to design a set of neighborhood structures N for the evolution of the workpiece sequence. K , where k∈{1,...,k max}, and k max It is set to the maximum value of 5, and the neighborhood structures include single-plant two-point insertion, single-plant two-point exchange, double-plant two-point insertion, single-plant subsequence insertion, and single-plant overall backward movement.

[0092] The main differences between INSGAII and NSGAII are as follows:

[0093] Difference 1: Fusion of three different strategies to generate workpiece population, sub-batch population and speed setting respectively;

[0094] Difference 2: Introducing multiple crossover and mutation operations to perturb the workpiece population and sub-batch sequence to explore potential non-dominated solutions;

[0095] Difference 3: The speed sequence remains unchanged, the workpiece population executes VNS and CFLS, and the sub-batch sequence executes exchange and insertion of local search operators.

[0096] The specific steps for experimental design and performance analysis verification are as follows:

[0097] The parameters of the flow shop scheduling problem model are received in real time through a data receiver. The experiment is set up on a desktop computer equipped with an Intel(R) Core(TM) i7-6700 CPU processor and 16GB RAM. INSGAII is implemented in MATLAB to calculate the hypervolume index of the flow shop scheduling process in real time. The hypervolume index is used to evaluate the performance of the algorithm. The hypervolume index HV value is the volume of the hypercube formed between the set S and the reference point R, where S is the Pareto front of the non-dominated solutions obtained by the algorithm. The larger the hypervolume index value HV, the better the algorithm performance. The calculation formula of the hypervolume index HV value is as follows:

[0098]

[0099] Here, HV(S,R) represents the hypervolume index between the solution s and the reference point R. Based on this index, the relative percentage increase is used to evaluate the performance of the algorithm. The smaller the RPI value, the better the algorithm performance. The calculation formula of RPI is as follows:

[0100]

[0101] Among them, RPI represents the relative percentage growth value, f best represents the HV value obtained in a given instance, which is the best HV value among all instances, f x It indicates the HV value obtained by the current algorithm on a certain instance. If RPI = 0%, it means that the algorithm has achieved the best performance; RPI > 0% indicates that there is a gap.

[0102] Experimental design and performance analysis verification are used to propose three initialization strategies. A random variant of NSGAII (denoted as N1) is designed for comparison. A total of 675 instances are used to calculate the HV value. At the same time, variance analysis is performed to evaluate the differences between the algorithms. If the RPI value of NSGAII is always lower than that of N1, it indicates that the initialization strategy significantly enriches the diversity of the population and improves the quality of the population. If the p-value is less than 0.05, it indicates that there is a statistically significant difference between NSGAII and N1.

[0103] Experimental design and performance analysis verification In order to analyze the impact of the designed crossover and mutation operations, INSGAII is compared with the INSGAII algorithm without the integration of these three initialization strategies. The INSGAII without crossover and mutation is called N2. The crossover probability P is calculated by c and mutation probability P m Set it to 0 while keeping the population size PS and the proportion of the population performing local search unchanged. If the p value is less than 0.05, it indicates that there is a significant difference between KDNSGAII and N2;

[0104] Experimental design and performance analysis verification In order to verify the effectiveness of the local search strategy, INSGAII with the local search strategy and N3 without the local search strategy are integrated. If the p-value is 0.0132, which is less than 0.05, it means that there is a significant difference between the two algorithms, and INSGAII is better than N3. It is judged that the proposed local search operator can not only improve the convergence speed of the solution, but also enhance the exploration and exploration capabilities at the same time.

[0105] The basic principles, main features, and advantages of the present invention are shown and described above. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The above embodiments and descriptions are merely illustrative of the principles of the present invention. Various changes and modifications may be made to the present invention without departing from the spirit and scope of the present invention. Such changes and modifications are intended to fall within the scope of the present invention. The scope of protection claimed in the present invention is defined by the appended claims and their equivalents.

Claims

1. A multi-objective optimization method for batch scheduling in a distributed blocked flow shop with workpiece arrival, characterized by: The method comprises the following implementation steps: Step 1: Establish the problem model, combine DBFSP_CSDJA to consider the two objectives of minimizing the maximum completion time and total energy consumption, set the model index, and obtain the optimization objectives and constraints of DBFSP_CSDJA; Step 2: Propose two problem attributes for DBFSP_CSDJA. The problem attributes are used to design knowledge for effective search operators. Step 3: Through the improved second-generation non-dominated genetic algorithm, the detailed construction methods of encoding, initialization, crossover, mutation, and local search strategies are given, as well as the main differences between INSGAII and NSGAII; Step 4: Design a complete solution through coding regarding the factory allocation of workpieces, the processing sequence of workpieces within each factory, the size and number of sub-batches, and the processing speed of workpieces; Step 5: Propose different initialization methods for workpiece population initialization, speed initialization and sub-batch population initialization; Step 6: Design crossover and mutation strategies for the workpiece sequence, sub-batch sequence, and machine speed, and perform local search on the evolution of the workpiece sequence; Step 7: Experimental design and performance analysis verification.

2. The method according to claim 1, wherein: The specific steps of establishing the problem model are as follows: The problem model is set to solve the main tasks of batch scheduling in a distributed blocked flow shop with job arrivals. The main tasks include determining the factory allocation of jobs, determining the job processing sequence, determining the number and size of sub-batches, and assigning speeds to operations. The model index, model parameters and model decision variables are constructed, and the objectives and constraints are optimized according to the model index, model parameters and model decision variables to obtain the problem model of batch scheduling in a distributed blocked flow shop with workpiece arrival.

3. The method according to claim 1, wherein: The encoding steps in step 3 are specifically as follows: In DBFSP_CSDJA, the complete solution contains the following information: the factory allocation of workpieces, the processing order of workpieces in each factory, the size and number of sub-batches, and the processing speed of workpieces. A one-dimensional vector is designed to represent the complete solution, which is denoted as (π, v, Z); π=(π1,π2,...,π n+f-1 ) represents the artifact sequence, where f-1 virtual artifacts act as factory separators; v=(v1,v2,...,v n×m ) is a speed sequence that specifies the processing speed of each workpiece on each machine; Z=(z1,z2,...,z n×L ) is the sub-batch sequence, providing information about how the workpieces are divided into sub-batches.

4. The method according to claim 1, wherein: The initialization includes workpiece population initialization, sub-batch population initialization and speed initialization; The workpiece population initialization is used to integrate a heuristic algorithm that combines a maximum processing time rule and a greedy iteration rule. The heuristic algorithm is represented as LPT IG. First, LPT is used to generate a workpiece sequence. The workpiece sequence is generated according to the descending processing time of all workpieces. Then, a destruction and reconstruction operation is performed on the workpiece sequence. In the destruction phase, for each processing plant, half of the workpieces are randomly removed. Then, the removed workpieces are reinserted into the remaining workpiece sequence, and the workpieces are inserted at the position with the best target value. The sub-batch population initialization algorithm includes three strategies: uniform initialization, random initialization and mixed initialization. The speed initialization adopts SAS rules to set an appropriate processing speed for each workpiece to reduce total energy consumption.

5. The method according to claim 1, wherein: The crossover strategy in step 6 is to design multiple crossover strategies for workpiece sequences, speed sequences, and sub-batch sequences, and enhance population diversity and improve global search capabilities through different gene recombination methods; The mutation strategy in step six is ​​to keep the speed sequence unchanged and design multiple mutation strategies for the workpiece sequence and sub-batch sequence to improve the diversity of the algorithm search space and the quality of the optimization solution.

6. The method according to claim 1, wherein: The local search strategy in step 3 is to design a set of neighborhood structures N for the evolution of the workpiece sequence. K , where k∈{1,...,k max }, and k max It is set to the maximum value of 5, and the neighborhood structures include single-plant two-point insertion, single-plant two-point exchange, double-plant two-point insertion, single-plant subsequence insertion, and single-plant overall backward movement.

7. The method according to claim 1, wherein: The main differences between INSGAII and NSGAII are as follows: Difference 1: Fusion of three different strategies to generate workpiece population, sub-batch population and speed setting respectively; Difference 2: Introducing multiple crossover and mutation operations to perturb the workpiece population and sub-batch sequence to explore potential non-dominated solutions; Difference 3: The speed sequence remains unchanged, the workpiece population executes VNS and CFLS, and the sub-batch sequence executes exchange and insertion of local search operators.

8. The method according to claim 1, wherein: The specific steps of the experimental design and performance analysis verification are as follows: The parameters of the flow shop scheduling problem model are received in real time through a data receiver. The experiment is set up on a desktop computer equipped with an Intel(R) Core(TM) i7-6700 CPU processor and 16GB RAM. INSGAII is implemented in MATLAB to calculate the hypervolume index of the flow shop scheduling process in real time. The hypervolume index is used to evaluate the performance of the algorithm. The hypervolume index HV value is the volume of the hypercube formed between the set S and the reference point R, where S is the Pareto front of the non-dominated solutions obtained by the algorithm. The larger the hypervolume index value HV, the better the algorithm performance. The calculation formula of the hypervolume index HV value is as follows: Here, HV(S,R) represents the hypervolume index between the solution s and the reference point R. Based on this index, the relative percentage increase is used to evaluate the performance of the algorithm. The smaller the RPI value, the better the algorithm performance. The calculation formula of RPI is as follows: Among them, RPI represents the relative percentage growth value, f best represents the HV value obtained in a given instance, which is the best HV value among all instances, f x It indicates the HV value obtained by the current algorithm on a certain instance. If RPI = 0%, it means that the algorithm has achieved the best performance; RPI > 0% indicates that there is a gap.

9. The method according to claim 1, wherein: The experimental design and performance analysis verification are used to propose three initialization strategies. A random variant of NSGAII (denoted as N1) is designed for comparison. A total of 675 instances are used to calculate the HV value. At the same time, variance analysis is performed to evaluate the differences between the algorithms. If the RPI value of NSGAII is always lower than that of N1, it indicates that the initialization strategy significantly enriches the diversity of the population and improves the quality of the population. If the p-value is less than 0.05, it indicates that there is a statistically significant difference between NSGAII and N1.

10. The method according to claim 1, wherein: The experimental design and performance analysis verification are carried out to analyze the influence of the designed crossover and mutation operations. INSGAII is also compared with the INSGAII algorithm without the fusion of the three initialization strategies. The INSGAII without crossover and mutation is called N2. The crossover probability P is calculated by c and mutation probability P m Set it to 0 while keeping the population size PS and the proportion of the population performing local search unchanged. If the p value is less than 0.05, it indicates that there is a significant difference between KDNSGAII and N2; The experimental design and performance analysis verification are conducted to verify the effectiveness of the local search strategy. INSGAII with the local search strategy and N3 without the local search strategy are integrated. If the p-value is 0.0132, which is less than 0.05, it indicates that there is a significant difference between the two algorithms, and INSGAII is better than N3. It is judged that the proposed local search operator can not only improve the convergence speed of the solution, but also enhance the exploration and exploration capabilities at the same time.

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