A dynamic tugboat scheduling method using multi-population multi-objective genetic programming algorithm

Abstract

The application provides a dynamic tug scheduling method using a multi-population multi-objective genetic programming algorithm, and comprises the following steps: establishing a simulation environment, defining a target function to be solved, and defining total flow time and total cost of tug operation as two optimization objectives; solving the target function to be solved through the multi-population multi-objective genetic programming algorithm to obtain an optimal decision rule individual; and calling allocation rules and sequence rules of the selected decision rule individual to make a tug scheduling decision according to a ship arrival event and an operation preparation event. The application improves the flexibility of ship scheduling, thereby improving the port operation efficiency and reducing the operation cost.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of port tug dynamic scheduling, in particular to a dynamic tug scheduling method using multi-population multi-objective genetic programming algorithm. BACKGROUND

[0002] In port operation, tug scheduling is crucial for ship berthing, unberthing and other operations. Traditional static modeling assumes that all information is known in advance, but in actual scenarios, there are dynamic events such as sudden unberthing requests, tug breakdowns, etc. Static models are difficult to adapt to dynamic changes and do not consider tug assistance for ship unberthing and fixed costs of tugs, making it difficult to meet the needs of dynamic ship arrival and real-time scheduling.

[0003] With the growth of port business volume and the dynamic nature of ship operations, there is a need for a method that can efficiently schedule tugs according to real-time ship needs. Currently, dynamic tug scheduling is of concern, which takes into account the dynamic request for service by ships, but existing scheduling methods have shortcomings in handling multi-objective optimization and real-time performance, making it difficult to balance scheduling efficiency while considering cost control. The existing technology has the following defects:

[0004] 1. Single target limitation: Most studies only optimize a single indicator (such as total time or total cost), which cannot balance the competitive relationship between multiple objectives;

[0005] 2. Strong rule dependency: Artificially designed scheduling rules are difficult to cover complex dynamic scenarios and lack adaptive optimization capabilities;

[0006] 3. Lack of real-time performance: Traditional mathematical programming methods are time-consuming to calculate and cannot meet the real-time response needs of dynamic scheduling. SUMMARY

[0007] To address the problems in the prior art, the present application proposes a dynamic tug scheduling method using multi-population multi-objective genetic programming algorithm, aiming to solve the problems of single target limitation, strong rule dependency and lack of real-time performance in current dynamic ship scheduling.

[0008] The invention aims to achieve the following technical solutions:

[0009] A dynamic tug scheduling method using multi-population multi-objective genetic programming algorithm, comprising the following steps:

[0010] Step 1: Establish a simulation environment and define the target function to be solved; in the target function to be solved, define the total flow time and total cost of tug operations as two optimization objectives;

[0011] Step 2: Solve the target function to be solved using the multi-population multi-objective genetic programming algorithm to obtain the optimal decision rule individual:

[0012] Randomly generate decision rule individuals for each population, define the population as a set consisting of Ni decision rule individuals, each decision rule individual consists of a first GP tree representing the tugboat allocation rule and a second GP tree representing the tugboat sequence rule; the tugboat allocation rule is used to specify which tugboat should be allocated to a certain operation, and the terminal set is substituted into the allocation rule to obtain the priority of the operation at each tugboat; the tugboat sequence rule calculates the priority of each operation allocated to the tugboat to determine the execution sequence when multiple operation tasks are prepared at the same time; define the central node population as the archive;

[0013] Use M populations to perform single-objective optimization on two optimization objectives using GP, and then use a central node population to fuse and select the M populations, thereby obtaining new M populations for the two optimization objectives;

[0014] The new M populations are merged into an archive with a size of NA; the selection of decision rule individuals in the archive is determined by non-dominated sorting and crowding calculation: first, select decision rule individuals with lower non-dominated levels according to the non-dominated sorting results; when the non-dominated levels are the same, select decision rule individuals with larger crowding degrees;

[0015] Step three, according to the ship arrival event and the operation preparation event, call the allocation rule and the sequence rule of the selected decision rule individual to make a tugboat scheduling decision.

[0016] The dynamic tugboat scheduling method using the multi-population multi-objective genetic programming algorithm further includes an evolution operation to generate new populations; the evolution operation includes sequentially performing selection, crossover, and mutation operations.

[0017] The selection operation uses a tournament selection algorithm; the crossover operation is completed by exchanging the sub-trees of two parent decision rule individuals according to a specified crossover probability to generate new child decision rule individuals; the mutation operator of the mutation operation includes sub-tree mutation of the parent decision rule individual and point mutation of the parent decision rule individual, the sub-tree mutation of the parent decision rule individual replaces the entire sub-tree corresponding to the node with a randomly generated sub-tree, and the point mutation of the parent decision rule individual mutates a node; the update population operation combines the parent decision rule individuals and the child decision rule individuals, and updates the population according to the fitness values of the corresponding objectives.

[0018] After the evolution operation, archiving and updating are performed, and after multiple iterations of optimization, an archive of excellent individuals with early non-dominated sorting is obtained in the training environment; in the test environment, the fitness values of all individuals in the archive are calculated, non-dominated sorting is performed, the corresponding Pareto front is found, and thus the optimal tugboat scheduling scheme is determined.

[0019] The archiving and updating is archiving and saving all decision rule individuals of each population to an archive library, and sorting according to a Pareto dominance level, reserving the top NA decision rule individuals in the sorting to the archive library, and sorting the decision rule individuals in the archive library according to a single optimization target, and forming the top Ni decision rule individuals into a new i-th population.

[0020] A server, comprising a processor and a memory, at least one program is stored in the memory, the program is loaded and executed by the processor to realize the above-mentioned dynamic tug scheduling method using multi-population multi-objective genetic programming algorithm.

[0021] A computer readable storage medium, at least one program is stored in the storage medium, the program is loaded and executed by the processor to realize the above-mentioned dynamic tug scheduling method using multi-population multi-objective genetic programming algorithm.

[0022] The beneficial effects of the present application are as follows:

[0023] (1) The present application automatically generates decision rules through genetic programming, which can quickly adapt to the dynamic arrival of ships and improve the real-time and accuracy of tug scheduling. The decision rules are composed of two GP trees, including allocation rules and sequence rules, which can flexibly arrange the scheduling of ships.

[0024] (2) The use of multi-population multi-objective genetic programming (MPMO-GP, Multiple Population for Multiple Objective Genetic Programming) can effectively balance the two goals of total flow time and total cost, improve port operation efficiency while reducing operating costs. And it does not need to calculate the crowding distance, avoiding the influence of the scale difference of the target on the result.

[0025] (3) Compared with the traditional scheduling method, the present application considers more comprehensive factors, including tugboat assisting ship departure and tugboat fixed cost, etc., so that the scheduling scheme is more in line with the actual port operation demand.

[0026] (4) By setting reasonable nodes and parameters, and using effective evaluation methods, a better tug scheduling strategy can be found in a complex port operation environment, and the overall port operation benefit can be improved. BRIEF DESCRIPTION OF DRAWINGS

[0027] Figure 1 It is a flow chart of a dynamic tug scheduling method using multi-population multi-objective genetic programming algorithm.

[0028] Figure 2 It is a flow chart of MPMO-GP algorithm.

[0029] Figure 3 Flow chart for three stages of berthing, moving and unberthing of the ship operation of the present application.

[0030] Figure 4 Flow chart for tugboat dispatching decision of the present application.

[0031] Figure 5 Schematic diagram of GP tree individual of the present application.

[0032] Figure 6 Comparison chart of first experimental results of the present application.

[0033] Figure 7 Comparison chart of second experimental results of the present application.

[0034] Figure 8 Comparison chart of third experimental results of the present application.

[0035] Figure 9 Comparison chart of fourth experimental results of the present application.

[0036] Figure 10 Comparison chart of fifth experimental results of the present application.

[0037] Figure 11 Comparison chart of sixth experimental results of the present application. DETAILED DESCRIPTION

[0038] The present application will be further described in conjunction with the embodiments and the accompanying drawings, but the embodiments of the present application are not limited thereto.

[0039] As Figure 1 , 2 A dynamic tugboat dispatching method using a multi-population multi-objective genetic programming algorithm, comprising the following steps:

[0040] S1, establishing a simulation environment and defining a target function to be solved; in the target function to be solved, defining the total flow time and total cost of tugboat operation as two optimization objectives;

[0041] The ship arrival time interval (a random variable, a preset hyperparameter) is subjected to an exponential distribution with a parameter λ, the operation processing time (the operation processing time required by the tugboat to tow the ship to the position, related to the tugboat horsepower and the ship tonnage) and the cost (the cost required by the tugboat to tow the ship to the position, related to the tugboat horsepower and the ship tonnage) are determined according to the ship type and the tugboat power;

[0042] The target function is defined as follows:

[0043]

[0044]

[0045] where F1, F2 represent the two optimization objectives of total flow time and total cost respectively, whose values are determined by the allocation rule and the order rule . That is, solve .

[0046] The formula of λ is:

[0047]

[0048] where M represents the number of tugboats, N represents the number of ship types, T m,n represents the time required for a tugboat to handle a corresponding ship, and μ is a constant representing the utilization rate of the tugboat.

[0049] Substitute the terminal set θ into to calculate:

[0050] 1. The priority of the ship's operation in each tugboat.

[0051] 2. The priority of each operation allocated to the tugboat.

[0052] The allocation rule and the order rule are functions of the terminal set, represented by the GP tree. The terminal set is a parameter set that can represent the current state, and its calculation method is given in Table 2. n represents the number of ships, q j represents the number of operations required for ship j to complete the scheduling process, is a random variable representing the arrival time of operation i, and its arrival time interval follows an exponential distribution with parameter λ, represents the completion time of operation i, determined by . cost i,j represents the cost of operation j, and the specific machine allocated is determined by .

[0053] is a random variable representing ship j, is a random variable representing the arrival time of ship j+1, and the difference between the two random variables, i.e. the arrival time interval is also a random variable, following an exponential distribution with parameter λ.

[0054] The constraints of the objective function include:

[0055] a. A tugboat can only handle one operation at the same time;

[0056] The formula expression is:

[0057]

[0058] wherein is the processing start time of the tugboat, represents the processing time of the tugboat;

[0059] b. The first operation of each ship must be processed after the release of the ship is completed;

[0060] The formula is:

[0061]

[0062] c. The relationship between the processing start time and the processing completion time of the dispatch operation is established; the formula is:

[0063]

[0064] d. When the dispatch operation is performed, the next dispatch operation instruction must wait for the previous dispatch operation to be completed on the assigned tugboat before starting processing;

[0065] The formula is:

[0066]

[0067] e. Each operation can only be processed on one of the candidate tugboats;

[0068] The formula is:

[0069]

[0070] The element in the jth row and mth column of Table 1 represents the operation processing time and cost of the jth ship on the mth tugboat.

[0071] Table 1

[0072] Time, cost Tug type 1 Tug type 2 Tug type 3 Tug type 4 Tug type 5 Tug type 6 Vessel type 1 3.33,0.30 1.53,0.65 1.25,0.80 1.00,1.00 0.80,1.25 0.66,1.52 Vessel type 2 - 2.56,0.39 2.08,0.48 1.66,0.60 1.33,0.75 1.11,0.90 Vessel type 3 - - 3.33,0.30 2.66,0.38 2.13,0.47 1.77,0.56 Vessel type 4 - - - 4.00,0.25 3.33,0.30 2.66,0.38 Vessel type 5 - - - - 4.00,0.25 3.33,0.30

[0073] S2, initialize the simulation environment and algorithm parameters: define the function set set = {+, -, *, / , Max, Min}; set the terminal set, including the ship waiting time (TWT) and the remaining operation number (NRS); at the same time, set the parameters of the MPMO-GP algorithm, including the population number M = 2 (positively correlated with the number of solving targets), the population size Ni = 200 (positively correlated with the complexity of the solving problem), the archive size NA = 400 (which can be set: population number * population size), the maximum depth of an individual is 8, and the proportion between crossover, mutation, and replication is 80% / 15% / 5%, respectively;

[0074] ​​S3, population initialization: randomly generate decision rule individuals for each population, define the population as a set consisting of Ni decision rule individuals, each decision rule individual consists of a first GP tree representing the tugboat allocation rule and a second GP tree representing the tugboat sequence rule; the tugboat allocation rule is used to specify which tugboat should be allocated to a certain operation, and the terminal set (as shown in Table 2) is substituted into the allocation rule to obtain the priority of the operation at each tugboat; the tugboat sequence rule calculates the priority of each operation allocated to the tugboat to determine the execution sequence when multiple operation tasks are prepared at the same time; define the central node population as the archive;

[0075] Table 2

[0076] Table 2: The terminal set of DTug-SP.

[0077]

[0078] Single-objective optimization is performed on two optimization objectives using M populations respectively, and a central node population is used to fuse and select the M populations, thereby obtaining new M populations for the two optimization objectives;

[0079] The new M populations are merged into an archive with a size of NA; the selection of decision rule individuals in the archive is determined by non-dominated sorting and crowding calculation: first, according to the non-dominated sorting result, preferentially select decision rule individuals with lower non-dominated level (i.e. better); when the non-dominated level is the same, select decision rule individuals with larger crowding degree;

[0080] Wherein:

[0081] MPMO-GP is a multi-objective solving algorithm combined by MPMO (Multi-Population Multi-Objective) and GP (Genetic Programming, generally single objective), the basic idea of which is to use M populations to perform single-objective optimization on M objectives using GP, and then use a central node population (i.e. archive) to fuse and select the M populations, thereby obtaining new M populations for the M objectives.

[0082] The calculation process and related formulas of single-objective GP are as follows (taking the optimization objective of minimum total flow time as an example):

[0083] 1. Initialize the population: randomly generate a population with a size of N, the individual of the population consists of two GP trees, the non-leaf nodes of which are uniformly generated by the function set, and the leaf nodes are uniformly generated by the terminal set.

[0084] function set = { +, -, *, / , Max, Min};

[0085] 2. Fitness evaluation: Evaluate the performance of each individual according to the objective function of the problem, and calculate its fitness. The fitness is calculated by fixing the random seed of the simulation environment and parsing the two GP trees of the individual to get the corresponding rules Thus the total flow time is calculated in the simulation environment Since our goal is to minimize the total flow time, it is generally desirable to maximize the fitness in GP, so here the fitness of a certain individual i fit i The reciprocal of the total flow time is used for calculation, i.e. (Remember, if the optimization goal is to minimize the total cost Then ).

[0086] 3. Elitism: Copy the top RP elite individuals in the population according to the fitness, RP represents the copy rate.

[0087] 4. Selection: According to the fitness, select the better performing programs as parents to generate the next generation. Common selection methods include roulette wheel selection, tournament selection, etc.

[0088] Roulette wheel calculation method:

[0089]

[0090] Where P(i) represents the probability of the ith individual being selected to remain in the individual, F 1,i represents the fitness of individual i, represents the sum of the fitness of all individuals in the population.

[0091] 5. Crossover (recombination): Generate a random number rand(), if

[0092] rand() > CR;

[0093] Randomly select two parent individuals and exchange their partial sub-trees to generate new offspring individuals. CR represents the crossover probability.

[0094] 6. Mutation: Generate a random number rand(), if

[0095] rand() > MR;

[0096] MR represents the mutation probability. Randomly modify the newly generated offspring program, such as replacing a certain node operation or operand, to increase the diversity of the program.

[0097] 7. Loop iteration: Repeat steps 2-6 until the termination condition is met, such as reaching the preset number of generations or the fitness no longer significantly improves.

[0098] When the optimization objective is to minimize the total cost, it is exactly the same as when the optimization objective is to minimize the total process time. Simply change the total process time F1 to the total cost F2, and everything else is exactly the same.

[0099] MPMO-GP archive fusion process:

[0100] 1. Archiving: Merge the M populations into a single archive of size NA;

[0101] 2. Multi-objective selection: The selection of individuals in the database is determined by non-dominated ranking and crowding calculation. First, based on the non-dominated ranking results, individuals with lower non-dominated levels (i.e., better) are selected. When non-dominated levels are the same, individuals with higher crowding are selected.

[0102] S4, such as Figure 4 The simulation scheduling process evaluates individual fitness values: In the simulation environment, based on ship arrival events and operational preparation events, the allocation rules and sequence rules of the selected decision rules are invoked to make tugboat scheduling decisions.

[0103] S5. Evolutionary Operations: Selection, crossover, and mutation operations are performed sequentially to generate a new population.

[0104] The selection operation employs a tournament selection algorithm; the crossover operation involves swapping the subtrees of two parent decision rule individuals according to a specified crossover probability to generate new child decision rule individuals; the mutation operation includes subtree mutation and point mutation of parent decision rule individuals. Subtree mutation of parent decision rule individuals selects a mutation node and replaces the entire subtree corresponding to that node with a randomly generated subtree, while point mutation of parent decision rule individuals mutates a single node; the population update operation merges parent and child decision rule individuals and updates the population based on the fitness values ​​of the corresponding targets.

[0105] S6. Archiving and Updating: Archive and save all decision rule individuals of each population to the archive, sort them according to Pareto dominance level, retain the top NA decision rule individuals in the archive, sort the decision rule individuals in the archive according to a single optimization objective, and form a new i-th population with the top Ni decision rule individuals.

[0106] S7. Iterative optimization: Repeat steps S4 to S7 until the termination condition is met. The termination condition is the set number of iterations. When the population reaches the set number of iterations, the loop exits.

[0107] S8, obtaining the Pareto front dispatching scheme: after multiple generations of evolution, the excellent individual library in the early non-dominated sorting is obtained in the training environment; in the test environment, the fitness values of all individuals in the library are calculated, non-dominated sorting is performed, the corresponding Pareto front is found, and thus the optimal tugboat dispatching scheme is determined.

[0108] In the above embodiment:

[0109] The S1 establishes a simulation environment, the ship is called Ship, the tugboat is called Tugboat, and the berthing and unberthing operations are called Operation, as shown in the following table: Figure 3 As shown, three stages of ship operation in the dynamic tugboat dispatching process are shown: berthing, moving and unberthing, and the dynamic characteristics of tugboat dispatching.

[0110] Then, the S2 sets the parameters of the MPMO-GP, in this embodiment, the population size M is set to 2, the population size Ni is set to 200, the library size NA is set to 100, the maximum depth of the individual is set to 8, and the proportions of the three operations of crossover, mutation and replication are set to 85%, 10% and 5% respectively. In addition, the iteration round is set to 50.

[0111] After setting the parameters of the MPMO-GP, the S3 is performed to randomly generate decision rule individuals for each population, as shown in the following table: Figure 5 As shown, an example of a GP tree individual is presented, where the function set includes addition, subtraction, multiplication, division, maximum value, minimum value and other operations.

[0112] Then, the S4 is performed to evaluate the individual fitness in the simulation dispatching process. In the current iteration round, all individuals of all populations will use the environment generated by the same random seed for simulation, and each individual will obtain the values of the two optimization objectives, i.e. operation processing time and cost, after simulation according to its own GP tree rule, which are the fitness values. If the iteration round of the individual has not reached 50, the S5 is entered to perform selection operation, crossover operation and mutation operation in turn. Finally, all individuals of each population are saved to the library, sorted according to the Pareto dominance level, and the top NA individuals are reserved to the library, and the individuals in the library are sorted according to the single optimization objective, and the top Ni individuals are combined to form the i-th population.

[0113] The S4 to S7 are repeated in a loop until the iteration round reaches 50, the loop is exited, and the experimental results are obtained.

[0114] In order to better reflect the advantages of the present application, under the same parameter settings, experiments are also carried out using the multi-objective evolutionary algorithm based on decomposition (MOEA / D) and the non-dominated sorting genetic algorithm (NSGA II) respectively. At the same time, in order to avoid the randomness of the experimental results, twenty independent repeated experiments are also carried out. The final results are shown in Table 3. As can be seen from the data in Table 3, the average value of the hyper-volume index (HV) of the multi-population multi-objective genetic algorithm (MPMO-GP) used in the present application is higher than that of the multi-objective evolutionary algorithm based on decomposition and the non-dominated sorting genetic algorithm, and the hyper-volume index is used to measure the performance of different algorithms in multiple test environments, and the larger the hyper-volume index value, the better the comprehensive performance of the algorithm.

[0115] Table 3

[0116]

[0117]

[0118] Figure 6 to Figure 11 The comparison chart of the experimental results of the six independent repeated experiments shows that Figure 6 to Figure 11 As can be seen from the comparison chart, in the six experiments, the average value of the hyper-volume index of the experimental results obtained by the multi-population multi-objective genetic algorithm is higher than that of the multi-objective evolutionary algorithm based on decomposition and the non-dominated sorting genetic algorithm.

[0119] A server, comprising a processor and a memory, at least one program is stored in the memory, the program is loaded and executed by the processor to realize the above-mentioned dynamic tugboat scheduling method using multi-population multi-objective genetic programming algorithm.

[0120] A computer readable storage medium, at least one program is stored in the storage medium, the program is loaded and executed by the processor to realize the above-mentioned dynamic tugboat scheduling method using multi-population multi-objective genetic programming algorithm.

[0121] In view of the defects of single-objective limitation, strong rule dependence and insufficient real-time performance, multi-objective genetic programming shows potential in automatic rule generation. However, in the multi-objective dynamic scheduling scene, there are still problems such as poor convergence of Pareto front and insufficient rule representation. Therefore, a dynamic tugboat scheduling method capable of automatically generating multi-objective optimization rules and adapting to dynamic events is urgently needed. The above-mentioned scheme can solve the problem well.

[0122] The above-mentioned only for the optimal solution embodiment of the present application, not for limiting the present application, the person skilled in the art makes various modifications or replacements to the present application without departing from the essence and protection scope of the present application, which should be within the protection scope of the present application.

Claims

1. A dynamic tugboat scheduling method using a multi-population multi-objective genetic programming algorithm, characterized in that: The method comprises the following steps: Step one, establishing a simulation environment, defining the target function to be solved; in the target function to be solved, defining the total flow time and total cost of the tugboat operation as two optimization objectives; Step two, solving the target function to be solved by using a multi-population multi-objective genetic programming algorithm to obtain an optimal decision rule individual: Randomly generating a decision rule individual for each population, defining the population as a set composed of Ni decision rule individuals, and each decision rule individual is composed of a first GP tree representing a tugboat allocation rule and a second GP tree representing a tugboat sequence rule; the tugboat allocation rule is used to specify which tugboat should be allocated to a certain operation, and the priority of the operation in each tugboat can be calculated by substituting the terminal set into the allocation rule; The tugboat sequence rule is used to calculate the priority of each operation allocated to the tugboat to determine the execution sequence when multiple operation tasks are prepared at the same time; the central node population is defined as an archive; Using M populations to perform single-objective optimization on the two optimization objectives by using GP, and then using a central node population to fuse and select the M populations, thereby obtaining new M populations for the two optimization objectives; The new M populations are merged into an archive with a size of NA; the selection of the decision rule individuals in the archive is determined by non-dominated sorting and congestion calculation: first, the decision rule individuals with lower non-dominated levels are preferentially selected according to the non-dominated sorting result; when the non-dominated levels are the same, the decision rule individuals with larger congestion degrees are selected; Setting the ship arrival time interval to follow an exponential distribution with a parameter λ, and determining the operation processing time and cost according to the ship type and the tugboat power; Defining the target function as follows: ； ； ； ； ； where denotes the number of ships, denotes the number of operations needed for ship j to complete the scheduling process, is a random variable denoting the arrival time of ship j, is a random variable denoting the arrival time of ship j+1, the difference between the two random variables, i.e. the arrival time interval - is also a random variable, - obeys an exponential distribution with a parameter ; denotes the completion time of operation i, determined by the allocation rule and the sequencing rule ; denotes the overhead of operation j, the specific machine to which it is assigned determined by the allocation rule ; , respectively represent two optimization objectives total flow time and total cost, whose sizes are determined by assignment rules and sequencing rules , i.e., solving for ; The calculation formula is: ； ； where M represents the number of tugs, N represents the number of ship types, T m,n represents the time required for a tug to handle a corresponding ship, and μ is a constant representing the utilization rate of the tug; Substitute the terminal set θ into , It can be calculated that: (1) the priority of the ship operation in each tugboat; (2) the priority of each operation allocated to the tugboat; Step three, calling the allocation rule and sequence rule of the selected decision rule individual to make a decision on the tugboat scheduling according to the ship arrival event and the operation preparation event.

2. The dynamic tugboat scheduling method using the multi-population multi-objective genetic programming algorithm according to claim 1, characterized in that: The method further comprises an evolution operation for generating a new population; the evolution operation comprises sequentially performing a selection operation, a crossover operation, and a mutation operation.

3. The dynamic tugboat scheduling method using the multi-population multi-objective genetic programming algorithm according to claim 2, characterized in that: The selection operation adopts a tournament selection algorithm; the crossover operation is performed by exchanging the sub-trees of two parent decision rule individuals according to a specified crossover probability, completing the crossover operation, and generating a new child decision rule individual; the mutation operator of the mutation operation includes sub-tree mutation of the parent decision rule individual and point mutation of the parent decision rule individual, the sub-tree mutation of the parent decision rule individual replaces the sub-tree corresponding to the node as a whole with a randomly generated sub-tree, and the point mutation of the parent decision rule individual mutates a node; the update population operation combines the parent decision rule individual and the child decision rule individual, and updates the population according to the fitness value of the corresponding target.

4. The dynamic tugboat scheduling method using the multi-population multi-objective genetic programming algorithm according to claim 2, characterized in that: After the evolution operation, archiving and updating are performed, and after multiple iterations of optimization, an archive of excellent individuals with a non-dominated sorting in the training environment is obtained; in the test environment, the fitness values of all individuals in the archive are calculated, non-dominated sorting is performed, the corresponding Pareto front is found, and thus the optimal tugboat scheduling scheme is determined.

5. The dynamic tugboat scheduling method using the multi-population multi-objective genetic programming algorithm according to claim 4, characterized in that: The archiving and updating is archiving and saving all decision rule individuals of each population to an archive, and sorting according to a Pareto dominance level, reserving the top NA decision rule individuals in the archive, and sorting the decision rule individuals in the archive according to a single optimization target, and grouping the top Ni decision rule individuals to form a new i-th population.

6. A server comprising a processor and a memory having stored therein at least one segment of a program, characterized in that, The program is loaded and executed by the processor to implement the dynamic tugboat scheduling method using the multi-population multi-objective genetic programming algorithm in any one of claims 1 to 5.

7. A computer-readable storage medium having stored therein at least one segment of a program, characterized in that, The program is loaded and executed by the processor to implement the dynamic tugboat scheduling method using the multi-population multi-objective genetic programming algorithm in any one of claims 1 to 5.

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