Multi-AGV path planning method based on constrained multi-objective optimization

Abstract

The invention discloses a multi-AGV path planning method based on constrained multi-objective optimization, and the method comprises the steps: dynamically dividing a whole population into three mutually exclusive subsets: an FNDS, an FNDS dominant subset and an FNDS-undominant subset, and not carrying out the balance convergence and constraint satisfaction in each subset according to the provided division of labor. The algorithm provided by the invention can effectively search feasible solutions with good diversity and convergence in a short time.

Description

Technical Field

[0001] The present invention belongs to the field of vehicle path optimization and relates to a constraint processing method based on evolutionary computing, and specifically, relates to a multi-AGV path planning method based on constrained multi-objective optimization. Background Art

[0002] Over the past years, many constrained multi-objective evolutionary algorithms (CMOEAs) have been designed to solve constrained multi-objective optimization problems (CMOPs). In these CMOEAs, some constraint handling techniques (CHTs) have been proposed to balance convergence and constraint satisfaction, however, they still face some serious challenges, such as premature convergence to local optimal regions and large workload of parameter tuning for specific CMOPs. For multi-objective optimization problems (MOPs), there exists a set of non-dominated optimal solutions, called the Pareto set (PS), and a corresponding objective vector, called the Pareto front (PF).

[0003] Solving a CMOP is slightly different from solving an unconstrained MOP because it requires satisfying three criteria simultaneously: (1) constraint satisfaction, (2) good convergence, and (3) good distribution. In particular, it is difficult to balance constraint satisfaction and convergence. For example, some complex CMOPs have many infeasible regions and local optimal solutions, such as Figure 1 shown.

[0004] make Pt (i) For population Pt The i-th feasible non-dominated individual in NPt (i) is a new variant individual. NPt (i) Domination of the original Pt (i), while NPt (i) is located in the infeasible region (shown on a white background). It is worth noting that NPt The convergence quality of (i) is better than Pt (i), while Pt The constraint satisfaction of (i) is better than NPt (i).

[0005] Regardless of the constraint handling technique used, when CMOEA accepts NPt (i), the population tends to converge to the unconstrained PF. If CMOEA rejects NPt (i), the population can easily fall into a local optimum. Ideally, a well-designed CMOEA should find a set of feasible, well-converged, and well-distributed non-dominated solutions. However, many CMOEAs can only obtain solutions with poor distribution.

[0006] In terms of constraint handling technology (CHT), existing CMOEAs can be roughly divided into: penalty function methods, representative designs include ShiP and dCMOEA. However, the setting of the penalty factor often depends on the specific problem, and for infeasible solutions, it is still necessary to continuously adjust to find the optimal degree of penalty. Although some adaptive penalty CMOEAs have been designed, the feedback information used to set the adaptive penalty factor often has deviations; goal and constraint separation methods, popular designs in this category are A-NSGA-III and MOEA / D-ACDP. Since feasible solutions usually have higher priority than infeasible solutions, CMOEAs in this category can easily fall into the local optimal feasible domain; special representation and operator methods, including POCEA, CPS, and feasible guided NSGA-II. However, most CMOEAs in this category require high computational costs to generate promising solutions and are extremely sensitive to parameter adjustments; hybrid methods, PPS, ToP, and DD-CMOEA divide the entire evolution process into multiple stages, each of which adopts different constraint handling strategies. But the generated acceptable solutions come at a great cost.

[0007] However, existing CMOEAs still face challenges such as premature convergence to local optimal regions, poor diversity, and laborious parameter tuning for specific CMOPs. Looking back at the literature over the past two decades, almost all existing constraint handling techniques are optimized by solving constrained single-objective problems. Therefore, the information hidden in feasible non-dominated sets (FNDS) has not been fully utilized to solve constrained multi-objective optimization problems. Summary of the invention

[0008] The purpose of the present invention is to achieve the two goals of minimum number of dispatched AGVs (NV) and minimum total distance (TD) when planning multi-AGV paths, while there are constraints such as time window and vehicle capacity. To overcome the problems existing in the prior art that the existing CMOEA still faces difficulties such as premature convergence to the local optimal area, poor diversity, and laborious parameter adjustment for a specific CMOP, a multi-AGV path planning method based on constrained multi-objective optimization is provided.

[0009] To achieve the above objectives, the present application provides a multi-AGV path planning method based on constrained multi-objective optimization, comprising the following steps: Step A, obtaining an environmental model of the path planning area, the environmental model including a warehouse node, multiple distribution nodes, edges between nodes, and the length of each edge in the path planning area, and constructing a mathematical model based on the environmental model with AGV capacity and total completion time as constraints and with the shortest total AGV running distance and the least number of AGVs as goals; The objective function and constraints are intended to meet the two goals of minimizing the number of dispatched AGVs (automatic guided vehicles) and minimizing the total AGV running distance in a multi-AGV scheduling scenario, while also meeting constraints such as total completion time and AGV capacity.

[0010] Step B, then solve the model based on the genetic algorithm of constrained multi-objective optimization according to the following steps to obtain the feasible non-dominated set FNDS.

[0011] Specifically, the model is solved by applying a genetic algorithm based on constrained multi-objective optimization, including the following steps: Step 1, initialize the maximum iteration number Gmax, population size P, current iteration number t, solution set Pt, and iterate; The maximum number of iterations is set to 1000, the population size is set to 100, the current number of iterations is set to 1, and the solution set P1 is initialized; Step 3, search and find the non-dominated set FNDS among all feasible solutions in the solution set Pt; Among them, a feasible solution refers to an individual in the solution set that satisfies all constraints; the solution set also includes individuals that do not satisfy any one or more constraints, and Pt(i) is an individual in the solution set; Domination means: if all the target solutions of a feasible individual are not inferior to all the target solutions of another individual, and it is superior to another individual in at least one target, then the individual dominates another individual; Non-dominance means: if there is no situation where an individual dominates another individual, and the individual is inferior to the other individual in at least one goal and the other individual is inferior to the individual in at least one goal, then the individual and the other individual are said to be in a non-dominant relationship; Step 4, let the individual number be i. If i is not less than P, go to step 1; otherwise, determine whether FNDS can dominate Pt(i). If it can dominate Pt(i), then Pt(i) is added to FNDS`, and FNDS` represents the set of individuals dominated by FNDS in the solution set; if it cannot dominate Pt(i), then Pt(i) is added to FNDS``, and FNDS`` represents the set of individuals not dominated by FNDS in the solution set; divide all individuals according to the three states in the solution set; mutate Pt(i) to obtain NPt(i); Step 5, calculate the FNDSDomCt values ​​of Pt(i) and NPt(i) respectively, assign FNDSDomCt(Pt(i)) to ODomCt, and assign FNDSDomCt(NPt(i)) to NDomCt, where FNDSDomCt(X) represents the number of individuals that dominate X in FNDS, where FNDSDomCt represents the function, and the number of individuals that dominate the specified individuals in the FNDS set is calculated. Assume that X is an individual in the population, and FNDSDomCt(X) represents the number of individuals that dominate X in FNDS; Step 6: According to the classification of Pt(i), the convergence, number of constraints satisfied, dominance relationship, and diversity of Pt(i) and NPt(i) are compared in turn. According to the comparison result, whether NPt(i) replaces Pt(i) is determined, and the individual sequence number is updated according to i=i+1, and then go to step 4; Step 7: Output the value in FNDS.

[0012] Furthermore, step 6 includes: S106, determine whether Pt(i+1) belongs to FNDS``, if so, determine whether ODomCt and NDomCt are equal, if they are equal and the number of constraints satisfied by NPt(i) is greater than the number of constraints satisfied by Pt(i), it means that NPt(i) satisfies the constraints better than Pt(i), and NPt(i) replaces Pt(i); if Pt(i) belongs to FNDS`, determine whether NDomCt is less than ODomCt, if less, it means that NPt(i) is more convergent, and NPt(i) replaces Pt(i); if they are equal and NPt(i) dominates Pt(i), it means that NPt(i) is better convergent, and NPt(i) replaces Pt(i); execution is completed, update the individual sequence number according to i=i+1, and go to step 4; if Pt(i) belongs to FNDS, go to step S107; S107, determine whether the number of constraints satisfied by NPt(i) and Pt(i) is equal. If not, it means that NPt(i) becomes infeasible and should be ignored. Update the individual sequence number according to i=i+1 and go to step 4. If the number of constraints satisfied by NPt(i) and Pt(i) is equal, determine whether NDomCt is less than ODomCt. If so, it means that NPt(i) has better convergence and NPt(i) replaces Pt(i). If equal, determine whether NPt(i) dominates Pt(i). If so, it means that NPt(i) has better convergence and NPt(i) replaces Pt(i). If they are non-dominated, determine whether the MED value of NPt(i) is greater than the MED value of Pt(i). If so, it means that the diversity is better and NPt(i) replaces Pt(i). After the execution is completed, update the individual sequence number according to i=i+1 and go to step 4.

[0013] Preferably, step 3 comprises: Step 1.1. Generate the t-th generation population; Step 1.2. Evaluate the individuals, calculate the objective function value for each individual, and check whether they satisfy all constraints; Step 1.3. Determine feasibility and select individuals that meet all constraints from the t-th generation population. These individuals are called feasible solutions. Step 1.4. Perform non-dominated sorting of feasible solutions: compare each feasible individual in the feasible solution population with all other feasible individuals in the t-th generation population; Step 1.5. Identify non-dominated individuals: During the comparison process, record the number of times each feasible individual is dominated by other individuals in the t-th generation population; those individuals with no domination times are considered non-dominated; Step 1.6. Construct the Pareto front: All non-dominated feasible individuals are grouped into a set, which represents the Pareto front of the current population.

[0014] The MED in step S107 is calculated according to the following formula, and the MED is compared to ensure uniform distance between individuals; MED(Pt(i))=NearDis(Pt(i))×TotalDis(Pt(i)) (1) in, (2) (3) Pt (i) represents the i-th individual in the t-th generation population Pt, and TotalDis is calculated as Pt (i) and all Pt (j) is the sum of the Euclidean distances; NearDist( Pt (i) Calculation Pt (i) and Pt (j) The minimum Euclidean distance between two entities; j = 1, ..., P and j ≠ i; NearDist( Pt The larger the value of (i)), the better the individual distance.

[0015] An electronic device of the present invention includes a memory and a processor, wherein the memory is used to store a program that supports the processor to execute the path planning method, and the processor is configured to execute the program stored in the memory.

[0016] The present invention provides a computer-readable storage medium, on which a computer program is stored. When the computer program is run by a processor, the steps of the path planning method are executed.

[0017] The beneficial effects produced by the present invention are: The present invention proposes a novel parameter-free constraint processing technology, which dynamically divides the entire solution set into three mutually exclusive subsets: a feasible non-dominated set FNDS, a solution set FNDS' dominated by FNDS, and a solution set FNDS'' dominating FNDS. According to whether the individual belongs to FNDS, FNDS', or FNDS'', the convergence of the individual's mutant offspring relative to the parent generation is judged, and the more convergent offspring replaces the parent generation. When the convergence is the same, the degree to which the individual's mutant offspring satisfies the constraints relative to the parent generation is judged. If they are equal, the convergence of the individual's mutant offspring relative to the parent generation is then determined, and the more convergent offspring replaces the parent generation. If the convergence cannot be compared, the offspring with better diversity replaces the parent generation. According to the proposed division of labor, there is no need to balance convergence and constraint satisfaction in each subset. The algorithm proposed in this experiment can effectively search for feasible solutions with good diversity and convergence in a short time. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 Distribution diagram of the solution set when the constrained multi-objective evolutionary algorithm (CMOEA) solves the constrained multi-objective optimization problem; Figure 2 Distribution of feasible solutions obtained by a genetic algorithm for constrained multi-objective optimization. DETAILED DESCRIPTION

[0019] In order to make the purpose, technical solution and advantages of the embodiments of the present disclosure clearer, the technical solution of the embodiments of the present disclosure will be clearly and completely described below in conjunction with the drawings of the embodiments of the present disclosure. Obviously, the described embodiments are part of the embodiments of the present disclosure, not all of the embodiments. Based on the described embodiments of the present disclosure, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present disclosure. Example

[0020] In order to make the present invention easier to understand, the specific implementation modes of the present invention will be further described below.

[0021] A multi-AGV path planning method based on constrained multi-objective optimization is designed to solve the AGV delivery task consisting of a single warehouse, N task nodes with delivery time constraints, and K undifferentiated AGVs with capacity constraints. This path planning method can combine the advantages of path planning schemes generated by different search operators, and find a low driving distance path planning scheme that meets the time window and capacity constraints, thereby improving delivery efficiency. It includes the following steps: Step 1: Obtain an environmental model of the path planning area, wherein the environmental model includes a warehouse node V0 and multiple distribution nodes V={ V n, n=0, 1, 2, ..., N}, the set of edges between nodes E={e rt |r, t=0, 1, 2, ..., N}, the length of each edge e rt , based on the environmental model, a mathematical model is constructed with AGV (automatic guided vehicle) capacity and total completion time as constraints, and the goal is to minimize the total AGV running distance and the minimum number of AGVs; The objective function and constraints are intended to meet the two goals of minimizing the number of dispatched AGVs (automatic guided vehicles) and minimizing the total AGV running distance in a multi-AGV scheduling scenario, while also meeting constraints such as total completion time and AGV capacity.

[0022] e rt is the rth node V r To the tth node V t The path, d rt Represents the rth node V r To the tth node V t distance.

[0023] The objective function is: f1=minK

[0024] K represents the number of AGVs; N represents the number of delivery nodes, Indicates whether the kth AGV passes through the edge between the rth node Vr and the tth node Vt. If so, let , otherwise, let .

[0025] The constraints are: (I) (II) (III) (IV) (V) Formula (I) and (II) ensure that each AGV is always dispatched from the warehouse; Formula (III) represents the loading capacity constraint of AGV; Formula (IV) and (V) are the time window constraints for distribution, which ensure that AGV provides services within the specified time window of each distribution node.

[0026] Q represents the maximum loading capacity of each AGV, q rrepresents the demand of the rth node Vr, Tr represents the time when the AGV arrives at the rth node Vr, Wr represents the waiting time of Vr at the rth node Vr, Sr represents the service time required by the rth Vr, Trt represents the travel time of the vehicle from the rth node Vr to the node Vt, e r and l r are the upper and lower limits of the service time window of the rth node Vr.

[0027] Step 2: Apply the genetic algorithm based on constrained multi-objective optimization to solve the model and obtain the feasible non-dominated set FNDS.

[0028] Specifically, the model is solved by applying a genetic algorithm based on constrained multi-objective optimization, including the following steps: S101, initialize the maximum number of iterations Gmax, the population size P, the current number of iterations t, and the solution set Pt; The maximum number of iterations is set to 1000, the population size is set to 100, the current number of iterations is set to 1, and the solution set P1 is initialized; S102, if the current iteration number t is less than Gmax, proceed to S103; otherwise, proceed to S108; S103, search and find the non-dominated set FNDS of all feasible solutions in the solution set Pt; for all individuals in the solution set Pt, perform non-dominated sorting of feasible solutions according to the evaluation function, and find the non-dominated individuals in all feasible solutions in the solution set, such as Figure 2 As shown in blue individuals; Among them, a feasible solution refers to the individual in the solution set that satisfies all constraints; Domination means: if all the target solutions of a feasible individual are not inferior to all the target solutions of another individual, and it is superior to another individual in at least one target, then the individual dominates another individual; Non-dominance means: if there is no situation where an individual dominates another individual, and the individual is inferior to the other individual in at least one goal and the other individual is inferior to the individual in at least one goal, then the individual and the other individual are said to be in a non-dominant relationship; The specific steps are as follows: Step 1.1. Generate the t-th generation population; Step 1.2. Evaluate the individuals, calculate the objective function value for each individual, and check whether they satisfy all constraints; Step 1.3. Determine feasibility and select individuals that meet all constraints from the t-th generation population. These individuals are called feasible solutions. Step 1.4. Perform non-dominated sorting of feasible solutions: compare each feasible individual in the feasible solution population with all other feasible individuals in the t-th generation population; Step 1.5. Identify non-dominated individuals: During the comparison process, record the number of times each feasible individual is dominated by other individuals in the t-th generation population; those individuals with no domination times are considered non-dominated; Step 1.6. Construct the Pareto front: All non-dominated feasible individuals are grouped into a set, which represents the Pareto front of the current population.

[0029] S104, if the current i is not less than P, enter S102; otherwise, determine whether the individual 𝑃𝑡(j) of FNDS can dominate Pt(i). If it can dominate Pt(i), then Pt(i) is added to FNDS`. FNDS` represents the set of individuals dominated by FNDS in the solution set, such as Figure 2 As shown by the red individuals in; if Pt(i) cannot be dominated, then Pt(i) is added to FNDS``, and FNDS`` represents the set of individuals in the solution set that are not dominated by FNDS, such as Figure 2 As shown by the green individuals in the figure; all individuals are divided according to the three states in the solution set; Pt(i) is mutated to obtain NPt(i); Among them, the mutation method can be to exchange the positions of the distribution nodes in the two routes to search the solution space. For example, in the path planning process of AGV, suppose the solution of the parent generation is from warehouse 7 to distribution node 2 to distribution node 6. By exchanging the distribution node positions, it can be changed from warehouse 7 to distribution node 6 to distribution node 2. Thus, the mutant individual is obtained.

[0030] S105, respectively calculating the FNDSDomCt values ​​of Pt(i) and NPt(i), assigning FNDSDomCt(Pt(i)) to ODomCt, and assigning FNDSDomCt(NPt(i)) to NDomCt, wherein FNDSDomCt(X) represents the number of individuals that dominate X in the FNDS, wherein FNDSDomCt represents a function, and the number of individuals that dominate a specified individual in the FNDS set in the calculation, assuming that X is an individual in the population, and FNDSDomCt(X) represents the number of individuals that dominate X in the FNDS; S106, determine whether Pt(i) belongs to FNDS``, if it does, determine whether ODomCt and NDomCt are equal, if they are equal and the number of constraints satisfied by NPt(i) is greater than the number of constraints satisfied by Pt(i), it means that NPt(i) satisfies the constraints better than Pt(i), and NPt(i) replaces Pt(i); if Pt(i) belongs to FNDS`, determine whether NDomCt is less than ODomCt, if it is less, it means that NPt(i) is more convergent, and NPt(i) replaces Pt(i); if they are equal and NPt(i) dominates Pt(i), it means that NPt(i) is better convergent, and NPt(i) replaces Pt(i); execution is completed, update the individual sequence number according to i=i+1, and enter S104; if Pt(i) belongs to FNDS, enter S107; S107, determine whether the number of constraints satisfied by NPt(i) and Pt(i) is equal. If not, it means that NPt(i) becomes infeasible and should be ignored. Update the individual sequence number according to i=i+1 and enter S104; if the number of constraints satisfied by NPt(i) and Pt(i) is equal, determine whether NDomCt is less than ODomCt. If less than, it means that NPt(i) has better convergence, and let NPt(i) replace Pt(i); if equal, determine whether NPt(i) dominates Pt(i). If dominated, it means that NPt(i) has better convergence, and let NPt(i) replace Pt(i); if they are mutually non-dominated, determine whether the MED value of NPt(i) is greater than the MED value of Pt(i). If greater than, it means that the diversity is better, and let NPt(i) replace Pt(i); execution is completed, update the individual sequence number according to i=i+1 and enter S104; S108, output the value in FNDS; In step S107, MED is calculated according to the following formula, and the purpose of comparing MED is to ensure uniform distance between individuals; MED(Pt(i))=NearDis(Pt(i))×TotalDis(Pt(i)) (1) in, (2) (3) Pt (i) represents the i-th individual in the t-th generation population Pt, and TotalDis is calculated as Pt (i) and all Pt (j), j = 1, ..., P, TotalDist(Pt(i)); NearDist( Pt (i) Calculation Pt (i) and Pt(j) the minimum Euclidean distance between; j = 1, ..., P and j ≠ i; NearDist( Pt The larger the value of (i)), the better the individual distance.

[0031] In this embodiment, an electronic device includes a memory and a processor, wherein the memory is used to store a program that supports the processor to execute the above method, and the processor is configured to execute the program stored in the memory.

[0032] In this embodiment, a computer-readable storage medium stores a computer program on the computer-readable storage medium, and the computer program executes the steps of the above method when executed by a processor.

[0033] The present invention proposes a novel parameter-free constraint processing technology, which divides the entire population dynamically into three mutually exclusive subsets: a feasible non-dominated set FNDS, a solution set FNDS' dominated by FNDS, and a solution set FNDS'' dominating FNDS. According to whether the individual belongs to FNDS, FNDS', or FNDS'', the convergence of the individual's mutant offspring relative to the parent generation is judged, and the more convergent offspring replaces the parent generation. When the convergence is the same, the degree to which the individual's mutant offspring satisfies the constraints relative to the parent generation is judged. If they are equal, the convergence of the individual's mutant offspring relative to the parent generation is then determined, and the more convergent offspring replaces the parent generation. If the convergence cannot be compared, the offspring with better diversity replaces the parent generation. According to the proposed division of labor, there is no need to balance convergence and constraint satisfaction in each subset. The algorithm proposed in this experiment can effectively search for feasible solutions with good diversity and convergence in a short time.

[0034] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention is described in detail with reference to the aforementioned embodiments, those skilled in the art can still modify the technical solutions described in the aforementioned embodiments or replace some of the technical features therein by equivalents. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A multi-AGV path planning method based on constrained multi-objective optimization, firstly obtaining an environmental model of the path planning area, the environmental model including a warehouse node, multiple distribution nodes, edges between nodes, and the length of each edge in the path planning area, setting objective functions and constraints, characterized in that: Then, the model is solved based on the genetic algorithm of constrained multi-objective optimization in the following steps: Step 1, initialize the maximum iteration number Gmax, population size P, current iteration number t, solution set Pt, and iterate; Step 2: If the current iteration number t is less than Gmax, go to step 3; Otherwise, go to step 8; Step 3, search and find the non-dominated set FNDS among all feasible solutions in the solution set Pt; Among them, a feasible solution refers to the individual in the solution set that satisfies all constraints; Domination means: if all the target solutions of a feasible individual are not inferior to all the target solutions of another individual, and it is superior to another individual in at least one target, then the individual dominates another individual; Non-dominance means: if there is no situation where an individual dominates another individual, and the individual is inferior to the other individual in at least one goal and the other individual is inferior to the individual in at least one goal, then the individual and the other individual are said to be in a non-dominant relationship; Step 4, if i is not less than P, go to step 2; otherwise, classify the individuals Pt(i) in all solutions obtained in each iteration. If Pt(i) is dominated by FNDS, add it to FNDS`; if Pt(i) is not dominated by FNDS, add it to FNDS``; mutate Pt(i) to obtain NPt(i); Step 5, calculate the number of Pt(i) and NPt(i) dominated by FNDS: ODomCt, NDomCt; Step 6: According to the classification of Pt(i), the convergence, number of constraints satisfied, dominance relationship, and diversity of Pt(i) and NPt(i) are compared in turn. According to the comparison result, whether NPt(i) replaces Pt(i) is determined, and the individual sequence number is updated according to i=i+1, and then go to step 4; Step 7: Output the value in FNDS.

2. The method according to claim 1, characterized in that Step 6 includes: Step S106, determine whether Pt(i) belongs to FNDS``, if so, determine whether ODomCt and NDomCt are equal, if they are equal and the number of constraints satisfied by NPt(i) is greater than the number of constraints satisfied by Pt(i), let NPt(i) replace Pt(i); if Pt(i) belongs to FNDS`, determine whether NDomCt is less than ODomCt, if less, let NPt(i) replace Pt(i); if they are equal and NPt(i) dominates Pt(i), let NPt(i) replace Pt(i); execution is completed, update the individual serial number according to i=i+1, and go to step 4; if Pt(i) belongs to FNDS, go to step S107; Step S107, determine whether the number of NPt(i) and Pt(i) that meet the constraints is equal, if not equal, update the individual serial number according to i=i+1, and go to step 4; if the number of NPt(i) and Pt(i) that meet the constraints is equal, determine whether NDomCt is less than ODomCt, if less, let NPt(i) replace Pt(i); if equal, determine whether NPt(i) dominates Pt(i), if dominated, let NPt(i) replace Pt(i); if they are mutually non-dominated, determine whether the MED value of NPt(i) is greater than the MED value of Pt(i), if greater, let NPt(i) replace Pt(i); execution is completed, update the individual serial number according to i=i+1, and go to step 4; Among them, ODomCt represents the number of Pt(i) dominated by FNDS, and NDomCt represents the number of NPt(i) dominated by FNDS.

3. The method according to claim 1, characterized in that Step 3 includes: Step 1.

1. Generate the t-th generation population; Step 1.

2. Evaluate the individuals, calculate the objective function value for each individual, and check whether they satisfy all constraints; Step 1.

3. Determine feasibility and select individuals that meet all constraints from the t-th generation population. These individuals are called feasible solutions. Step 1.

4. Perform non-dominated sorting of feasible solutions: compare each feasible individual in the feasible solution population with all other feasible individuals in the t-th generation population; Step 1.

5. Identify non-dominated individuals: During the comparison process, record the number of times each feasible individual is dominated by other individuals in the t-th generation population; those individuals with no domination times are considered non-dominated; Step 1.

6. Construct the Pareto front: All non-dominated feasible individuals are grouped into a set, which represents the Pareto front of the current population.

4. The method according to claim 2, characterized in that: The MED in step S107 is calculated according to the following formula: MED(Pt(i))=NearDis(Pt(i))×TotalDis(Pt(i)) (1) in, (2) (3) Pt (i) represents the i-th individual in the t-th generation population Pt, and TotalDis is calculated as Pt (i) and all Pt (j) is the sum of the Euclidean distances; NearDist( Pt (i) Calculation Pt (i) and Pt (j) The minimum Euclidean distance between two entities; j=1,...,P and j≠i.

5. An electronic device, comprising a memory and a processor, characterized in that: The memory is used to store a program that supports the processor to execute the path planning method described in any one of claims 1 to 4, and the processor is configured to execute the program stored in the memory.

6. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the path planning method according to any one of claims 1 to 4 are executed.

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