Self-adaptive rapid non-dominated sorting genetic method and system, storage medium and equipment

Abstract

The embodiment of the invention discloses a self-adaptive rapid non-dominated sorting genetic method and system, a storage medium and equipment. The method comprises the following steps: setting a population scale, a maximum iteration generation number and a generation channel parameter; selecting a preset number of individuals from the initial population as a parent population according to the individual fitness on the basis of the population scale and the generational channel parameters; determining a self-adaptive crossover probability and a self-adaptive mutation probability according to the non-dominated level and the congestion degree of the parent population; performing crossover variation according to the adaptive crossover probability and the adaptive variation probability in the progressive stage and the mutation stage; performing non-dominated solution sorting on individuals in the parent population after crossover variation to form a new offspring population; and determining a final filial generation population according to the non-dominated level and the congestion degree of the combined parent population and the new filial generation population until the maximum iteration generation number is reached, and outputting a non-dominated optimal solution set. And multiple crossover and mutation are carried out through the adaptive crossover probability and the adaptive mutation probability, so that the convergence speed is accelerated.

Description

Technical Field

[0001] The present invention relates to the technical field of production scheduling optimization, and in particular to an adaptive fast non-dominated sorting genetic method, system, storage medium and device. Background Art

[0002] After decades of rapid development, China's manufacturing industry structure has been gradually improved, key technologies have made new breakthroughs, and it has become the world's largest industrial manufacturing country. Due to changes in people's consumption concepts and personalized demands for consumer goods, manufacturing companies are encouraged to integrate resources and make changes to production plans and business models to adapt to the diversity and rapidity of market demand.

[0003] As an important part of production planning and control, the quality of the scheduling plan made by production scheduling will have a direct impact on the smoothness, real-timeness and utilization of equipment resources of production execution. Production scheduling and workshop scheduling system is a typical discrete system with complex calculation degree, multi-objective, multi-constraint and dynamic randomness. The complexity is mainly reflected in the complex production environment and NP-hard (non-deterministic polynomial) optimization calculation; in actual production, different departments expect different performance goals, making the scheduling goals diversified; from the perspective of production process, the process of each workpiece must follow a certain order and constraint, so the scheduling presents multi-constraint performance, including: manufacturing resource constraints, workpiece processing logic order, delivery time constraints and some additional constraints; dynamic is reflected in the actual production workshop environment, the state of the workpiece and the machine is changing all the time, and different accidents will occur during the processing of parts. Manual scheduling guided by human experience has always been the main method of traditional manufacturing enterprises, but it cannot meet the increasing production scale and further shortened delivery time. Therefore, optimizing the scheduling results through optimization algorithms and computer technology is the development trend of workshop production scheduling today.

[0004] In the prior art, the production scheduling optimization and algorithm of enterprises use traditional genetic algorithms. The crossover and mutation probabilities cannot be adjusted dynamically according to the quality of individuals. When the mutation probability is fixed and low, the search range of the algorithm is relatively small, and it is easy to fall into the local optimal solution. In addition, the fixed crossover probability and mutation probability make the algorithm lack of pertinence in the search process, and it is impossible to dynamically adjust the search strategy according to the fitness distribution of the current population, resulting in the algorithm wasting a lot of time in the low fitness area during the search process, while ignoring the high fitness area. Summary of the invention

[0005] Based on this, it is necessary to propose an adaptive fast non-dominated sorting genetic method, system, storage medium and device to address the above problems.

[0006] An adaptive fast non-dominated sorting genetic method, the method comprising:

[0007] Set the population size, maximum number of iterations, and generation gap parameters.

[0008] Based on the population size and generation gap parameters, a preset number of individuals are selected from the initial population according to individual fitness as the parent population.

[0009] An adaptive crossover probability and an adaptive mutation probability are determined according to the non-dominated level and the crowding degree of the parent population.

[0010] In the gradual stage and the sudden change stage, crossover and mutation are performed according to the adaptive crossover probability and the adaptive mutation probability.

[0011] The individuals in the parent population after crossover mutation are sorted by non-dominated solutions to form a new offspring population.

[0012] The parent population and the new child population are merged, and a final child population is determined according to the non-dominated levels and congestion degrees of the merged parent population and the new child population, until the maximum iteration number is reached, and a non-dominated optimal solution set is output.

[0013] Wherein, before determining the adaptive crossover probability and the adaptive mutation probability according to the non-dominated level and the crowding degree of the parent population, the method specifically includes:

[0014] The individuals in the parent population are sorted by non-dominated solutions, the non-dominated individual sets are determined level by level, and all individuals in each level of the non-dominated individual set are assigned the same non-dominated level.

[0015] The non-dominated level of each individual in the parent population is obtained by sorting the non-dominated solutions.

[0016] The crowding degrees of the two boundary individuals in each level of non-dominated individual set are set to fixed values, and the crowding degrees of the remaining individuals except the boundary are determined according to the individual objective function values.

[0017] The step of determining the adaptive crossover probability and the adaptive mutation probability according to the non-dominated level and the crowding degree of the parent population specifically includes:

[0018] according to Determine the comprehensive consideration value of individual non-dominated level and crowding, where r is the comprehensive consideration value of individual non-dominated level and crowding, i rank is the non-dominated level of individual i, i d is the crowding degree of individual i, is the maximum value of the non-dominated level, It is the maximum value of the non-dominated level of individual i excluding the boundary individuals.

[0019] according to Determine the adaptive crossover probability, where k1 is the adaptive crossover operator, Among them, r max is the maximum r value among individuals in each generation, r avg is the average r value of individuals in each generation of the population, and r1 is the larger r value between the two individuals used for crossover;

[0020] according to Determine the adaptive mutation probability, where k2 is the adaptive mutation operator, Among them, r max is the maximum r value among individuals in each generation, r min is the average r value of individuals in each generation of the population, and r2 is the individual r value used for mutation.

[0021] The step of performing crossover and mutation operations according to the adaptive crossover probability and the adaptive mutation probability in the gradual stage and the sudden stage specifically includes:

[0022] In the gradual stage and the mutation stage, the number of adaptive crossover bits and the number of adaptive mutation bits in the crossover mutation operation are determined according to the individual fitness.

[0023] Whether to perform a crossover operation on the individuals in the primary population is determined according to a comparison between the adaptive crossover probability and the first randomly generated number.

[0024] If the first randomly generated number is less than the adaptive crossover probability, a crossover operation is performed according to the adaptive crossover bit number.

[0025] If the first randomly generated number is greater than or equal to the adaptive crossover probability, no crossover operation is performed.

[0026] Whether to perform a mutation operation on the individuals in the primary population after the crossover operation is determined based on a comparison between the adaptive mutation probability and the second randomly generated number.

[0027] If the second randomly generated number is less than the adaptive mutation probability, a mutation operation is performed, and crossover is performed according to the number of adaptive mutation bits.

[0028] If the second randomly generated number is greater than or equal to the adaptive mutation probability, no mutation operation is performed.

[0029] The crossover operation and mutation operation are repeated three times to generate three offspring individuals with the preset number of individuals.

[0030] Wherein, in the gradual stage and the mutation stage, determining the number of adaptive crossover bits and the number of adaptive mutation bits in the crossover mutation operation according to the individual fitness specifically includes:

[0031] according to Determine the number of adaptive crossover bits, where f max is the maximum fitness value of individuals in each generation, f min is the minimum fitness value among individuals in each generation of the population, and f′ is the larger fitness value between the two individuals used for crossover.

[0032] according to Determine the number of adaptive mutations, where f max is the maximum fitness value of individuals in each generation, f min is the minimum fitness value of individuals in each generation of the population, and f is the individual fitness value used for mutation.

[0033] The step of determining the final offspring population according to the non-dominated level and the crowding degree of the merged parent population and the new offspring population specifically includes:

[0034] The individuals in the merged parent population and the new child population are sorted by non-dominated solutions, the non-dominated individual sets are determined level by level, and all individuals in each level of the non-dominated individual set are given the same non-dominated level.

[0035] The non-dominated level of each individual in the merged parent population and the new child population is obtained through sorting the non-dominated solutions.

[0036] The crowding degrees of the two boundary individuals in each level of non-dominated individual set are set to fixed values, and the crowding degrees of the remaining individuals except the boundary are determined according to the individual objective function values.

[0037] The individuals are sorted according to the non-dominated levels and crowding degrees of the merged parent population and the new child population to determine the individuals to be selected preferentially.

[0038] If the non-dominated levels of two individuals are different, the individual with the smaller level is preferentially selected.

[0039] If the non-dominated levels of two individuals are the same, the individual with the smaller crowding degree is selected preferentially.

[0040] The final offspring population is determined through the preferentially selected individuals.

[0041] The crowding degree of the two boundary individuals in each level of the non-dominated individual set is set to a fixed value, and the crowding degree of the remaining individuals except the boundary is determined according to the individual objective function value, specifically including:

[0042] according to Determine the crowding degree of the remaining individuals except the boundary, where i d is the crowding degree of individual i, f l k is the lth objective function value of the kth individual, is the maximum value of the lth objective function, is the minimum value of the lth objective function.

[0043] An adaptive fast non-dominated sorting genetic system, the system comprising:

[0044] The setting module is used to set the population size, the maximum number of iterations, and the selection gap.

[0045] The parent population selection module is used to select a preset number of individuals as the parent population in the initial population according to individual fitness based on the population size and generation gap parameters.

[0046] The module for determining the adaptive crossover probability and the adaptive mutation probability is used to determine the adaptive crossover probability and the adaptive mutation probability according to the non-dominated level and the crowding degree of the parent population.

[0047] The crossover and mutation module is used to perform crossover and mutation according to the adaptive crossover probability and the adaptive mutation probability in the gradual stage and the mutation stage.

[0048] The new offspring population forming module is used to sort the individuals in the parent population after crossover mutation by non-dominated solutions to form a new offspring population.

[0049] The non-dominated optimal solution set output module is used to merge the parent population and the new child population, determine the final child population according to the non-dominated level and crowding degree of the merged parent population and the new child population, until the maximum iteration number is reached, and output the non-dominated optimal solution set.

[0050] A computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the processor is caused to execute the steps of the method described above.

[0051] A computer device comprises a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor executes the steps of the above method.

[0052] The embodiments of the present invention have the following beneficial effects:

[0053] The present invention adaptively adjusts the adaptive crossover probability and adaptive mutation probability according to the non-dominated level and crowding degree of the parent population, and proposes a segmented progressive evolution strategy, which divides the iterative process into a progressive stage and a mutation stage to improve convergence and evolution efficiency. In the progressive stage and the mutation stage, multiple crossover and mutation improvements are performed through the adaptive crossover probability and the adaptive mutation probability, which enhances the search capability of the feasible solution space, increases the population size of the offspring that can be selected, and then increases the probability of the emergence of excellent individuals to a certain extent, providing a better feasible solution set for the subsequent non-dominated sorting, thereby accelerating the convergence speed, and the searched non-dominated optimal solution set is better. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0055] in:

[0056] Figure 1 A schematic diagram of a flow chart of an embodiment of an adaptive fast non-dominated sorting genetic method provided by the present invention;

[0057] Figure 2 A schematic flow chart of another embodiment of an adaptive fast non-dominated sorting genetic method provided by the present invention;

[0058] Figure 3 A schematic flow chart of another embodiment of an adaptive fast non-dominated sorting genetic method provided by the present invention;

[0059] Figure 4 A schematic diagram of the structure of an embodiment of an adaptive fast non-dominated sorting genetic system provided by the present invention;

[0060] Figure 5 A schematic structural diagram of an embodiment of the device provided by the present invention;

[0061] Figure 6 A schematic structural diagram of an embodiment of a storage medium provided by the present invention. DETAILED DESCRIPTION

[0062] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0063] like Figure 1 As shown, Figure 1 A schematic diagram of a flow chart of an embodiment of an adaptive fast non-dominated sorting genetic method provided by the present invention. An adaptive fast non-dominated sorting genetic method, the method comprising:

[0064] S101: Set the population size, maximum number of iterations, and select the generation gap.

[0065] Exemplarily, the operating parameters are set, the population size Popnumber is set to 40, the maximum iteration number is set to 200, and the selection gap GGAP is set to 0.9 to ensure that the execution environment of the algorithm is normal.

[0066] S102: Based on the population size and the generation gap parameter, a preset number of individuals are selected from the initial population as the parent population.

[0067] Exemplarily, an integer MSOS encoding method is used to generate an initial population with a scale of Popnumber, and the initial population is sorted by non-dominated solutions. Further, a set selection method and generation gap parameter GGAP are used to select multiple individuals in the initial population as the parent generation for breeding offspring. Specifically, the fitness value of each individual in the initial population is first evaluated using a fitness function. According to the set selection method (such as a bet selection method, a tournament selection method, a sorting selection method, etc.) and the fitness value of the individual, an individual with a preset number of individuals is selected from the initial population. According to the generation gap parameter, the individuals with a preset number of individuals replace some individuals in the initial population to form a parent population.

[0068] S103: Determine an adaptive crossover probability and an adaptive mutation probability according to the non-dominated level and the crowding degree of the parent population.

[0069] Exemplarily, before determining the adaptive crossover probability and the adaptive mutation probability based on the non-dominated level and crowding degree of the parent population, it is necessary to sort the individuals in the parent population by non-dominated solutions, determine the non-dominated individual sets step by step, and assign the same non-dominated level to all individuals in the non-dominated individual sets at each level; the non-dominated level of each individual in the parent population is obtained by sorting the non-dominated solutions; the crowding degree of the two boundary individuals in the non-dominated individual sets at each level is set to a fixed value, and the crowding degree of the remaining individuals except the boundary is determined according to the individual objective function value.

[0070] A piecewise progressive evolution strategy is proposed. The progressive stage is a search of the entire space, and the expected effect is to quickly find the optimal solution. The mutation stage is a full search for solutions within a certain local range, and the expected effect is to enhance the richness of the population and find the global optimal solution with a greater probability. In the progressive stage, a larger crossover probability, a smaller mutation probability, and a strengthened dominant selection operator are set. In the mutation stage, a smaller crossover probability, a larger mutation probability, and a weakened dominant selection operator are set.

[0071] In order to realize the idea of ​​piecewise gradual progress, the piecewise expressions of the gradual stage and the sudden stage are designed as follows:

[0072]

[0073] in, is the Sigmoid function, r max is the maximum r value among individuals in each generation, r min is the average r value in each generation of individuals in the population, ε is the set scale value, which is set to 0.99 in the present invention, and r is a comprehensive consideration of the individual non-dominated level and crowding. The Sigmoid function is a common S-shaped function in biology, also known as the S-shaped growth curve. This function has the properties of monotonically increasing and inverse monotonically increasing. The slope of the curve changes from fast to slow when the function value is between 0.5 and 1, which meets the requirements of algorithm design.

[0074] Furthermore, firstly, the comprehensive consideration value of individual non-dominated level and crowding degree is determined according to the individual non-dominated level and crowding degree, as shown in the following formula:

[0075]

[0076] Among them, r is the comprehensive consideration value of individual non-dominated level and crowding degree, i rank is the non-dominated level of individual i, i d is the crowding degree of individual i, is the maximum value of the non-dominated level, is the maximum value of the non-dominated level of individual i excluding the border individuals;

[0077] Furthermore, the adaptive crossover probability is determined according to the comprehensive consideration of individual non-dominated level and crowding degree, as shown in the following formula:

[0078]

[0079] Among them, k1 is the adaptive crossover operator, Among them, r max is the maximum r value among individuals in each generation, r avg is the average r value in each generation of population individuals, and r1 is the larger value of r between the two individuals used for crossover.

[0080] Furthermore, the adaptive mutation probability is determined according to the comprehensive consideration value of individual non-dominated level and crowding degree, as shown in the following formula:

[0081]

[0082] Among them, k2 is the adaptive mutation operator, Among them, r max is the maximum r value among individuals in each generation, r min is the average r value of individuals in each generation of the population, and r2 is the individual r value used for mutation.

[0083] S104: In the gradual stage and the mutation stage, crossover and mutation are performed according to the adaptive crossover probability and the adaptive mutation probability.

[0084] Exemplarily, in the gradual stage and the mutation stage, the number of adaptive crossover bits and the number of adaptive mutation bits in the crossover mutation operation are determined according to the individual fitness. The adaptive crossover bit is determined according to the following formula:

[0085]

[0086] Among them, f max is the maximum fitness value among individuals in each generation, and f′ is the larger fitness value between the two individuals used for crossover;

[0087] The adaptive mutation bit number is determined according to the following formula:

[0088]

[0089] Among them, f max is the maximum fitness value of individuals in each generation of the population, and f is the individual fitness value used for mutation.

[0090] Furthermore, whether to perform a crossover operation on the individuals in the initial population is determined based on the comparison between the adaptive crossover probability and the first randomly generated number; if the first randomly generated number is less than the adaptive crossover probability, a crossover operation is performed according to the number of adaptive crossover bits; if the first randomly generated number is greater than or equal to the adaptive crossover probability, no crossover operation is performed.

[0091] Furthermore, based on the comparison between the adaptive mutation probability and the second randomly generated number, it is determined whether to perform a mutation operation on the individuals in the initial population after the crossover operation; if the second randomly generated number is less than the adaptive mutation probability, a mutation operation is performed, and crossover is performed according to the number of adaptive mutation bits; if the second randomly generated number is greater than or equal to the adaptive mutation probability, no mutation operation is performed; the crossover operation and mutation operation are repeated three times to generate three offspring individuals with a preset number of individuals.

[0092] S105: Sort the individuals in the parent population after crossover mutation by non-dominated solutions to form a new child population.

[0093] Exemplarily, the individuals in the parent population after crossover mutation (three offspring individuals with a preset number of individuals) are sorted for non-dominated solutions, and the number of feasible solutions of the dominated individuals in the population and the set of feasible solutions that the individuals in the population can control are determined for each individual in the current population; for each individual in the current population, if the set of feasible solutions that the individuals in the population can control is not empty, the number of feasible solutions of the dominated individuals in the population is reduced by 1, and the individuals whose number of feasible solutions that dominate the individuals in the population is 0 are extracted and stored in the first-level non-dominated individual set, and all individuals in the set are given the same non-dominated level; the above process is repeated for the remaining individuals in the current population, and the non-dominated individual set is determined level by level, and all individuals in each level of the non-dominated individual set are given the same non-dominated level, until all individuals in the current population are hierarchically sorted. Finally, according to the hierarchical sorting results, Popnumber individuals are selected from the best to the worst as the new offspring population.

[0094] S106: Merge the parent population and the new child population, and determine the final child population according to the non-dominated level and crowding degree of the merged parent population and the new child population, until the maximum iteration number is reached, and output the non-dominated optimal solution set.

[0095] Exemplarily, the parent population and the new offspring population are merged, the individuals in the merged parent population and the new offspring population are sorted by non-dominated solutions, the non-dominated individual sets are determined level by level, and all individuals in the non-dominated individual sets at each level are assigned the same non-dominated rank; the non-dominated rank of each individual in the merged parent population and the new offspring population is obtained by sorting the non-dominated solutions.

[0096] Furthermore, the crowding degrees of two boundary individuals in each level of non-dominated individual set are set to fixed values, and the crowding degrees of the remaining individuals except the boundary are determined according to the individual objective function values.

[0097] Furthermore, the individuals are sorted according to the non-dominated levels and crowding degrees of the merged parent population and the new child population to determine the priority individuals; if the non-dominated levels of two individuals are different, the individual with the smaller level is given priority; if the non-dominated levels of two individuals are the same, the individual with the smaller crowding degree is given priority; the final child population is determined by the priority individuals until the maximum iteration number is reached, and the non-dominated optimal solution set is output.

[0098] From the above description, it can be seen that the present invention adaptively adjusts the adaptive crossover probability and the adaptive mutation probability according to the non-dominated level and crowding degree of the parent population, and proposes a segmented progressive evolution strategy, which divides the iterative process into a progressive stage and a mutation stage to improve convergence and evolution efficiency. In the progressive stage and the mutation stage, multiple crossover and mutation improvements are performed through the adaptive crossover probability and the adaptive mutation probability, which enhances the search capability of the feasible solution space, increases the population size of the offspring that can be selected, and then increases the probability of the appearance of excellent individuals to a certain extent, providing a better feasible solution set for the subsequent non-dominated sorting, thereby accelerating the convergence speed, and the searched non-dominated optimal solution set is better.

[0099] like Figure 2 As shown, Figure 2 A schematic diagram of another embodiment of an adaptive fast non-dominated sorting genetic method provided by the present invention. An adaptive fast non-dominated sorting genetic method, the method comprising:

[0100] S201: Set the population size, maximum iteration number and generation gap parameters.

[0101] S202: Based on the population size and the generation gap parameter, a preset number of individuals are selected from the initial population according to individual fitness as the parent population.

[0102] It should be noted that steps S201-S202 are Figure 1 This has been discussed in detail in the implementation scenario shown and will not be repeated here.

[0103] S203: Sort the non-dominated solutions of the individuals in the parent population, determine the non-dominated individual sets level by level, and assign the same non-dominated level to all individuals in each level of the non-dominated individual sets.

[0104] Exemplarily, the individuals in the current population are sorted by non-dominated solutions using a fast non-dominated sorting algorithm with an elite strategy. Specifically, the number of feasible solutions of the dominated individuals in the population of each individual in the parent population and the set of feasible solutions that the individuals in the population can control are determined; for each individual in the current population, if the set of feasible solutions that the individuals in the population can control is not empty, the number of feasible solutions of the dominated individuals in the population is reduced by 1, and the individuals in the population whose number of feasible solutions that dominate the individual is 0 are extracted and stored in the first-level non-dominated individual set, and all individuals in the set are given the same non-dominated level; the above process is repeated for the remaining individuals in the current population, and the non-dominated individual sets are determined level by level, and all individuals in each level of the non-dominated individual set are given the same non-dominated level, until all individuals in the current population are hierarchically sorted.

[0105] S204: Obtain the non-dominated level of each individual in the parent population by sorting the non-dominated solutions.

[0106] S205: The crowding degrees of two boundary individuals in each level of non-dominated individual set are set to fixed values, and the crowding degrees of the remaining individuals except the boundary are determined according to the individual objective function values.

[0107] For example, crowding refers to the degree of crowding between a given point in the population and other surrounding points, denoted by i d Indicates that the crowding degree of the two boundary individuals in each level of non-dominated individuals is set to ∞, and the crowding degree of other individuals is set to 0; the crowding degree of other individuals except the boundary is calculated according to the following formula:

[0108]

[0109] Among them, i d is the crowding degree of individual i, f l k is the lth objective function value of the kth individual, is the maximum value of the lth objective function, is the minimum value of the lth objective function.

[0110] S206: Determine an adaptive crossover probability and an adaptive mutation probability according to the non-dominated level and the crowding degree of the parent population.

[0111] For example, in order to realize the idea of ​​piecewise gradual progress, the piecewise expressions of the gradual stage and the sudden stage are designed as follows:

[0112]

[0113] in, is the Sigmoid function, r max is the maximum r value among individuals in each generation, r min is the average r value in each generation of individuals in the population, ε is the set scale value, which is set to 0.99 in the present invention, and r is a comprehensive consideration of the individual non-dominated level and crowding. The Sigmoid function is a common S-shaped function in biology, also known as the S-shaped growth curve. This function has the properties of monotonically increasing and inverse monotonically increasing. The slope of the curve changes from fast to slow when the function value is between 0.5 and 1, which meets the requirements of algorithm design.

[0114] Furthermore, firstly, the comprehensive consideration value of individual non-dominated level and crowding degree is determined according to the individual non-dominated level and crowding degree, as shown in the following formula:

[0115]

[0116] Among them, r is the comprehensive consideration value of individual non-dominated level and crowding degree, i rank is the non-dominated level of individual i, i d is the crowding degree of individual i, is the maximum value of the non-dominated level, is the maximum value of the non-dominated level of individual i excluding the border individuals;

[0117] Furthermore, the adaptive crossover probability is determined according to the comprehensive consideration of individual non-dominated level and crowding degree, as shown in the following formula:

[0118]

[0119] Among them, k1 is the adaptive crossover operator, Among them, r max is the maximum r value among individuals in each generation, r avg is the average r value in each generation of population individuals, and r1 is the larger value of r between the two individuals used for crossover.

[0120] Furthermore, the adaptive mutation probability is determined according to the comprehensive consideration value of individual non-dominated level and crowding degree, as shown in the following formula:

[0121]

[0122] Among them, k2 is the adaptive mutation operator, Among them, r max is the maximum r value among individuals in each generation, r min is the average r value of individuals in each generation of the population, and r2 is the individual r value used for mutation.

[0123] S207: In the gradual stage and the mutation stage, the number of adaptive crossover bits and the number of adaptive mutation bits in the crossover mutation operation are determined according to the individual fitness.

[0124] Exemplarily, in the gradual stage and the mutation stage, the number of adaptive crossover bits and the number of adaptive mutation bits in the crossover mutation operation are determined according to the individual fitness. The adaptive crossover bit is determined according to the following formula:

[0125]

[0126] Among them, f max is the maximum fitness value of individuals in each generation, f min is the minimum fitness value among individuals in each generation, and f′ is the larger fitness value between the two individuals used for crossover;

[0127] The adaptive mutation bit number is determined according to the following formula:

[0128]

[0129] Among them, f max is the maximum fitness value of individuals in each generation, f minis the minimum fitness value of individuals in each generation of the population, and f is the individual fitness value used for mutation.

[0130] S208: Determine whether to perform a crossover operation on the individuals in the initial population based on a comparison between the adaptive crossover probability and the first randomly generated number.

[0131] S2081: If the first randomly generated number is less than the adaptive crossover probability, a crossover operation is performed according to the number of adaptive crossover bits.

[0132] S2082: If the first randomly generated number is greater than or equal to the adaptive crossover probability, no crossover operation is performed.

[0133] S209: Determine whether to perform a mutation operation on the individuals in the primary population after the crossover operation according to the comparison between the adaptive mutation probability and the second randomly generated number.

[0134] S2091: If the second randomly generated number is less than the adaptive mutation probability, a mutation operation is performed according to the adaptive mutation bit number.

[0135] S2092: If the second randomly generated number is greater than or equal to the adaptive mutation probability, no mutation operation is performed.

[0136] Exemplarily, the parent individuals are randomly paired in pairs, and whether to perform a crossover operation is determined based on the adaptive crossover probability, that is, if the first randomly generated number is less than the adaptive crossover probability, a crossover operation is performed, and crossover is performed based on the number of adaptive crossover bits; if the first randomly generated number is greater than or equal to the adaptive crossover probability, no crossover operation is performed. Further, the individuals generated after the crossover operation are subjected to gene position mutation. Whether to perform a mutation operation on the individuals in the primary population after the crossover operation is determined based on the comparison between the adaptive mutation probability and the second randomly generated number. If the second randomly generated number is less than the adaptive mutation probability, a mutation operation is performed, and crossover is performed based on the number of adaptive mutation bits; if the second randomly generated number is greater than or equal to the adaptive mutation probability, no mutation operation is performed.

[0137] S210: Repeat the crossover operation and mutation operation three times to generate three offspring individuals with a preset number of individuals.

[0138] S211: Sort the individuals in the parent population after crossover mutation by non-dominated solutions to form a new offspring population.

[0139] Exemplarily, combined with the comparison between the adaptive crossover probability and the first randomly generated number, as well as the comparison between the adaptive mutation probability and the second randomly generated number, the above crossover and mutation operations are repeated three times to generate 3*Popnumber*GGAP offspring individuals, which are combined into a new population. The new population with 3*Popnumber*GGAP individuals is sorted by non-dominated solutions, and finally, based on the sorting results, Popnumber individuals are selected from best to worst as the new offspring population.

[0140] S212: Merge the parent population and the new child population.

[0141] S213: Determine the final child population according to the non-dominated levels and crowding degrees of the merged parent population and the new child population, until the maximum iteration number is reached, and output the non-dominated optimal solution set.

[0142] Exemplarily, the individuals in the merged parent population and the new child population are sorted by non-dominated solutions, the non-dominated individual set is determined level by level, and all individuals in each level of the non-dominated individual set are assigned the same non-dominated level; the non-dominated level of each individual in the merged parent population and the new child population is obtained by sorting the non-dominated solutions; the crowding degree of the two boundary individuals in each level of the non-dominated individual set is set to a fixed value, and the crowding degree of the remaining individuals except the boundary is determined according to the individual objective function value; the individuals are sorted according to the non-dominated level and crowding degree of the merged parent population and the new child population, and the preferred individuals are determined; if the non-dominated levels of the two individuals are different, the individual with a smaller level is preferred; if the non-dominated levels of the two individuals are the same, the individual with a smaller crowding degree is preferred; the final child population is determined by the preferred individuals. At this time, the iteration number Gen is incremented by 1. If Gen is less than or equal to 200, the above steps are repeated until the maximum iteration number 200 is reached, and the non-dominated optimal solution set is output.

[0143] It can be seen from the above description that the present invention makes improvements on the basis of the adaptive genetic algorithm, introduces multiple crossover and mutation operations and adaptive crossover and adaptive mutation numbers, and adopts a segmented progressive evolution strategy that can improve convergence and evolution efficiency, and divides the iterative process into a gradual stage and a mutation stage to improve convergence and evolution efficiency. In the gradual stage and the mutation stage, multiple crossover and mutation improvements are performed through adaptive crossover probability and adaptive mutation probability, and the corresponding different stages of the convergence process are adjusted automatically. When the evolutionary process is in the gradual stage, the number of crossovers increases and the number of mutations decreases; when it is in the mutation stage, the number of crossovers decreases and the number of mutations increases. Such improvements will speed up the convergence speed and also enhance the search for the optimal solution to a certain extent.

[0144] Then, the proposed improved adaptive genetic algorithm is integrated with the fast non-dominated sorting algorithm with elite strategy. Combining the advantages of the adaptive genetic algorithm in fast convergence speed, stronger global search ability and stable search performance and the advantages of the Pareto non-dominated solution set sorting of the fast non-dominated sorting algorithm with elite strategy, an adaptive fast non-dominated sorting genetic method is proposed to solve multi-objective optimization problems in order to better search for the non-dominated optimal solution set.

[0145] like Figure 3 As shown, Figure 3 A schematic diagram of a flow chart of another embodiment of an adaptive fast non-dominated sorting genetic method provided by the present invention. An adaptive fast non-dominated sorting genetic method, the method comprising:

[0146] S301: sorting the individuals in the merged parent population and the new child population by non-dominated solutions, determining the non-dominated individual sets level by level, and assigning the same non-dominated level to all individuals in each level of the non-dominated individual sets.

[0147] Exemplarily, determining the number of feasible solutions that dominate individuals in the population and the set of feasible solutions that are dominated by individuals in the population for each individual in the merged parent population and the new child population;

[0148] For each individual in the current population, if the set of feasible solutions that the individual in the population can control is not empty, the number of feasible solutions that dominate the individual in the population is reduced by 1, and the individual whose number of feasible solutions that dominate the individual in the population is 0 is extracted and stored in the first-level non-dominated individual set, and all individuals in the set are given the same non-dominated level;

[0149] Repeat the above process for the remaining individuals in the current population, determine the non-dominated individual set level by level, and assign the same non-dominated level to all individuals in each level of the non-dominated individual set until all individuals in the current population are hierarchically sorted.

[0150] S302: Obtain the non-dominated level of each individual in the merged parent population and the new child population by sorting the non-dominated solutions.

[0151] S303: The crowding degrees of two boundary individuals in each level of non-dominated individual set are set to fixed values, and the crowding degrees of the remaining individuals except the boundary are determined according to the individual objective function values.

[0152] For example, let the crowding degree of the two boundary individuals in each level of non-dominated individuals be ∞, and the crowding degree of other individuals be 0; the crowding degree of other individuals except the boundary is calculated according to the following formula:

[0153]

[0154] Among them, i dis the crowding degree of individual i, f l k is the lth objective function value of the kth individual, is the maximum value of the lth objective function, is the minimum value of the lth objective function.

[0155] S304: Sort the individuals according to the non-dominated levels and crowding degrees of the merged parent population and the new child population to determine the individuals to be selected first.

[0156] S305: If the non-dominated levels of two individuals are different, the individual with the smaller level is selected first.

[0157] S306: If the non-dominated levels of two individuals are the same, the individual with the smaller crowding degree is selected first.

[0158] For example, it is known that the non-dominated level i can be determined from the non-dominated solution sorting rank and congestion degree i d The crowding comparison operator is used to measure an individual i from two aspects, and then an operator is needed to sort and compare the individuals so that the algorithm can converge to a uniformly distributed Pareto surface as much as possible. rank and i d These two variables compare individuals to determine the order of preference. Suppose two individuals i and j are compared:

[0159] 1) When condition i is met rank <j rank , then i<j;

[0160] 2) When condition i is met rank =j rank And i d >j d , then i<j;

[0161] The principle of the dominance relationship determined above is: if the non-dominance levels of two individuals are different, the individual with a smaller level is preferred; if the non-dominance levels of two individuals are the same, the individual with a smaller crowding degree is preferred.

[0162] S307: Determine the final offspring population through the preferentially selected individuals.

[0163] like Figure 4 As shown, Figure 4 The schematic diagram of the structure of an embodiment of an adaptive fast non-dominated sorting genetic system provided by the present invention. An adaptive fast non-dominated sorting genetic system 10, the system comprises:

[0164] The setting module 11 is used to set the population size, the maximum number of iterations and the selection generation gap.

[0165] The parent population selection module 12 is used to select a preset number of individuals as the parent population in the initial population according to individual fitness based on the population size and the generation gap parameter.

[0166] The adaptive crossover probability and adaptive mutation probability determination module 13 is used to determine the adaptive crossover probability and the adaptive mutation probability according to the non-dominated level and the crowding degree of the parent population.

[0167] The crossover and mutation module 14 is used to perform crossover and mutation according to the adaptive crossover probability and the adaptive mutation probability in the gradual stage and the mutation stage.

[0168] The new offspring population forming module 15 is used to sort the individuals in the parent population after crossover mutation by non-dominated solutions to form a new offspring population.

[0169] The non-dominated optimal solution set output module 16 is used to merge the parent population and the new child population, determine the final child population according to the non-dominated level and crowding degree of the merged parent population and the new child population, until the maximum iteration number is reached, and output the non-dominated optimal solution set.

[0170] Exemplarily, in the setting module 11, the population size, the maximum iteration number and the selection generation gap are set. In the parent population selection module, based on the population size and generation gap parameters, a preset number of individuals are selected from the initial population according to individual fitness as the parent population. In the adaptive crossover probability and adaptive mutation probability determination module 13, the adaptive crossover probability and the adaptive mutation probability are determined according to the non-dominated level and crowding degree of the parent population. Further, in the crossover mutation module 14, in the gradual stage and the mutation stage, the adaptive crossover bit number and the adaptive mutation bit number in the crossover mutation operation are determined according to the individual fitness; whether to perform a crossover operation on the individuals in the primary population is determined according to the comparison between the adaptive crossover probability and the first randomly generated number; if the first randomly generated number is less than the adaptive crossover probability, a crossover operation is performed, and crossover is performed according to the adaptive crossover bit number; if the first randomly generated number is greater than or equal to the adaptive crossover probability, no crossover operation is performed; whether to perform a mutation operation on the individuals in the primary population after the crossover operation is determined according to the comparison between the adaptive mutation probability and the second randomly generated number; if the second randomly generated number is less than the adaptive mutation probability, a mutation operation is performed, and crossover is performed according to the adaptive mutation bit number; if the second randomly generated number is greater than or equal to the adaptive mutation probability, no mutation operation is performed; the crossover operation and mutation operation are repeated three times to generate three offspring individuals of a preset number of individuals. Further, in the new offspring population formation module 15, the individuals in the parent population after the crossover mutation are sorted by non-dominated solutions to form a new offspring population. Finally, in the non-dominated optimal solution set output module 16, the parent population and the new child population are merged, and the final child population is determined according to the non-dominated level and crowding degree of the merged parent population and the new child population, until the maximum iteration number is reached, and the non-dominated optimal solution set is output. Specifically, the individuals in the current population are sorted by non-dominated solutions, the non-dominated individual set is determined level by level, and all individuals in each level of the non-dominated individual set are given the same non-dominated level; the non-dominated level of each individual in the merged parent population and the new child population is obtained by sorting the non-dominated solutions; the crowding degree of the two boundary individuals in each level of the non-dominated individual set is set to a fixed value, and the crowding degree of the remaining individuals except the boundary is determined according to the individual objective function value; the individuals are sorted according to the non-dominated level and crowding degree of the merged parent population and the new child population, and the preferred individuals are determined; if the non-dominated levels of the two individuals are different, the individual with the smaller level is preferred; if the non-dominated levels of the two individuals are the same, the individual with the smaller crowding degree is preferred; the final child population is determined by the preferred individuals.

[0171] like Figure 5 As shown, Figure 5 The device 20 includes a memory 21 and a processor 22. The memory 21 stores a computer program, and the processor 22 executes the computer program when working to implement the following. Figure 1 , Figure 2 and Figure 3 The method shown.

[0172] The specific technical details of an adaptive fast non-dominated sorting genetic method implemented when the above-mentioned device 20 executes a computer program have been discussed in detail in the above-mentioned method steps, so they will not be repeated here.

[0173] like Figure 6 As shown, Figure 6 The storage medium 30 stores at least one computer program 31, which is executed by the processor 22 to implement the following. Figure 1 , Figure 2 and Figure 3 In one embodiment, the storage medium 30 may be a storage chip, a hard disk, a mobile hard disk, a USB flash drive, an optical disk, or other readable and writable storage tools, or a server, etc.

[0174] The above describes specific embodiments of the present specification, and other embodiments are within the scope of the appended claims. In some cases, the actions or steps recorded in the claims can be performed in an order different from that in the embodiments and still achieve the desired results. In addition, the processes depicted in the accompanying drawings do not necessarily have to be performed in the specific order or sequential order shown to achieve the desired results. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0175] Each embodiment in this specification is described in a progressive manner, and the same or similar parts between the embodiments can be referred to each other, and each embodiment focuses on the differences from other embodiments. In particular, for the device, equipment, and non-volatile computer-readable storage medium embodiments, since they are basically similar to the method embodiments, the description is relatively simple, and the relevant parts can be referred to the partial description of the method embodiments.

[0176] The apparatus, device, non-volatile computer-readable storage medium and method provided in the embodiments of this specification correspond to each other, and therefore, the apparatus, device, and non-volatile computer storage medium also have similar beneficial technical effects as the corresponding methods. Since the beneficial technical effects of the methods have been described in detail above, the beneficial technical effects of the corresponding apparatus, device, and non-volatile computer storage medium will not be repeated here.

[0177] The systems, devices, modules or units described in the above embodiments may be implemented by computer chips or entities, or by products with certain functions. A typical implementation device is a computer. Specifically, the computer may be, for example, a personal computer, a laptop computer, a cellular phone, a camera phone, a smart phone, a personal digital assistant, a media player, a navigation device, an email device, a game console, a tablet computer, a wearable device, or a combination of any of these devices.

[0178] For the convenience of description, the above device is described by being divided into various units according to their functions and described separately. Of course, when implementing this specification, the functions of each unit can be implemented in one or more software and / or hardware. It should be understood by those skilled in the art that this specification embodiment can be provided as a method, system, or computer program product. Therefore, this specification embodiment can adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, this specification embodiment can adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0179] This specification is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of this specification. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0180] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0181] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0182] In a typical configuration, a computing device includes one or more processors (CPU), input / output interfaces, network interfaces, and memory.

[0183] The memory may include non-permanent storage in a computer-readable medium, random access memory (RAM) and / or non-volatile memory in the form of read-only memory (ROM) or flash RAM. The memory is an example of a computer-readable medium.

[0184] Computer readable media include permanent and non-permanent, removable and non-removable media that can be implemented by any method or technology to store information. Information can be computer readable instructions, data structures, program modules or other data. Examples of computer storage media include, but are not limited to, phase change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technology, compact disk read-only memory (CD-ROM), digital versatile disk (DVD) or other optical storage, magnetic cassettes, magnetic disk storage or other magnetic storage devices or any other non-transmission media that can be used to store information that can be accessed by a computing device. As defined herein, computer readable media does not include temporary computer readable media (transitory media), such as modulated data signals and carrier waves.

[0185] It should also be noted that the terms "include", "comprises" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, method, commodity or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, commodity or device. In the absence of more restrictions, the elements defined by the sentence "comprises a ..." do not exclude the existence of other identical elements in the process, method, commodity or device including the elements.

[0186] This specification may be described in the general context of computer-executable instructions executed by a computer, such as program modules. Generally, program modules include routines, programs, objects, components, data structures, etc. that perform specific tasks or implement specific abstract data types. This specification may also be practiced in distributed computing environments where tasks are performed by remote processing devices connected through a communication network. In a distributed computing environment, program modules may be located in local and remote computer storage media, including storage devices.

[0187] Each embodiment in this specification is described in a progressive manner, and the same or similar parts between the embodiments can be referred to each other, and each embodiment focuses on the differences from other embodiments. In particular, for the system embodiment, since it is basically similar to the method embodiment, the description is relatively simple, and the relevant parts can be referred to the partial description of the method embodiment.

[0188] The above disclosure is only the preferred embodiment of the present invention, which certainly cannot be used to limit the scope of the present invention. Therefore, equivalent changes made according to the claims of the present invention are still within the scope of the present invention.

Claims

1. An adaptive fast non-dominated sorting genetic method, characterized in that: The method comprises: Set the population size, maximum number of iterations, and generation gap parameters; Based on the population size and generation gap parameters, a preset number of individuals are selected from the initial population according to individual fitness as the parent population; Determining an adaptive crossover probability and an adaptive mutation probability according to the non-dominated level and crowding degree of the parent population; In the gradual stage and the sudden change stage, crossover and mutation are performed according to the adaptive crossover probability and the adaptive mutation probability; Sorting the individuals in the parent population after crossover mutation by non-dominated solutions to form a new offspring population; The parent population and the new child population are merged, and a final child population is determined according to the non-dominated levels and congestion degrees of the merged parent population and the new child population, until the maximum iteration number is reached, and a non-dominated optimal solution set is output.

2. The adaptive fast non-dominated sorting genetic method according to claim 1, characterized in that: Before determining the adaptive crossover probability and the adaptive mutation probability according to the non-dominated level and the crowding degree of the parent population, the method specifically includes: The individuals in the parent population are sorted by non-dominated solutions, non-dominated individual sets are determined level by level, and all individuals in each level of non-dominated individual sets are given the same non-dominated level; Obtaining the non-dominated level of each individual in the parent population by sorting the non-dominated solutions; The crowding degrees of the two boundary individuals in each level of non-dominated individual set are set to fixed values, and the crowding degrees of the remaining individuals except the boundary are determined according to the individual objective function values.

3. The adaptive fast non-dominated sorting genetic method according to claim 2, characterized in that: The step of determining the adaptive crossover probability and the adaptive mutation probability according to the non-dominated level and the crowding degree of the parent population specifically includes: according to Determine the comprehensive consideration value of individual non-dominated level and crowding, where r is the comprehensive consideration value of individual non-dominated level and crowding, i rank is the non-dominated level of individual i, i d is the crowding degree of individual i, is the maximum value of the non-dominated level, is the maximum value of the non-dominated level of individual i excluding the border individuals; according to Determine the adaptive crossover probability, where k1 is the adaptive crossover operator, Among them, r max is the maximum r value among individuals in each generation, r avg is the average r value of individuals in each generation of the population, and r1 is the larger r value between the two individuals used for crossover; according to Determine the adaptive mutation probability, where k2 is the adaptive mutation operator, Among them, r max is the maximum r value among individuals in each generation, r min is the average r value of individuals in each generation of the population, and r2 is the individual r value used for mutation.

4. The adaptive fast non-dominated sorting genetic method according to claim 3, characterized in that: In the gradual stage and the sudden stage, the crossover and mutation operations are performed according to the adaptive crossover probability and the adaptive mutation probability, specifically including: In the gradual stage and the mutation stage, the number of adaptive crossover bits and the number of adaptive mutation bits in the crossover mutation operation are determined according to the individual fitness; Determining whether to perform a crossover operation on the individuals in the primary population according to a comparison between the adaptive crossover probability and the first randomly generated number; If the first randomly generated number is less than the adaptive crossover probability, a crossover operation is performed, and crossover is performed according to the number of adaptive crossover bits; If the first randomly generated number is greater than or equal to the adaptive crossover probability, no crossover operation is performed; Determining whether to perform a mutation operation on the individuals in the primary population after the crossover operation according to a comparison between the adaptive mutation probability and the second randomly generated number; If the second randomly generated number is less than the adaptive mutation probability, a mutation operation is performed, and crossover is performed according to the number of adaptive mutation bits; If the second randomly generated number is greater than or equal to the adaptive mutation probability, no mutation operation is performed; The crossover operation and mutation operation are repeated three times to generate three offspring individuals with the preset number of individuals.

5. The adaptive fast non-dominated sorting genetic method according to claim 4, characterized in that: In the gradual stage and the mutation stage, determining the adaptive crossover bit number and the adaptive mutation bit number in the crossover mutation operation according to the individual fitness specifically includes: according to Determine the number of adaptive crossover bits, where f max is the maximum fitness value of individuals in each generation, f min is the minimum fitness value among individuals in each generation, and f′ is the larger fitness value between the two individuals used for crossover; according to Determine the number of adaptive mutations, where f max is the maximum fitness value of individuals in each generation, f min is the minimum fitness value of individuals in each generation of the population, and f is the individual fitness value used for mutation.

6. The adaptive fast non-dominated sorting genetic method according to claim 1, characterized in that: Determining the final offspring population according to the non-dominated level and the crowding degree of the merged parent population and the new offspring population specifically includes: Sorting the individuals in the merged parent population and the new child population by non-dominated solutions, determining the non-dominated individual set level by level, and assigning the same non-dominated level to all individuals in each level of the non-dominated individual set; Obtaining the non-dominated level of each individual in the merged parent population and the new child population through sorting of the non-dominated solutions; The crowding degrees of two boundary individuals in each level of non-dominated individual set are set to fixed values, and the crowding degrees of the remaining individuals except the boundary are determined according to the individual objective function values; Sort the individuals according to the non-dominated levels and crowding degrees of the merged parent population and the new child population to determine the individuals to be selected first; If the non-dominated levels of two individuals are different, the individual with the smaller level is selected first; If the non-dominated levels of two individuals are the same, the individual with the smaller crowding degree is selected first; The final offspring population is determined through the preferentially selected individuals.

7. The adaptive fast non-dominated sorting genetic method according to claim 2 or 6, characterized in that: The crowding degree of the two boundary individuals in each level of non-dominated individual set is set to a fixed value, and the crowding degree of the remaining individuals except the boundary is determined according to the individual objective function value, specifically including: according to Determine the crowding degree of the remaining individuals except the boundary, where i d is the crowding degree of individual i, is the lth objective function value of the kth individual, is the maximum value of the lth objective function, is the minimum value of the lth objective function.

8. An adaptive fast non-dominated sorting genetic system, characterized in that: The system comprises: The setting module is used to set the population size, the maximum number of iterations and the selection gap; A parent population selection module is used to select a preset number of individuals as the parent population in the initial population according to individual fitness based on the population size and generation gap parameters; An adaptive crossover probability and adaptive mutation probability determination module, used to determine the adaptive crossover probability and the adaptive mutation probability according to the non-dominated level and crowding degree of the parent population; A crossover and mutation module, used for performing crossover and mutation according to the adaptive crossover probability and the adaptive mutation probability in the gradual stage and the mutation stage; A new offspring population forming module is used to sort the individuals in the parent population after crossover mutation by non-dominated solutions to form a new offspring population; The non-dominated optimal solution set output module is used to merge the parent population and the new child population, determine the final child population according to the non-dominated level and crowding degree of the merged parent population and the new child population, until the maximum iteration number is reached, and output the non-dominated optimal solution set.

9. A computer-readable storage medium storing a computer program, wherein when the computer program is executed by a processor, the processor is caused to perform the steps of the method according to any one of claims 1 to 7.

10. A computer device comprising a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor executes the steps of the method according to any one of claims 1 to 7.

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