An assembly sequence planning method based on multi-objective genetic optimization

Abstract

This invention discloses an assembly sequence planning method based on multi-objective genetic optimization. Taking a set of parts, a set of assembly predecessor constraints, tool requirement annotations, and contact area data between parts as input, the assembly sequence is represented as chromosomes using integer permutation encoding. A valid initial population is generated through a predecessor-aware random initialization method based on topological sorting. Three multi-dimensional fitness evaluation indicators are proposed: direction switching weighted cost, tool continuity index, and sub-assembly support ratio. Two types of genetic operations are designed to maintain constraint validity: sequential crossover and predecessor repair operators, and insertion mutation and predecessor verification operators. These operations drive iterative evolution of the population and output the optimal assembly sequence that satisfies all assembly predecessor constraints, along with assembly direction annotations for each step. This invention achieves multi-objective assembly sequence optimization that balances assembly direction continuity, tool usage continuity, and sub-assembly structural stability without relying on real-time geometric kernel calls.

Description

Technical Field

[0001] This invention belongs to the field of intelligent manufacturing and assembly process planning technology, specifically relating to an assembly sequence planning method based on multi-objective genetic optimization. Background Technology

[0002] Assembly sequence planning is a core component of discrete manufacturing process design. Its goal is to determine the optimal assembly sequence of parts while satisfying geometric and process constraints, thereby reducing non-value-adding operation time and improving assembly process efficiency. For mechanical products with a large number of parts and complex spatial constraints, the number of feasible assembly sequences increases exponentially with the number of parts, making it difficult for exact solution methods to provide results within an engineeringly acceptable timeframe. Therefore, metaheuristic algorithms have become the mainstream solution method for this problem.

[0003] However, existing metaheuristic methods have the following three shortcomings when applied to assembly sequence planning:

[0004] 1) The fitness index lacks sufficient granularity to accurately reflect the actual differences in switching costs between different types of process operations. Existing methods typically use a simple count of the number of direction changes and tool changes as the evaluation index for process efficiency, penalizing all types of direction and tool changes equally. However, in actual assembly work, coaxial reverse switching (such as changing from +X to −X) usually requires extensive repositioning of the assembly platform or robotic arm, which is far more costly than cross-axis switching; the switching costs of different tool combinations also vary significantly due to differences in tooling configuration. Fitness functions based on simple counts cannot distinguish these differences, leading to a discrepancy between the optimization results and the actual process costs.

[0005] 2) The offspring sequences generated by conventional genetic operations generally violate assembly predecessor constraints, lacking an effective mechanism for maintaining constraint validity. Standard genetic operations such as sequential crossover and single-point crossover target all permutations of parts, and their outputs are valid at the syntactic level (permutation validity), but often violate assembly process requirements at the semantic level (predecessor constraint validity). Existing methods typically use penalty functions to include infeasible sequences in the evaluation system, applying a fixed penalty coefficient to the number of constraint violations in fitness calculations. This approach results in a significant consumption of computational resources on evaluating infeasible solutions, and the value of the penalty coefficient has a significant impact on convergence behavior, requiring repeated debugging for specific products and reducing the method's generality.

[0006] 3) Existing methods for evaluating the stability of subassemblies only consider the direct connection between adjacent operations, failing to reflect the actual contribution of the contact area to the physical support strength. Some existing methods use the existence of a direct physical connection between two adjacent operations as the criterion for structural stability, and use the number of adjacent operations without a connection as a stability penalty. This binary evaluation method treats large-area transition fits and small-area precision fits equally, failing to reflect the different contributions of contact area size to the overall support strength of the subassembly, which may lead to instability in the subassembly structure during actual assembly.

[0007] In summary, there is currently no method that can simultaneously address the above three shortcomings. Under the premise of maintaining the legality of assembly precursor constraints throughout the genetic operation, a multi-dimensional fitness index with higher quantification granularity can be used to drive sequence optimization and output a high-quality assembly sequence that balances actual process costs and structural stability. Summary of the Invention

[0008] Purpose of the invention: This invention provides an assembly sequence planning method based on multi-objective genetic optimization, which solves the technical problems of insufficient quantification granularity of fitness index, lack of feasibility maintenance mechanism for genetic operations of offspring, and single dimension of sub-assembly stability evaluation in existing methods.

[0009] Technical solution: The present invention provides an assembly sequence planning method based on multi-objective genetic optimization, comprising the following steps:

[0010] S1: The assembly sequence is represented as chromosomes using integer permutation encoding. An initial population is generated using a predecessor-aware random initialization method based on topological sorting, ensuring that each chromosome in the population satisfies all constraints in the assembly predecessor constraint set.

[0011] S2: For each chromosome in the population, calculate the three fitness components in turn: the direction switching weighted cost, the tool use continuity index, and the subassembly support ratio. Then, weight and fuse them into a comprehensive fitness value, with the goal of minimizing the comprehensive fitness value.

[0012] S3: Use a tournament selection mechanism to select parent individuals from the current population. Randomly select a subset from the population with a preset tournament size and select the individual with the lowest overall fitness value to enter the next round of operation.

[0013] S4: Perform sequential crossover operator on the selected parent to generate offspring chromosomes, and perform precursor repair operation on offspring that violate the assembly predecessor constraint set to restore the constraint legality of offspring chromosomes;

[0014] S5: Perform insertion mutation operation on individuals in the population with a preset mutation probability. Before mutation, enumerate the set of legal insertion positions for the target part and perform insertion only at legal positions to ensure that the chromosome satisfies all predecessor constraints in the predecessor constraint set after mutation.

[0015] S6: Merge the offspring generated in steps S3 to S5 with the current population and use an elite retention strategy to form the next generation population; detect the termination condition, and when it is met, output the chromosome with the smallest overall fitness value in the current population as the optimal assembly sequence, and mark the assembly direction of each step.

[0016] Furthermore, the process of generating the initial population using the predecessor-aware random initialization method based on topological sorting in step S1 is as follows:

[0017] Construct the precursor counting vector of the part , Record parts Number of unsatisfied predecessor constraints in the current state; Initialize the set of optional parts. ;

[0018] Repeat the following steps until the chromosomes are filled: From Parts are selected in a uniform random manner. , This is the current input position. The number of parts; written into chromosome number 1. Position; will China and Israel Decrement the predecessor count of all successor parts of the predecessor by one, and add the newly qualified parts. The above process is executed independently multiple times for the same population size, and a legal initial population with diversity is generated by random selection at each step.

[0019] Furthermore, the direction switching weighted cost calculation method described in step S2 is as follows:

[0020] Predefined switching cost matrix between six orthogonal directions Matrix elements are assigned values ​​based on their direction: elements in the same direction are assigned different types. Coaxial reverse elements have higher substitution value. Elements in the cross-axis direction have lower generational value. ,satisfy The , For each pair of adjacent operations in the sequence, combine the assembly direction query cost matrix, sum them, and then normalize by the sequence length:

[0021]

[0022] in, For parts The assembly direction in the current step is determined according to the rules described in claim 7. The number of parts; the assembly direction The rules for determining it are as follows:

[0023] The preferred direction is determined based on the current set of feasible assembly directions. If multiple feasible directions exist for the part, the direction selected is the one from the previous step. Same direction; if no same direction, select according to the preset priority order of +z, -z, +y, -y, +x, -x; the first step is to select directly according to priority.

[0024] Furthermore, the tool continuity index described in step S2 is calculated as follows:

[0025] The proportion of consecutive steps in a statistical sequence that use the same instrument is defined as the instrument continuity rate. :

[0026]

[0027] in, For parts The required tool types, The indicator function is used; the fitness component is taken as... , The smaller the value, the higher the concentration of tool usage.

[0028] Furthermore, the sub-assembly support ratio is calculated in step S2 as follows:

[0029] For the sequence number Step, let the assembled parts set be... Calculate the currently assembled parts The cumulative added value of the contact surface with assembled parts accounts for The ratio of the total potential contact area:

[0030]

[0031] in, For parts collection Except Any part other than For parts and The shared contact area between them, with a denominator of zero. ;

[0032] Take the complement of the support ratio of each step in the entire sequence as the mean:

[0033]

[0034] The smaller the value, the better the overall sub-assembly structure support of the sequence.

[0035] Furthermore, step S4 is implemented as follows:

[0036] Randomly select the intersection interval [l, r]. Parents The [l, r] segment is directly copied to the corresponding position in the offspring; according to the parent... The parts are arranged in the correct order. The parts that do not appear in the child generation are then filled into the remaining empty spaces in the child generation to obtain the initial child generation C'.

[0037] Scan C' bit by bit from left to right, for each position... parts at the location ,examine China and Israel To determine whether all subsequent front-end components appear in the same location. Previously; if there exists located at Subsequent front-wheel drive parts Positioning in C' Current location , ,Will From position Pull out and insert position The remaining elements are shifted one position to the right in sequence; repeat the above check until the position is reached. All precursors of the repaired part are in place before moving to the next position; the repair process is completed in linear time, ensuring that the offspring chromosomes meet the required standards after repair. All constraints.

[0038] Furthermore, the implementation process of step S5 is as follows:

[0039] From chromosomes The target parts are selected in a uniform random manner. ;enumerate exist The set of all legal insertion positions in :Location belong If and only if middle All front-wheel drive components are located in position Previously, and All subsequent parts appear in position Afterwards; if Not empty, from Randomly select target location ,Will Remove from the original position and insert. The remaining elements are shifted sequentially; if If the result is empty, the mutation is abandoned; the above operations ensure that the mutated chromosome always satisfies the assembly predecessor constraint set. All constraints in the [context].

[0040] Furthermore, step S6 is implemented as follows:

[0041] After merging contemporary offspring individuals with the current population, they are sorted in ascending order of overall fitness value, and the top-ranked individuals are retained. Individuals form the next generation population;

[0042] Termination conditions include any of the following: the current evolutionary generation reaches the preset maximum generation. ;continuous The optimal overall fitness value of the generation population did not decrease, among which... This is a preset threshold for the stagnation algebra.

[0043] Beneficial effects: Compared with the prior art, the beneficial effects of the present invention are as follows:

[0044] 1. This invention replaces the direction change counting with a direction switching cost matrix, and introduces the actual cost difference of different direction switching combinations into the fitness evaluation, so that the direction scheduling scheme in the optimization result is more consistent with the platform reversal cost in the assembly site, which helps to reduce the frequency of high-cost direction switching.

[0045] 2. This invention designs a sequential crossover cooperation predecessor repair operator and an insertion mutation cooperation predecessor verification operator, which maintains the legality of the assembly predecessor constraint throughout the genetic operation, avoiding the invalid construction of infeasible individuals; compared with the method that relies on the penalty function, the repair process is completed in linear time, without introducing an additional penalty coefficient parameter tuning burden, thus improving the versatility of the method.

[0046] 3. This invention quantifies the sub-assembly support by the ratio of the contact area coverage of the assembled parts to the current part in each assembly step, and incorporates the contact area size into the stability evaluation dimension. Compared with the binary connection relationship judgment method, this index can distinguish the support contribution of different contact areas, so that the optimized sequence has better physical support characteristics in the sub-assembly formation process.

[0047] 4. This invention uses the assembly precursor constraint set as a unified representation of geometric feasibility. The genetic operation relies solely on memory queries of the constraint set throughout the entire process, without needing to call the CAD geometry kernel during the optimization process. It supports independent deployment in a computing environment physically isolated from CAD tools, adapting to the deployment requirements of system independence in industrial sites. Attached Figure Description

[0048] Figure 1 This is a flowchart of the present invention;

[0049] Figure 2 This is a schematic diagram of the multi-objective fitness evaluation module;

[0050] Figure 3 This is a schematic diagram of the direction switching cost matrix K;

[0051] Figure 4 This is the flowchart for the random initialization of the precursor perception.

[0052] Figure 5 This is a schematic diagram of sequential crossover and position-by-position predecessor repair operation. Detailed Implementation

[0053] The present invention will now be described in further detail with reference to the accompanying drawings.

[0054] like Figure 1 As shown, this invention proposes an assembly sequence planning method based on multi-objective genetic optimization. This method is applicable to situations where, given a set of parts, a set of assembly precursor constraints, tool requirement annotations, and contact area data between parts, a multi-objective genetic algorithm with integer permutation encoding searches for the optimal assembly sequence that balances assembly direction continuity, tool usage continuity, and sub-assembly structure stability within a feasible sequence space that satisfies all assembly precursor constraints. Specifically, it includes the following steps:

[0055] Step S1: Chromosome coding and precursor sensing are randomly initialized.

[0056] Assemblies of parts Assembly Precursor Constraint Set , Collection of tooling requirements for each part and data set of contact area between parts For input.

[0057] The assembly The number of valid parts is: to , with length as Integer permutation This represents an assembly sequence, where For the first The part numbers of the assembly steps. The integer permutation encoding scheme allows genetic operations to be applied directly to the part permutation itself, without the need for an intermediate decoding layer, which facilitates the implementation of dedicated genetic operators for permutation structures.

[0058] A legal chromosome must satisfy the following conditions: Arbitrary constraint pairs , Its position on the chromosome is earlier than .

[0059] An initial population is generated using a predecessor-aware random initialization method based on topological sorting, ensuring that each chromosome in the population satisfies the assembly predecessor constraint set. All constraints in the framework. For example... Figure 4As shown, the predecessor perception random initialization uses a topological sorting framework to ensure validity, while introducing population diversity through random selection. A predecessor counting vector for each part is constructed. ,initialization For parts exist The number of constraint pairs that appear as successors, i.e., the number of initial unsatisfied predecessor constraints. Initial set of optional parts. It contains all parts that currently have no preceding dependencies.

[0060] Repeat the following steps until the chromosomes are filled: From Parts are selected in a uniform random manner. Write into chromosome number 1 Position; will China and Israel Decrement the predecessor count of all successor parts of the predecessor by one; add parts whose predecessor count has dropped to zero. .

[0061] Regarding population size The above process is executed independently, with each independent random selection ensuring population diversity. Compared to random generation followed by filtering, this initialization method can directly generate valid chromosomes in linear time complexity, avoiding invalid construction of infeasible individuals.

[0062] Step S2: As Figure 2 As shown, the direction-switching weighted cost is calculated sequentially for each chromosome in the population. Instrumental continuity index and sub-assembly support ratio The three fitness components are weighted and fused into a comprehensive fitness score. To minimize To optimize the objective.

[0063] ① Weighted cost of direction switching The motivation behind this indicator is that different types of orientation switching have different operational costs in actual assembly work—coaxial reverse switching requires a large-angle rotation of the workpiece or assembly platform, while cross-axis switching only requires adjustment between different coordinate planes, resulting in a significant difference in cost. Simple counting cannot capture this difference, while the cost matrix scheme directly incorporates it into the fitness evaluation at the numerical level.

[0064] like Figure 3 As shown, the set of six orthogonal directions Switching cost matrix Fill in according to the following rules: diagonal elements Coaxial reverse elements (such as) and )Pick ; other cross-axis elements take In the preferred embodiment , .

[0065] Assembly direction of each step The determination rule is: if There are multiple feasible assembly directions; the one that aligns with the previous step should be selected first. Same direction; if no same direction, press Prioritize and select the first feasible direction; Step 1 Select directly based on priority.

[0066]

[0067] The smaller the value, the lower the cost of switching directions.

[0068] ② Instrument continuity index :

[0069] The proportion of consecutive steps in a statistical sequence that use the same instrument is defined as the instrument continuity rate. :

[0070]

[0071] in, For parts The required tool types, This is the indicator function. This metric uses the same tool rate for adjacent steps as the core evaluation metric. Compared to the number of switching operations, the same tool rate is insensitive to sequence length, making it suitable for cross-sectional comparisons between products with different numbers of parts.

[0072] fitness components The smaller the value, the more concentrated the tool usage and the fewer the number of times it is switched.

[0073] ③ Sub-assembly support ratio The core idea of ​​this indicator is that after each assembly operation, the physical support gained by the current part comes from the contact area between it and the assembled parts; the larger the area, the more stable the connection. By calculating the coverage ratio of the contact area between the assembled parts and the current part, the stability of the sub-assembly structure after that assembly operation can be reflected.

[0074] For the sequence number Step, let the assembled parts set ( hour ):

[0075]

[0076] in, For parts collection Except Any part other than For parts and The shared contact area between them is taken from the input data set. If the denominator is zero, then let .

[0077]

[0078] The smaller the value, the more assembled parts provide contact support at each step of the sequence, and the better the structural stability.

[0079] Therefore, the overall fitness is:

[0080]

[0081] The weighting coefficients satisfy , In the preferred embodiment, take , , Of the three weights The weight is slightly higher, reflecting that the stability of the sub-assembly structure usually has a higher priority than process continuity in engineering practice. In actual use, it can be adjusted according to the characteristics of the product process.

[0082] Step S3: Use a tournament selection mechanism to select parent individuals from the current population. Randomly select a subset from the population with a preset tournament size, and select the individual with the lowest overall fitness value to enter the next round of operation.

[0083] Let the size of the tournament be (Preferred) Each selection operation draws a uniformly random sample from the current population. Among the individuals, the one with the lowest overall fitness value was selected as the parent.

[0084] The selection pressure of the tournament selection is due to control: The larger the size, the stronger the selection pressure, and the higher the probability that high-quality individuals will be selected; A balance is struck between preserving population diversity and guiding convergence. Compared to roulette wheel selection, tournament selection does not require pre-calculation of total population fitness, is insensitive to population size, and has lower computational overhead.

[0085] Step S4: Execute the sequential crossover operator on the selected parents to generate offspring chromosomes, and address any violations of the assembly predecessor constraint set. The offspring undergo precursor repair operations to restore the binding legitimacy of the offspring chromosomes.

[0086] With preset crossover probability For the selected parent pairs Perform the following operations:

[0087] Sequential crossover: Randomly select the crossover interval [l, r] ( ),Will The part sequence in the [l, r] section is copied in situ to the corresponding position of the offspring C'; according to The order in which the parts appear in C' is used to fill the remaining empty spaces in C' with the parts that do not appear in C', thus obtaining the initial offspring. The order of intersection can preserve... The local assembly sequence of the cross section is introduced simultaneously. The global arrangement information takes into account both local inheritance and global exploration.

[0088] Predecessor repair: The output of sequential crossover is valid in terms of permutation validity, but it does not guarantee that the predecessor constraint is satisfied. The repair operator scans every position of C' from left to right. Query China and Israel This refers to the set of all preceding parts; if preceding parts exist... Current location Then From position Pull out, insert position Original position to The elements are shifted one position to the right. For the same position... Repeat the check until all preceding constraints at that position are satisfied, then move to the next position. Continue the inspection. The repair process involves scanning each location at most once, completing the entire process in linear time without significantly increasing the computational overhead per generation. After the repair is complete, C' satisfies... With all predecessor constraints in place, the fitness evaluation can proceed directly without imposing constraint penalties.

[0089] like Figure 5As shown, the execution process of sequential crossover and position-by-position predecessor repair is illustrated using a 6-part example. The first stage is sequential crossover: the crossover interval is selected as the 3rd to 4th position, and parts 5 and 2 of the parent A in this segment are copied in their original positions to the corresponding positions of the initial offspring, marked with a gray background; then, according to the part arrangement order of the parent B, parts 4, 1, 6, and 3 that do not appear in the initial offspring are filled into the remaining empty positions in sequence, resulting in the initial offspring: parts 4, 1, 5, 2, 6, and 3. The second stage is the position-by-position predecessor repair: Assume there is a predecessor constraint requiring part 3 to be assembled before part 5. When scanning to part 5 at position 3, its predecessor part 3 is detected to be currently at position 6. The parts involved in the shift are marked with a thick border. Part 3 is pulled out from position 6 and inserted into position 3. Parts 5, 2, and 6 are shifted one position to the right in sequence. After repair, part 3 is marked with a slash background, indicating that this part is the predecessor part that was moved forward and repaired. The repaired sequence is: part 4, part 1, part 3, part 5, part 2, and 6, which satisfies all predecessor constraints.

[0090] Step S5: Perform insertion mutation operation on individuals in the population with a preset mutation probability. Before mutation, enumerate the set of legal insertion positions for the target part, and only perform insertion at legal positions to ensure that the chromosome satisfies the mutation condition. All precursor constraints.

[0091] With preset mutation probability Perform the following operations on individuals in a population: from chromosomes The target parts are selected in a uniform random manner. ,enumerate The set of all valid insertion positions : for Each candidate position outside the original position ,judge middle Are all front-wheel drive components present in the location? Previously, and Are all subsequent parts present in the location? After that, if all conditions are met... .like Not empty, randomly select from. ,Will Remove from the original position and insert. The remaining elements are shifted sequentially; if If empty, abandon this mutation and keep the individual unchanged.

[0092] Compared to methods that involve mutation followed by punishment or mutation followed by repair, the design of performing predecessor checks before mutation eliminates infeasible mutations at the source. The enumeration only requires traversal Each position and the time consumed for each judgment are... The number of constraints is proportional to the overall fitness, and the computational cost is acceptable. For all offspring generated in steps S3 to S5, the same multi-objective fitness evaluation method as in step S2 is used to calculate the comprehensive fitness value of each offspring, which is then used for merging and sorting in step S6.

[0093] Step S6: Merge the offspring generated in steps S3 to S5 with the current population and use an elite retention strategy to form the next generation population; detect the termination condition, and when it is met, output the chromosome with the smallest overall fitness value in the current population as the optimal assembly sequence, and mark the assembly direction of each step.

[0094] After each generation completes steps S3 to S5, the resulting offspring individuals are merged with the current population, sorted by overall fitness value from smallest to largest, and the previous generation is retained. Individuals form the next generation of the population. The elite preservation strategy ensures that the best individuals from previous generations are not lost due to random genetic operations, guaranteeing that the optimal fitness of the population monotonically does not increase.

[0095] The termination condition is determined after each generation: the current generation reaches the preset maximum number of generations. , or continuous The optimal overall fitness value of the current generation population does not decrease. The process terminates when any condition is met, and the chromosome with the lowest overall fitness value in the current generation population is output as the optimal assembly sequence. And according to the direction allocation rules in step S2, for Each step of the operation is marked with the assembly direction to form the final planning result.

[0096] A structural component assembly (32 parts, 48 ​​precursor constraints, 4 types of tools) was used for verification, with a population size of 50 and a maximum generation of 200. Precursor-aware initialization directly generated all 50 legal chromosomes, with an initial population fitness mean of 0.47. After 200 generations of evolution, the fitness of the optimal individual converged to 0.36, a decrease of approximately 23% from the initial mean. The optimal sequence was compared with the mean of 100 feasible sequences randomly selected from the same constraint space: direction switching weighted cost. The instrumental continuity index decreased from a mean of 0.68 to 0.47. The subassembly support ratio decreased from 0.34 to 0.26. The index decreased from 0.41 to 0.34, with all three indicators showing improvement. The improvement was relatively limited, which is related to the strong spatial constraints of the assembly and the low degree of freedom in the assembly sequence. No infeasible individuals were generated throughout the genetic operation, and the additional computational cost introduced by the predecessor repair and predecessor verification operators in a single generation was relatively controllable and did not have a significant impact on the overall convergence speed.

[0097] The above description is merely a specific embodiment of the present invention and should not be construed as limiting the scope of the invention patent. For those skilled in the art, various modifications and improvements can be made without departing from the concept of the present invention, and these all fall within the protection scope of the present invention. Therefore, the protection scope of this invention patent should be determined by the appended claims.

Claims

1. A method for planning assembly sequences based on multi-objective genetic optimization, characterized in that, Includes the following steps: S1: The assembly sequence is represented as chromosomes using integer permutation encoding. An initial population is generated using a predecessor-aware random initialization method based on topological sorting, ensuring that each chromosome in the population satisfies all constraints in the assembly predecessor constraint set. S2: For each chromosome in the population, calculate the three fitness components in turn: the direction switching weighted cost, the tool use continuity index, and the subassembly support ratio. Then, weight and fuse them into a comprehensive fitness value, with the goal of minimizing the comprehensive fitness value. S3: Use a tournament selection mechanism to select parent individuals from the current population. Randomly select a subset from the population with a preset tournament size and select the individual with the lowest overall fitness value to enter the next round of operation. S4: Perform sequential crossover operator on the selected parent to generate offspring chromosomes, and perform precursor repair operation on offspring that violate the assembly predecessor constraint set to restore the constraint legality of offspring chromosomes; S5: Perform insertion mutation operation on individuals in the population with a preset mutation probability. Before mutation, enumerate the set of legal insertion positions for the target part and perform insertion only at legal positions to ensure that the chromosome satisfies all predecessor constraints in the predecessor constraint set after mutation. S6: Merge the offspring generated in steps S3 to S5 with the current population and use an elite retention strategy to form the next generation population; detect the termination condition, and when it is met, output the chromosome with the smallest overall fitness value in the current population as the optimal assembly sequence, and mark the assembly direction of each step.

2. The assembly sequence planning method based on multi-objective genetic optimization according to claim 1, characterized in that, The process of generating the initial population using the predecessor-aware random initialization method based on topological sorting in step S1 is as follows: Construct the precursor counting vector of the part , Record parts Number of unsatisfied predecessor constraints in the current state; Initialize the set of optional parts. ; Repeat the following steps until the chromosomes are filled: From Parts are selected in a uniform random manner. , This is the current input position. The number of parts; written into chromosome number 1. Position; will China and Israel Decrement the predecessor count of all successor parts of the predecessor by one, and add the newly qualified parts. The above process is executed independently multiple times for the same population size, and a legal initial population with diversity is generated by random selection at each step.

3. The assembly sequence planning method based on multi-objective genetic optimization according to claim 1, characterized in that, The weighted cost calculation method for the direction switching mentioned in step S2 is as follows: Predefined switching cost matrix between six orthogonal directions Matrix elements are assigned values ​​based on their direction: elements in the same direction are assigned different types. ; Coaxial reverse elements are given higher substitution value ; Cross-axis elements are assigned lower generation value ,satisfy For each pair of adjacent operations in the sequence, combine the assembly direction query cost matrix, sum them, and then normalize by the sequence length: in, For parts The assembly direction in the current step is determined according to the rules described in claim 7. This represents the number of parts.

4. The assembly sequence planning method based on multi-objective genetic optimization according to claim 1, characterized in that, The tool continuity index is calculated in step S2 as follows: The proportion of consecutive steps in a statistical sequence that use the same instrument is defined as the instrument continuity rate. : in, For parts The required tool types, The indicator function is used; the fitness component is taken as... , The smaller the value, the higher the concentration of tool usage.

5. The assembly sequence planning method based on multi-objective genetic optimization according to claim 1, characterized in that, The sub-assembly support ratio calculation method in step S2 is as follows: For the sequence number Step, let the assembled parts set be... Calculate the currently assembled parts The cumulative added value of the contact surface with assembled parts accounts for The ratio of the total potential contact area: in, For parts collection Except Any part other than For parts and The shared contact area between them, with a denominator of zero. ; Take the complement of the support ratio of each step in the entire sequence as the mean: The smaller the value, the better the overall sub-assembly structure support of the sequence.

6. The assembly sequence planning method based on multi-objective genetic optimization according to claim 1, characterized in that, The implementation process of step S4 is as follows: Randomly select the intersection interval [l, r]. Parents The [l, r] segment is directly copied to the corresponding position in the offspring; according to the parent... The parts are arranged in the correct order. The parts that do not appear in the child generation are then filled into the remaining empty spaces in the child generation to obtain the initial child generation C'. Scan C' bit by bit from left to right, for each position... parts at the location ,examine China and Israel To determine whether all subsequent front-end components appear in the same location. Previously; if there exists located at Subsequent front-wheel drive parts Positioning in C' Current location , ,Will From position Pull out and insert position The remaining elements are shifted one position to the right in sequence; repeat the above check until the position is reached. All the precursors of the parts have been in place before moving to the next position; The repair process is completed in linear time, ensuring that the offspring chromosomes meet the required standards after repair. All constraints.

7. The assembly sequence planning method based on multi-objective genetic optimization according to claim 1, characterized in that, The implementation process of step S5 is as follows: From chromosomes The target parts are selected in a uniform random manner. ;enumerate exist The set of all legal insertion positions in :Location belong If and only if middle All front-wheel drive components are located in position Previously, and All subsequent parts appear in position Afterwards; if Not empty, from Randomly select target location ,Will Remove from the original position and insert. The remaining elements are shifted sequentially; if If the result is empty, the mutation is abandoned; the above operations ensure that the mutated chromosome always satisfies the assembly predecessor constraint set. All constraints in the [context].

8. The assembly sequence planning method based on multi-objective genetic optimization according to claim 1, characterized in that, The implementation process of step S6 is as follows: After merging contemporary offspring individuals with the current population, they are sorted in ascending order of overall fitness value, and the top-ranked individuals are retained. Individuals form the next generation population; Termination conditions include any of the following: the current evolutionary generation reaches the preset maximum generation. ;continuous The optimal overall fitness value of the generation population did not decrease, among which... The threshold for the stagnation algebra is set.

9. The assembly sequence planning method based on multi-objective genetic optimization according to claim 3, characterized in that, The , .

10. The assembly sequence planning method based on multi-objective genetic optimization according to claim 3, characterized in that, The assembly direction The rules for determining it are as follows: The preferred direction is determined based on the current set of feasible assembly directions. If multiple feasible directions exist for the part, the direction selected is the one from the previous step. Same direction; if no same direction, select according to the preset priority order of +z, -z, +y, -y, +x, -x; the first step is to select directly according to priority.

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