Manufacturing task cloud decomposition method for complex orders

Abstract

The invention discloses a manufacturing task on-cloud decomposition method for complex orders, which is used for solving the problem of manufacturing task on-cloud decomposition under the condition that a plurality of complex orders are issued at the same time. The method comprises the following steps: firstly, considering a relationship between decomposed procedures and components on a manufacturing task cloud, and constraining a part processing sequence; secondly, establishing an on-cloud task decomposition model of the complex order; and finally, solving and manufacturing an on-cloud decomposition model by using an improved NSGA-II algorithm. According to the method, the workload balance degree index, linear ranking, guide type crossing and Gaussian variation are introduced, the feasibility of the model and the global search capability of the algorithm are improved, and the method can be used for solving the complex order decomposition problem in the cloud manufacturing environment.

Description

Technical Field

[0001] The present invention belongs to the field of manufacturing task decomposition on the cloud, and specifically relates to the solution of a manufacturing task decomposition model for complex orders, and proposes a manufacturing task decomposition method on the cloud for complex orders. Background Art

[0002] Reasonable and effective task decomposition is the cornerstone of optimal allocation of production resources in cloud manufacturing environment. It can not only make complex manufacturing activities easier to carry out, but also save time and resources by improving task processing efficiency. Cloud manufacturing tasks are complex and diverse. Decomposing received orders into reasonable subtasks (ST) can effectively improve the matching efficiency and accuracy of subtasks and service resources, improve the collaboration between participating entities, and reduce cooperation costs. Most task decomposition methods only consider the similarity between parts (PT) in manufacturing orders, without considering the balance of subsequent manufacturing subtasks in manufacturing time, which may lead to waste of waiting time and affect the overall progress. In the actual production process, the manufacturing tasks contained in the order are complex and diverse, so the constraints of complex manufacturing tasks in the process should also be considered. At present, the algorithm used for the decomposition problem of manufacturing tasks on the cloud is usually the improved non-dominated sorting genetic algorithm (NSGA-II) with elite strategy. However, NSGA-II lacks good local search capabilities, which makes it easy to fall into local optimality during the optimization process. Therefore, the NSGA-II algorithm is improved. Summary of the invention

[0003] The purpose of the present invention is to overcome the defects of the prior art and provide a method for decomposing manufacturing tasks on the cloud for complex orders. In view of the incomplete consideration of existing task decomposition indicators and local optimal problems, workload balance indicators, linear ranking, guided crossover and Gaussian mutation are introduced to improve the feasibility of the model and the global search capability of the algorithm.

[0004] A cloud-based decomposition method for manufacturing tasks for complex orders involves a multi-objective optimization problem (MOP), which can be described as:

[0005] Problem A includes multiple complex orders uploaded to the cloud platform, which are merged into a manufacturing task T. The manufacturing task T contains n parts T = {PT1, PT2, ..., PT n}, decompose it into m subtasks through task decomposition.

[0006] A method for decomposing manufacturing tasks on the cloud for complex orders includes the following steps:

[0007] Step 1: Establish a mathematical model for decomposing manufacturing tasks on the cloud

[0008] Problem A introduces the concepts of workload and similarity between parts, and considers the similarity between parts and the workload of each subtask to obtain the decomposition target;

[0009] Task decomposition in a cloud manufacturing environment is to classify parts according to the principle of "high cohesion, low coupling, and balanced workload", so the three concepts of intra-group relevance, extra-group coupling, and workload balance are introduced. In order to ensure that the subtasks after grouping are "high cohesion and low coupling" and that the workload of each subtask is balanced, the intra-subtask relevance is required to be maximized, the coupling between subtasks to be minimized, and the workload balance of subtasks to be minimized.

[0010] (1) Relevance within subtasks

[0011] The uth subtask ST u The intra-group correlation is expressed as follows:

[0012]

[0013] Among them, r ij is the similarity between parts i and j in process, gp iu The value is 0 or 1. 0 means that part i is not in subtask ST u , 1 indicates that part i is in subtask ST u middle.

[0014] Then the intra-group correlation of m subtasks is:

[0015]

[0016] (2) Coupling between subtasks

[0017] Two different subtasks ST u and ST c The inter-group coupling degree is:

[0018]

[0019] Coupling degree between m subtasks:

[0020]

[0021] (3) Subtask workload balance

[0022] If the time levels of subtasks are uneven, it will lead to a waste of waiting time and affect the overall progress. Therefore, workload balance is introduced to represent the quantitative level of consistency of subtasks in manufacturing time.

[0023] The demand matrix corresponding to n parts is EG = {eg i} 1×n , e.g. i represents the demand for the i-th part, then the average workload of m subtasks is for:

[0024]

[0025] Among them, w i represents the manufacturing time of a single part i, st i Indicates PT i Total manufacturing time, t j Indicates subtask ST j Manufacturing time, gp ij Indicates whether part i is in subtask ST j middle.

[0026] When the workload of each group of subtasks is equal to the average workload The smaller the deviation is, the more balanced the workload of each subtask is. The workload balance calculation formula for m subtasks is:

[0027]

[0028] In summary, in order to maximize the intra-group correlation, minimize the inter-group coupling and minimize the workload balance, a multi-objective cloud task decomposition model is established as follows:

[0029]

[0030] Step 2: Based on the mathematical model, a mathematical model of the constrained manufacturing task decomposition on the cloud is established by considering the part processing sequence and part position.

[0031] (1) Process constraints

[0032] There is a sequence relationship between the t parts in the order received by the platform in the process. To ensure that the parts (Part, PT) in the serial structure are manufactured in the order of k→k+1→k+t, these parts may be decomposed into different subtasks, introducing the concepts of remaining time and leading time.

[0033] Remaining time: Remaining time means, part PT p (p≠k) In the subtask STu, except for the parts in the serial structure (excluding PT k ) is calculated using the following formula:

[0034]

[0035] Where p = k + 1, ..., k + t, rtimep represents the remaining time of part p, w i represents the manufacturing time of part i, gp iu Indicates whether part i is in STu.

[0036] Leading time: The manufacturing time of the part that must be ranked earlier than part p. The formula is as follows:

[0037]

[0038] Where p = k + 1, ..., k + t, rtime p Indicates the leading time of part p, time already Represents other parts that have been scheduled and must be manufactured before part p.

[0039] Therefore, the remaining time of part p must be greater than the previous time, which can greatly reduce the waste of waiting time. The process constraint is expressed as follows:

[0040] rtime p >ftime p (13)

[0041] (2) Position constraints

[0042] In the process of aggregating parts into subtasks, each part can only appear in one subtask, which can be expressed as follows:

[0043]

[0044] In summary, the cloud decomposition model of manufacturing tasks with constraints is as follows:

[0045]

[0046] Step 3: using an improved fast non-dominated sorting-II (NSGA-II) algorithm to solve the mathematical model of the manufacturing task decomposition on the cloud;

[0047] In order to speed up the convergence and promote the global search capability of the NSGA-II algorithm, the following three improvements were made:

[0048] (1) Linear ranking to select parent population

[0049] In the linear selection ranking, the ranks are first sorted in descending order, and then the crowding distance is sorted in ascending order. The lower the rank, the higher the selection probability. Therefore, the selection probability of the i-th individual in the sorted population is as follows:

[0050]

[0051] (2) Guided hybridization

[0052] Guided hybridization makes the generated individuals evolve in the best direction possible. Drawing on the way in which individuals in the particle swarm algorithm are influenced by the individual's historical optimality and the population optimality, and thus move in the optimal direction; the hybridization method of evolutionary calculation is improved so that the direction of the offspring evolution generated by each hybridization is determined by the optimal direction of the two parent individuals and the common genes of the two parent individuals. The specific hybridization method is as follows:

[0053] Assume that p1 and p2 are parent individuals, and p1 is better than p2 (if the levels are the same, it is judged according to the crowding distance), and c1 and c2 represent the offspring individuals generated.

[0054] The genetic difference between the two parents is expressed as follows:

[0055] cp=p1-p2(17)

[0056] The commonality of genes between the two parents is expressed as follows:

[0057]

[0058] The generation of offspring is as follows:

[0059]

[0060] Among them, k is a constant with a value between [0.5, 1], h1 is a constant with a value between [1, 2], h2 is a constant with a value between (0, 1], and r1, r2, r3, and r4 are random numbers between 0 and 1.

[0061] (3) Gaussian variation

[0062] The Gaussian mutation operator introduces a certain degree of randomness and diversity by randomly changing certain characteristic values ​​of individuals, thus promoting global search capabilities. Generally speaking, the value of ξ affects the degree of mutation. A larger ξ may lead to a larger mutation step, while a smaller ξ may lead to a smaller mutation step. A larger mutation step is required at the beginning of the iteration. In the later stages of the iteration, when the value is close to the optimal solution, the mutation should become smaller. Therefore, the formula is as follows:

[0063] x j =x i +S(0,1)·ξ (20)

[0064] Among them, xi is the parent individual, x j is the offspring individual, S(0,1) represents a normal distribution with 0 as mean and 1 as standard deviation. T is the maximum number of iterations, and t is the current number of iterations.

[0065] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0066] 1. The present invention expands the evaluation indicators of the decomposition scheme of manufacturing tasks on the cloud, which not only considers the similarity between parts, but also the workload balance of subtasks, making the result of task decomposition more reasonable.

[0067] 2. The present invention takes into account the characteristics of complex manufacturing tasks and introduces process constraints and location constraints, so that the results of task decomposition are more realistic.

[0068] 3. This invention introduces linear ranking to select parent population, guided crossover, and Gaussian mutation to accelerate the convergence speed of the algorithm and promote the global search capability of the algorithm BRIEF DESCRIPTION OF THE DRAWINGS

[0069] Figure 1 The manufacturing task decomposition flow chart on the cloud of the present invention;

[0070] Figure 2 The flowchart of the improved NSGA-II of the present invention for solving the decomposition model of manufacturing tasks on the cloud;

[0071] Figure 3 It is a manufacturing task T of a specific implementation case of the present invention. DETAILED DESCRIPTION

[0072] Combination Figure 1-3 , the resource optimization configuration method of the present invention is further explained.

[0073] 1. Establish a mathematical model for decomposing manufacturing tasks on the cloud

[0074] Problem A includes multiple complex orders uploaded to the cloud platform, which are merged into a manufacturing task T. The manufacturing task T contains n parts T = {PT1, PT2, ..., PT n}, decompose it into m subtasks through task decomposition.

[0075] The grouping of n parts is represented by G as follows:

[0076]

[0077] Where n>m, g ij The value is 0 or 1. 0 means that part i is not in subtask ST j , 1 indicates that part i is in subtask ST j middle.

[0078] According to the similarity of the processes between the parts, without considering the number and order of repetitions of the processes, the process similarity of two parts is calculated as follows:

[0079]

[0080] Among them, PT max represents the maximum number of processes between parts i and j, PT same Represents the number of repeated processes between parts i and j.

[0081] Therefore, the dependency matrix between parts is expressed as follows:

[0082]

[0083] Task decomposition in a cloud manufacturing environment is to classify parts according to the principle of "high cohesion, low coupling, and balanced workload", so the three concepts of intra-group relevance, extra-group coupling, and workload balance are introduced. In order to ensure that the subtasks after grouping are "high cohesion and low coupling" and that the workload of each subtask is balanced, the intra-subtask relevance is required to be maximized, the coupling between subtasks to be minimized, and the workload balance of subtasks to be minimized.

[0084] (1) Relevance within subtasks

[0085] The uth subtask ST u The intra-group correlation is expressed as follows:

[0086]

[0087] Among them, r ij is the similarity between parts i and j in process, gp iu Indicates whether part i is divided into subtask ST u middle.

[0088] Then the intra-group correlation of m subtasks is:

[0089]

[0090] (2) Coupling between subtasks

[0091] Two different subtasks ST u and ST c The inter-group coupling degree is:

[0092]

[0093] Coupling degree between m subtasks:

[0094]

[0095] (3) Subtask workload balance

[0096] If the time levels of subtasks are uneven, it will lead to a waste of waiting time and affect the overall progress. Therefore, workload balance is introduced to represent the quantitative level of consistency of subtasks in manufacturing time.

[0097] The demand matrix corresponding to n parts is EG = {eg i} 1×n , e.g. i represents the demand for the i-th part, then the average workload of m subtasks is for:

[0098]

[0099] Among them, w i represents the manufacturing time of a single part i, st i Indicates PT i Total manufacturing time, t j Indicates subtask ST j Manufacturing time, gp ij Indicates whether part i is in subtask ST j middle.

[0100] When the workload of each group of subtasks is equal to the average workload The smaller the deviation is, the more balanced the workload of each subtask is. The workload balance calculation formula for m subtasks is:

[0101]

[0102] In summary, in order to maximize the intra-group correlation, minimize the inter-group coupling and minimize the workload balance, a multi-objective cloud task decomposition model is established as follows:

[0103]

[0104] 2. Based on the mathematical model, consider the processing sequence and location of parts, and establish a mathematical model for the cloud decomposition of manufacturing tasks with constraints

[0105] (1) Process constraints

[0106] There is a sequence relationship between the t parts in the order received by the platform in the process. To ensure that the parts (Part, PT) in the serial structure are manufactured in the order of k→k+1→k+t, these parts may be decomposed into different subtasks, introducing the concepts of remaining time and leading time.

[0107] Remaining time: Remaining time means, part PT p (p≠k) In the subtask STu, except for the parts in the serial structure (excluding PT k ) is calculated using the following formula:

[0108]

[0109] Where p = k + 1, ..., k + t, rtimep represents the remaining time of part p, w i represents the manufacturing time of part i, gp iu Indicates whether part i is in STu.

[0110] Leading time: The manufacturing time of the part that must be ranked earlier than part p. The formula is as follows:

[0111]

[0112] Where p = k + 1, ..., k + t, rtime p Indicates the leading time of part p, time already Represents other parts that have been scheduled and must be manufactured before part p.

[0113] Therefore, the process constraints are expressed as follows:

[0114] rtime p >ftime p (10)

[0115] (2) Position constraints

[0116] In the process of aggregating parts into subtasks, each part can only appear in one subtask, which can be expressed as follows:

[0117]

[0118] In summary, the cloud decomposition model of manufacturing tasks with constraints is as follows:

[0119]

[0120] 3. Use the improved fast non-dominated sorting-II (NSGA-II) algorithm to solve the mathematical model of the manufacturing task decomposition on the cloud.

[0121] In order to speed up the convergence and promote the global search capability of the NSGA-II algorithm, the following three improvements were made:

[0122] (1) Linear ranking to select parent population

[0123] In the linear selection ranking, the ranks are first sorted in descending order, and then the crowding distance is sorted in ascending order. The lower the rank, the higher the selection probability. Therefore, the selection probability of the i-th individual in the sorted population is as follows:

[0124]

[0125] (2) Guided hybridization

[0126] Guided hybridization makes the generated individuals evolve in the best direction possible. Drawing on the way in which individuals in the particle swarm algorithm are influenced by the individual's historical optimality and the population optimality, and thus move in the optimal direction; the hybridization method of evolutionary calculation is improved so that the direction of the offspring evolution generated by each hybridization is determined by the optimal direction of the two parent individuals and the common genes of the two parent individuals. The specific hybridization method is as follows:

[0127] Assume that p1 and p2 are parent individuals, and p1 is better than p2 (if the levels are the same, it is judged according to the crowding distance), and c1 and c2 represent the offspring individuals generated.

[0128] The genetic difference between the two parents is expressed as follows:

[0129] cp=p1-p2(17)

[0130] The commonality of genes between the two parents is expressed as follows:

[0131]

[0132] The generation of offspring is as follows:

[0133]

[0134] Among them, k is a constant with a value between [0.5, 1], h1 is a constant with a value between [1, 2], h2 is a constant with a value between (0, 1], and r1, r2, r3, and r4 are random numbers between 0 and 1.

[0135] (3) Gaussian variation

[0136] The Gaussian mutation operator introduces a certain degree of randomness and diversity by randomly changing certain characteristic values ​​of individuals, thus promoting global search capabilities. Generally speaking, the value of ξ affects the degree of mutation. A larger ξ may lead to a larger mutation step, while a smaller ξ may lead to a smaller mutation step. A larger mutation step is required at the beginning of the iteration. In the later stages of the iteration, when the value is close to the optimal solution, the mutation should become smaller. Therefore, the formula is as follows:

[0137] x j =x i +S(0,1)·ξ (20)

[0138] Among them, x i is the parent individual, x j is the offspring individual, S(0,1) represents a normal distribution with 0 as mean and 1 as standard deviation. T is the maximum number of iterations, and t is the current number of iterations.

[0139] Implementation Cases:

[0140] This case is a heavy equipment manufacturing process in an equipment manufacturing industry. A total of 17 parts to be distributed are received. The relationship between the parts is as follows: Figure 3 , the manufacturing tasks are decomposed with the optimization objectives of maximizing the intra-group correlation, minimizing the inter-group coupling and minimizing the workload balance.

[0141] The case details are shown in the following table:

[0142]

[0143]

[0144] <![CDATA[PT i ]]> 1 2 3 4 5 6 7 8 9 <![CDATA[w i (h)]]> 6.3 7.5 7.3 4.25 3 7 6 3.7 5.16 <![CDATA[eg i ]]> 50 10 21 4 5 11 50 48 6 <![CDATA[st i ]]> 315 75 153.3 17 15 77 300 177.6 30.96

[0145] <![CDATA[PT i ]]> 10 11 12 13 14 15 16 17 <![CDATA[w i (h)]]> 7.3 5.8 7.8 12.4 10 10.4 6.6 4.8 <![CDATA[eg i ]]> 11 11 30 3 22 16 50 11 <![CDATA[st i ]]> 80.3 63.8 234 37.2 220 166.4 330 52.8

[0146] The solutions that can be obtained using the technical solution provided by this application are as follows:

[0147]

[0148]

[0149] From the data provided in the above table, it can be concluded that the grouped subtasks of each part under this complex order can better arrange the subtasks of different groups to be allocated to different manufacturing resources for manufacturing, reducing the complexity of resource manufacturing allocation, and through the regulation of workload, it can better balance the production capacity and reduce the waste of manufacturing time caused by waiting.

Claims

1. A method for decomposing manufacturing tasks on the cloud for complex orders, characterized in that: The configuration method comprises the following steps: Step 1: Establish a mathematical model for decomposing manufacturing tasks on the cloud; Step 2: Based on the mathematical model, a mathematical model of the constrained manufacturing task decomposition on the cloud is established by considering the part processing sequence and part position; Step 3: Using the improved fast non-dominated sorting-II NSGA-II algorithm, the mathematical model of the constrained manufacturing task decomposition on the cloud is solved.

2. The method for decomposing manufacturing tasks on the cloud for complex orders according to claim 1 is characterized in that: The step 1 is: Combine multiple orders received by the cloud platform into a manufacturing task T, and decompose it into m subtasks through task decomposition. Manufacturing task T = {ST1, ST2, ..., ST m }, the manufacturing task T contains n parts, and the grouping of parts is represented by G as follows: Among them, gp ij Used to identify whether part i is in subtask ST j middle; According to the similarity of the processes between the parts, without considering the number and order of repetitions of the process, the process similarity of two parts is calculated as follows: Among them, PT max represents the maximum number of processes between parts i and j, PT same Represents the number of repeated processes between parts i and j; Then, the correlation matrix between all parts is expressed as follows: Based on the correlation matrix, a mathematical model for decomposing manufacturing tasks on the cloud is established by combining the intra-group correlation, extra-group coupling and workload balance indicators to maximize the intra-group correlation, minimize the inter-group coupling and minimize the workload balance, and establish a multi-objective task decomposition model on the cloud.

3. The method for decomposing manufacturing tasks on the cloud for complex orders according to claim 2 is characterized in that: The intra-group correlation is specifically: Set the uth subtask ST u The intra-group correlation is expressed as follows: Among them, r ij is the similarity between parts i and j in process, gp iu Used to indicate whether part i is divided into subtask ST u middle; Then the intra-group correlation of m subtasks is:

4. The method for decomposing manufacturing tasks on the cloud for complex orders according to claim 2 is characterized in that: The group external coupling degree is specifically: Set up two different subtasks ST u and ST c The inter-group coupling degree is: Then the coupling degree between m subtasks is:

5. The method for decomposing manufacturing tasks on the cloud for complex orders according to claim 2 is characterized in that: The workload balance is specifically: Assume that the demand matrix corresponding to n parts is EG = {eg i } 1×n , e.g. i represents the demand for the i-th part, then the average workload of m subtasks is for: Among them, w i represents the manufacturing time of a single part i, st i represents the total manufacturing time of part i, t j Indicates subtask ST j Manufacturing time, gp ij Used to identify whether part i is in subtask ST j middle; Then the workload balance calculation formula for m subtasks is:

6. The method for decomposing manufacturing tasks on the cloud for complex orders according to claim 2 is characterized in that: The mathematical model of manufacturing task decomposition on the cloud is: In order to maximize the intra-group correlation, minimize the inter-group coupling and minimize the workload balance, a multi-objective cloud task decomposition model is established as follows: in, is the coupling degree between m subtasks, is the coupling degree among m subtasks; A is the workload balance among m subtasks.

7. The method for decomposing manufacturing tasks on the cloud for complex orders according to claim 6 is characterized in that: The constraints in step 2 include process constraints, specifically, Remaining time means part PT p In the subtask STu, the manufacturing time of the remaining parts except the parts in the serial structure is as follows: Where p = k + 1, ..., k + t, rtime p represents the remaining time of part p, w i represents the manufacturing time of part i, gp iu Indicates whether part i is in STu; Leading time: The manufacturing time of the part that must be ranked earlier than part p. The formula is as follows: Where p = k + 1, ..., k + t, rtime p Indicates the leading time of part p, time already It indicates other parts that have been scheduled to be manufactured before part p; The remaining time of part p must be greater than the previous time. The process constraint is expressed as follows: rtime p >ftime p (13)。 8. The method for decomposing manufacturing tasks on the cloud for complex orders according to claim 7 is characterized in that: The constraints in step 2 include position constraints, specifically, In the process of aggregating parts into subtasks, each part only appears in one subtask, which can be expressed as follows:

9. The method for decomposing manufacturing tasks on the cloud for complex orders according to claim 8 is characterized in that: The mathematical model for establishing the constrained manufacturing task decomposition on the cloud in step 2 is specifically as follows:

10. The method for decomposing manufacturing tasks on the cloud for complex orders according to claim 1, characterized in that: The step 3 is specifically as follows: First, the parent population is selected through linear ranking. In the linear selection ranking, the levels are first sorted in descending order, and then the crowding distance is sorted in ascending order. After sorting, the probability of selecting the i-th individual in the population is as follows: Second, the population is iterated according to the guided hybridization method: Let p1 and p2 be parent individuals, and p1 is better than p2, and c1 and c2 represent the offspring individuals produced; The genetic difference between the two parents is expressed as follows: cp=p1-p2 (17) The commonality of genes between the two parents is expressed as follows: The generation of offspring is as follows: Among them, k, h1, h2 are constants, r1, r2, r3, r4 are random numbers; Third, the Gaussian mutation operator is introduced to promote global search capabilities. A larger variable step length is used at the beginning of the iteration, and a smaller variable step length is used in the later stages of the iteration when the value is close to the optimal solution. The formula is as follows: x j =x i +S(0,1)·ξ (20) Among them, x i is the parent individual, x j is the offspring individual, S(0,1) represents a normal distribution with 0 as mean and 1 as standard deviation. T is the maximum number of iterations, and t is the current number of iterations.

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