CN115204696B - Aircraft production line assembly operation scheduling method based on ATC and ALC algorithms - Google Patents
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Abstract
The invention discloses an aircraft production line assembly operation scheduling method based on ATC and ALC algorithms, and belongs to the technical field of aircraft assembly. Constructing an aircraft production line assembly operation scheduling frame comprising an upper production line layer and a lower station layer based on an ATC method, and providing an ATC-based production line-station scheduling model based on the frame; constructing an optimization model facing to a production line layer and a station layer; parallel separation and solution are carried out on the optimization model of the production line layer and the station layer by using a mixed squirrel and physics algorithm based on an ALC algorithm; and outputting the optimal scheduling scheme. The invention provides a production line-station layering model based on ATC and ALC theories, and realizes decoupling and separation among layers; the solving process integrates biology geography and squirrel algorithm, improves the knowing quality, is suitable for solving large-scale problems, has high solving speed, can quickly converge, and shortens solving time.
Description
Technical Field
The invention relates to the technical field of aircraft assembly, in particular to an aircraft production line assembly operation scheduling method based on ATC and ALC algorithms.
Background
An aircraft assembly impulse production line with a plurality of stations is an effective means for realizing rapid delivery of batch production, improving aircraft quality and reducing cost. In the aircraft assembly process, the aircraft is used as a most complex large-scale assembly product, and has multiple constraint conditions such as a plurality of parts, complex assembly flow, time, space, resources and the like for each assembly operation of each station. How to optimally schedule each assembly operation of each station and reasonably decide the starting and finishing time, required resources, assembly operation sequence and the like of each assembly operation of each station under the condition of meeting multiple constraints such as delivery cycle, cost and the like are urgent technology for the pulsation production line of the aircraft. The traditional aircraft assembly production line operation scheduling mainly focuses on models and algorithms for balancing the whole production line, dynamically scheduling the production line, distributing production line workers and the like, however, the number of aircraft assembly operations is huge, the traditional method has the problems of high complexity of the models and algorithms, long solving time and the like, and a decoupled production line scheduling model and solving algorithm are needed to realize a parallel collaborative scheduling method for the production line and the station.
Therefore, the patent provides an ATC-based production line layered scheduling model and an ATC-based production line-station scheduling model. Aiming at the model, an ALC-based method is adopted to realize parallel collaborative solution of the model, and finally, an efficient and low-cost assembly job scheduling scheme is obtained.
Disclosure of Invention
The invention aims to provide an aircraft production line assembly operation scheduling method based on ATC and ALC algorithms for an aircraft pulsation production line, which can intelligently determine the assembly operation assembly sequence, the finishing time and other schemes of each station in parallel and can reduce the assembly cost of the whole production line to the minimum under the condition of meeting the assembly period of each station.
In order to achieve the above object, the present invention has the following technical scheme:
the aircraft production line assembly operation scheduling method based on the ATC and ALC algorithms is characterized by comprising the following steps of:
step one, assume an aircraft pulse line consisting of N stations, each station having J i Each station is equipped with a period of T i ；
Constructing an aircraft production line assembly operation scheduling frame comprising an upper production line layer and a lower station layer based on an ATC method, and providing an ATC-based production line-station scheduling model based on the frame;
step three, constructing an optimization model facing the upper production line layer, wherein the optimization target is that the total assembly cost of the production line is minimum;
step four, constructing an optimization model facing to a lower station layer, wherein the optimization goal is that the assembly time difference between the assembly time of each assembly operation and the assembly time transferred by an upper production line layer is minimum;
step five, parallel separation solution is carried out on the optimization model of the production line layer and the station layer by using a mixed squirrel SSA and physical BBO algorithm based on an ALC algorithm;
and step six, outputting the optimal scheduling scheme.
Further, the third step specifically includes:
1) An optimization objective is constructed, which is the overall assembly cost tzp=zp+cf+ys,
wherein ZP is the sum of the assembly cost of each station assembly operation,assembly time, pst, of the j-th assembly operation for the i-th station of the production line layer planning ij The assembly cost per unit time of the j-th assembly operation for the i-th station;
CF is a penalty cost for deferring each assembly operation,assembly time cf of j-th assembly operation for i-th station of production line layer planning i Penalty unit time cost for i-th station lead delivery;
YS is the cost of transportation and,yus ij the material transportation cost per unit time of the j-th assembly operation for the i-th station;
2) Constructing constraint conditions:assembly time of the j-th assembly operation of the i-th station planned for the production line layer.
Further, the third step further includes:
3) And (3) correcting an upper production line layer optimization target: the penalty function of the upper production line layer based on ALC isWherein v is i ,w i Punishment of multipliers for lagrangian; the line layer target is further modified to +.>
Further, the fourth step specifically includes:
1) Constructing an optimization target: the optimization target is that the assembly time difference between the assembly time of each assembly operation and the assembly time transferred by the upper layer production line layer is the minimum, and the target is that
2) Constructing constraint conditions: (1)calculation period TT of assembly period i i zw Less than or equal to theoretical period, TT i zw ≤T i ，TT i zw Is->Is a function of (2);
(2) while the amount of kth resources required for each assembly job is no greater than its total supply, i.eη k Is the total supply of the kth resource, l ijk The unit time usage of the resource in the kth of the job is assembled for the jth of the i stations.
In the fifth step, the model solving is based on a distributed Hadoop computing cluster, and the distributed Hadoop computing cluster comprises an upper computer responsible for solving the production line layer optimization model and a lower computer used for solving the N station optimization models of the station layer, wherein the lower computer mutually transmits variables with the upper computer through TCP/IP real-time interaction.
In the fifth step, the squirrel SSA algorithm is used for solving an upper layer production line layer optimization model, and when the iteration frequency requirement is met, an optimization variable is returned to a lower layer computer; the physical BBO algorithm is used for solving the lower-layer station-level optimization model, and when the iteration times are reached, the lower-layer computer outputs feedback variables to the upper-layer computer, and the ALC algorithm is used for controlling and converging the overall solving flow.
In summary, the invention has the following advantages:
(1) The invention provides a production line-station layering model for a pulsation production line based on ATC and ALC theory, and compared with a traditional model, the model realizes decoupling and separation among layers; the method is suitable for solving the large-scale problem, has high solving speed, can quickly converge, and shortens the solving time; meanwhile, the method fuses a biological geography BBO algorithm and a squirrel SSA algorithm, so that the quality of understanding is improved;
(2) In order to efficiently obtain the solution of the established model, the invention provides an ALC-based mixed SSA and BBO algorithm which can realize parallel separation solution of a production line layer and a station layer, ensure the efficient acquisition of the solution of the model, satisfy the assembly period of each assembly station and realize the minimization of the overall assembly cost of the whole production line;
(3) Compared with the traditional assembly operation assembly time difficult to quantitatively determine, the operation scheduling method provided by the invention can determine the optimal assembly time for each assembly operation of each station, and further provides basic data for visual operation and regulation of the production line.
Drawings
FIG. 1 is an ATC method framework;
FIG. 2 is a block P ij Is an optimization model of (a);
FIG. 3 is a flow chart of the solution of the invention based on the ALC algorithm combined with the SSA and BBO algorithms;
FIG. 4 is an ATC model constructed in accordance with the present invention;
FIG. 5 illustrates a preferential constraint relationship between assembly jobs;
FIG. 6 is a proposed solution framework;
fig. 7 shows the coding scheme of the lower station layer.
Detailed Description
The present invention will be described in further detail with reference to examples, but embodiments of the present invention are not limited thereto.
Example 1
The invention provides an aircraft production line assembly operation scheduling method based on ATC (object cascade) and ALC (Lagrange relaxation) algorithms.
Step one, establishing a scheduling framework based on an ATC method
An aircraft pulse line comprising N stations, each station having J i Each station is assembled with a theoretical assembly period of T i 。
The framework of the ATC (object cascade) method is shown in fig. 1, the optimization design of the whole system is divided into modules such as a super system layer, a subsystem layer and a component layer, the optimization model of the module Pij is shown in fig. 2 through the cooperation between the layering solution of each module and each layer to achieve the optimization of the system design object.
The invention provides an aircraft pulsation production line assembly operation scheduling frame based on an ATC method, which mainly comprises a production line layer and a station layer, wherein the production line layer and the station layer respectively correspond to an ultra-system and a system in the ATC method. Based on the framework and the ATC method, the invention constructs an aircraft pulsation production line assembly operation scheduling model shown in fig. 4, wherein the model comprises an upper production line optimization layer and a lower station optimization layer, and the two optimization layers are mainly issued and fed back through the assembly time of each assembly operation of each station.
Step two, constructing an optimization model
The optimization model for the production line layer comprises an optimization objective function and constraints, and the model construction process is as follows:
1) The optimization objective of the production line layer is built, and the optimization objective of the production line layer is the total assembly cost of the production line, including the total cost, delay penalty cost and transportation cost of all assembly operations.
Namely: the optimization objective is the overall assembly cost tzp=zp+cf+ys,
wherein ZP is the sum of the assembly cost of each station assembly operation,assembly time, pst, of the j-th assembly operation for the i-th station of the production line layer planning ij The assembly cost per unit time of the j-th assembly operation for the i-th station;
CF is a penalty cost for deferring each assembly operation,assembly time cf of j-th assembly operation for i-th station of production line layer planning i Penalty unit time cost for i-th station lead delivery;
YS is the cost of transportation and,yus ij and the material transportation cost per unit time of the j-th assembly operation for the i-th station.
2) Constructing constraint conditions:
the constraints met by the production line layer are:penalty function of line layer based on ALC algorithm is +.>Wherein v is i ,w i The multiplier is penalized for lagrangian. The goal of the production line layer is further modified as:
the site layer oriented model includes optimization objective functions and constraints. The model construction process is as follows:
1) Constructing an optimization target, wherein the optimization target is that the time difference between the down-feeding and feedback assembly operation of the upper layer and the lower layer is the smallest, and the target is that
2) Constructing constraint conditions:a ij and b ij Respectively representing an upper limit and a lower limit of the assembly operation time; />Set of all assembly work time representing the ith station, calculation period TT of assembly period i i zw Less than or equal to theoretical period T i TT, i.e i zw ≤T i ，TT i zw Is->Is a function of (2);
the preferential constraint relationship between the individual assembly jobs can be represented using a preferential constraint graph as shown in fig. 5, where nd represents no preferential relationship between the two assembly jobs, "→" represents compliance with the preferential constraint relationship between the two jobs, or represents that only one of the two job branches can be selected, and based on the above description, one possible constraint relationship for this assembly process is (the numbers in the circles represent the process code): 4- & gt 5- & gt 11- & gt 14- & gt 12- & gt 15;
while the amount of kth resources required for each assembly job is no greater than its total supply, i.eη k Is the total supply of the kth resource, l ijk The unit time usage of the resource in the kth of the job is assembled for the jth of the i stations.
Step three, model solving
The above-described optimization model is solved based on the solution framework shown in fig. 6 and the solution flow shown in fig. 3. The solution framework shown in FIG. 6 adopts a distributed Hadoop computing cluster, and the upper layer uses a Hadoop computer to mainly take charge of a production line layer optimization model PP cx Is calculated by (a)The solution, the lower layer adopts N Hadoop computers to respectively solve the optimization model PP of N stations zw The N Hadoop computers at the lower layer mutually transmit variables with the Hadoop computers at the upper layer through TCP/IP real-time interaction.
FIG. 3 shows a solution flow based on an ALC algorithm and an SSA and BBO algorithm, wherein v and w represent penalty factors, k represents a cyclic variable, τ represents a convergence threshold, β represents a undetermined coefficient and β > 1; PP (Polypropylene) cx Represents the production line layer optimization model, PP zw Representing a site level optimization model, c k The k-th assembly time calculation is shown. As shown in FIG. 4, the ATC model built by the present invention is that in whichRepresenting the assembly time of the mth assembly operation of the production line layer; />And (5) representing the assembly time of the solved mth assembly operation of the station layer.
The solving process is carried out according to the following steps:
initializing the setting: setting initial values of a loop variable and a penalty factor and the maximum iteration times;
parallel separation and solving of upper and lower models: solving an upper production line layer optimization model by adopting an SSA algorithm, and returning an optimization variable when the iteration number requirement set by the SSA algorithm is metN computers for the lower station layer;
the BBO algorithm is adopted to solve N stations respectively, the sequence code adopted in the embodiment is shown in figure 7, when the assembly period of a certain habitat does not meet the constraint condition, the adaptability index HIS of the habitat is added with a maximum value to punish, and when the iteration times set by the BBO algorithm are reached, each computer outputs a feedback variableTo go upA tier computer;
judging whether the solving result meets the termination condition, stopping the algorithm when the solving result reaches the ATC convergence threshold value, and outputting the optimal scheduling scheme. Otherwise, updating the penalty factor and entering the next cycle of calculation.
The foregoing description is only a preferred embodiment of the present invention, and is not intended to limit the present invention in any way, and any simple modification, equivalent variation, etc. of the above embodiment according to the technical matter of the present invention fall within the scope of the present invention.
Claims (3)
1. The aircraft production line assembly operation scheduling method based on the target cascade analysis algorithm ATC and the enhanced Lagrangian relaxation ALC algorithm is characterized by comprising the following steps of:
step one, assume an aircraft pulse line consisting of N stations, each station having J i Each station is equipped with a period of T i ；
Constructing an aircraft production line assembly operation scheduling frame comprising an upper production line layer and a lower station layer based on an ATC method, and providing an ATC-based production line-station scheduling model based on the frame, wherein the ATC-based production line-station scheduling model comprises an optimization model of the upper production line layer and an optimization model of the lower station layer;
step three, constructing an optimization model facing the upper production line layer, wherein the optimization target is that the total assembly cost of the production line is minimum; comprising the following steps:
1) An optimization objective is constructed, which is the overall assembly cost tzp=zp+cf+ys,
wherein ZP is the sum of the assembly cost of each station assembly operation,assembly time, pst, of the j-th assembly operation for the i-th station of the production line layer planning ij The assembly cost per unit time of the j-th assembly operation for the i-th station;
CF is a penalty cost for deferring each assembly operation,assembly time cf of j-th assembly operation of i-th station for production line layer planning i Penalty unit time cost for i-th station lead delivery;
YS is the cost of transportation and,yus ij the material transportation cost per unit time of the j-th assembly operation for the i-th station;
2) Constructing constraint conditions:the assembly time of the j-th assembly operation of the i-th station position planned for the production line layer;
3) And (3) correcting an upper production line layer optimization target: the penalty function of the upper production line layer based on ALC isWherein v is i ,w i Punishment of multipliers for lagrangian; the line layer target is further modified to +.>
Step four, constructing an optimization model facing to a lower station layer, wherein the optimization goal is that the assembly time difference between the assembly time of each assembly operation and the assembly time transferred by an upper production line layer is minimum; comprising the following steps:
1) Constructing an optimization target: the optimization target is that the assembly time difference between the assembly time of each assembly operation and the assembly time transferred by the upper layer production line layer is the minimum, and the target is that
2) Constructing constraint conditions: (1)calculation period TT of assembly period i i zw Less than or equal to theoretical period, TT i zw ≤T i ，TT i zw Is->Is a function of (2);
(2) while the amount of kth resources required for each assembly job is no greater than its total supply, i.eη k Is the total supply of the kth resource, l ijk A unit time usage amount of resources in a kth of the assembly operation for a jth of the i stations;
step five, parallel separation solution is carried out on the optimization model of the production line layer and the station layer by using a mixed squirrel SSA and physical BBO algorithm based on an ALC algorithm;
and step six, outputting the optimal scheduling scheme.
2. The method of claim 1, wherein in step five, the model solution is based on a distributed Hadoop computation cluster including an upper computer responsible for solving the line level optimization model and a lower computer for solving the N level optimization models of the level layer, the lower computer communicating variables with the upper computer through TCP/IP real-time interactions.
3. The method according to claim 2, wherein in the fifth step, the squirrel SSA algorithm is used for solving an upper layer production line layer optimization model, and when the iteration number requirement is met, the optimization variable is returned to the lower layer computer; the physical BBO algorithm is used for solving the lower-layer station-level optimization model, and when the iteration times are reached, the lower-layer computer outputs feedback variables to the upper-layer computer, and the ALC algorithm is used for controlling and converging the overall solving flow.
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