Resource-constrained parallel machine interactive two-stage scheduling method with flexible boundary constraint

Abstract

The embodiment of the invention discloses a resource-constrained parallel machine interactive two-stage scheduling method with flexible boundary constraint. The method comprises the following steps: acquiring boundary constraint parameters; calculating an initial solution vector set according to the boundary constraint parameters; and optimizing the initial solution vectors contained in the initial solution vector set according to a dual-neighborhood serial search strategy to obtain an optimal flexible constraint parameter combination and an optimal constraint boundary parameter. By implementing the embodiment of the invention, a reasonable and efficient boundary constraint resource two-stage scheduling target can be realized.

Description

Technical Field

[0001] The present application relates to the technical field of parallel machine scheduling, and in particular to an interactive two-level scheduling method for resource-constrained parallel machines with flexible boundary constraints. Background Art

[0002] The resource-constrained parallel machine scheduling (RCPMS) problem is a more realistic extension of the traditional parallel machine scheduling (PMS) problem. It not only needs to consider the availability of parallel machines, but also the limited nature of one or more types of additional resources such as molds, tools, and tooling during machine processing. That is, it is necessary to simultaneously allocate parallel machines and limited additional resources to the best tasks in the form of optimal groups. Therefore, it has a higher complexity than the traditional PMS problem and has been proved to be an NP-complete problem.

[0003] RCPMS exists in many real manufacturing scenarios, such as injection molding, foaming and sheet metal forming with molds as additional resources, involving many industries such as home appliances, semiconductors and mechanical processing. With the globalization of the economy, multi-variety and small batch production has become an important production method. In the production and manufacturing process of these enterprises, planners often need to combine their own experience and consider various flexible constraints, such as the available number of resources, machine qualification restrictions, etc., to ensure the feasibility and production efficiency of the production process. Due to the large number of constraints, planners often use existing algorithm technology to assist scheduling.

[0004] In terms of solution methods, most researchers use various sophisticated intelligent algorithms or mathematical programming methods to solve RCPMS problems, and intelligent algorithms are the main ones. However, as manufacturing scenarios become increasingly complex, RCPMS problems that focus on more specific real-world scheduling needs have gradually become a research hotspot, such as scheduling scenarios with variable constraint values ​​or boundaries, namely flexible constraints. Constraints are essentially used to define the boundaries of the feasible domain of decision variables. The tightness of their settings is related to the efficiency of problem solving and whether the target solution space can be covered. Flexible constraints are set to adapt to dynamic and changeable input data, define reasonable feasible domain boundaries, improve solution efficiency and the probability of covering the target solution space, and can largely meet the bottom line requirements of decision makers for corresponding indicators. Existing RCPMS problem-solving methods are difficult to solve the difficulty of setting flexible constraint parameters. If flexible constraints are used as optimization targets for multi-objective optimization, the search space may be too large due to the large boundaries of the feasible domain, resulting in low search efficiency, and it is difficult to specifically meet the bottom line requirements of decision makers for certain indicators.

[0005] Constraint satisfaction problem (CSP) is a classic problem in artificial intelligence, which involves a set of variables that need to satisfy certain constraints. These problems have wide applications in scheduling, optimization, and many other fields. In CSP, the goal is to find a combination of variable assignments such that all constraints are satisfied. In particular, in RCPMS problems, the concept of CSP is used to solve the challenge of how to efficiently schedule multiple projects or tasks with limited resources. These problems are particularly critical in manufacturing, construction, and project management, which require optimizing cost and time efficiency while meeting resource constraints and time requirements. Summary of the invention

[0006] The embodiment of the present application discloses an interactive two-level scheduling method for resource-constrained parallel machines with flexible boundary constraints, which can achieve the goal of two-level scheduling of boundary-constrained resources with both rationality and efficiency.

[0007] The present application embodiment discloses an interactive two-level scheduling method for resource-constrained parallel machines with flexible boundary constraints, the method comprising:

[0008] Get boundary constraint parameters;

[0009] Calculating an initial solution vector set according to the boundary constraint parameters;

[0010] The initial solution vectors contained in the initial solution vector set are optimized according to a dual-neighborhood serial search strategy to obtain an optimal flexible constraint parameter combination and an optimal constraint boundary parameter.

[0011] As an optional implementation manner, before obtaining the boundary constraint parameters, the method further includes:

[0012] Get order data;

[0013] Extracting features from the order data to obtain order data features;

[0014] Boundary constraint parameters are set according to the order data characteristics.

[0015] As an optional implementation manner, after obtaining the boundary constraint parameters, the method further includes:

[0016] Generate corresponding constraint conditions according to the boundary constraint parameters; the constraint conditions include available quantity limit constraint for box body molds, shift capacity limit constraint for door body molds, production scheduling constraints for mutually exclusive product models that are not scheduled at the same time during the general assembly phase, quantity constraint for box body mold types that are foaming at the same time, production scheduling tolerance limit for domestic and foreign periodic delivery, production scheduling completion rate limit for each product demand, and capacity utilization rate constraint;

[0017] The step of calculating an initial solution vector set according to the boundary constraint parameters comprises:

[0018] An initial solution vector set is calculated according to the constraint conditions corresponding to the boundary constraint parameters.

[0019] As an optional implementation manner, calculating the initial solution vector set according to the boundary constraint parameters includes:

[0020] Calculating a plurality of feasible solution vectors according to the boundary constraint parameters;

[0021] The multiple feasible solution vectors are screened to obtain the initial solution vector set.

[0022] As an optional implementation manner, the screening of the multiple feasible solution vectors to obtain the initial solution vector set includes:

[0023] Substituting the multiple feasible solutions into a preset objective function for calculation, to obtain objective function values ​​corresponding to the multiple feasible solutions respectively;

[0024] An initial solution vector is screened out according to the objective function values ​​respectively corresponding to the multiple feasible solutions.

[0025] As an optional implementation manner, after calculating the initial solution vector set according to the boundary constraint parameters, the method further includes:

[0026] Determining whether the initial solution vector set includes at least one initial solution vector;

[0027] The step of optimizing the initial solution vectors contained in the initial solution vector set according to the dual-neighborhood serial search strategy to obtain the target solution vector includes:

[0028] If it is determined that the initial solution vector set includes at least one initial solution vector, the initial solution vectors included in the initial solution vector set are optimized according to a dual-neighborhood serial search strategy to obtain an optimal flexible constraint parameter combination and an optimal constraint boundary parameter.

[0029] As an optional implementation, the initial solution vectors included in the initial solution vector set are optimized according to the dual-neighborhood serial search strategy to obtain the optimal flexible constraint parameter combination and the optimal constraint boundary parameter, including:

[0030] Optimizing the configuration parameters corresponding to the initial solution vector according to a dual-neighborhood serial search strategy to obtain optimized configuration parameters;

[0031] According to the optimized configuration parameters and the initial solution vectors corresponding to the optimized configuration parameters, an optimal flexible constraint parameter combination and an optimal constraint boundary parameter are obtained.

[0032] As an optional implementation manner, optimizing the configuration parameters corresponding to the initial solution vector according to the dual-neighborhood serial search strategy to obtain the optimized configuration parameters includes:

[0033] Calculating process parameters corresponding to each initial solution vector; the process parameters are used to describe the complexity of the resource production process;

[0034] The process parameters corresponding to the initial solution vectors are compared, and the configuration parameters corresponding to the initial solution vector with the smallest process parameters are selected as the optimized configuration parameters.

[0035] As an optional implementation, the method further includes:

[0036] The number of box molds scheduled for production in shifts is defined as the capacity base, and the decision variables of the CP model are constructed based on the number of foaming machines. The method for calculating the shift capacity based on the capacity base is: Powe i =Cd Num ×TM i .

[0037] As an optional implementation, the method further includes:

[0038] Using the efficient Element(Expr i ,Expr j ,Arry) function to establish the decision variable salesF ij , fridge i j,mould ij The relationship between them, Expr i With Expr j are single decision variables, Arry is an array, and the array index is the same as Expr j The value range of Eleme(Expr i ,Expr j ,Arry) is used to establish constraints: Expr i The value of is equal to the index Expr in Arry j The value of .

[0039] Compared with the related art, the embodiments of the present application have the following beneficial effects:

[0040] The embodiment of the present application provides an interactive two-level scheduling method for resource-constrained parallel machines with flexible boundary constraints, obtains boundary constraint parameters, calculates an initial solution vector set according to the boundary constraint parameters, optimizes the initial solution vectors contained in the initial solution vector set according to the dual-neighborhood serial search strategy, and obtains the optimal flexible constraint parameter combination and the optimal constraint boundary parameter. Implementing the embodiment of the present application, the initial solution vector set is calculated according to the obtained boundary constraint parameters, and the target solution vector can be optimized in the initial solution vector set, thereby reducing the search space for the target solution vector and improving the efficiency of solving the boundary constraint resource two-level scheduling problem. The initial solution vector contained in the initial solution vector set is optimized according to the dual-neighborhood serial search strategy to obtain the optimal flexible constraint parameter combination and the optimal constraint boundary parameter. The initial solution vector set can be further optimized through the dual-neighborhood serial search strategy, thereby obtaining the optimal flexible constraint parameter combination and the optimal constraint boundary parameter, which can effectively improve the production efficiency of the implementation of the production plan, and also ensure the rationality of production, balance various production constraints and resource allocation, and improve data production, thereby achieving the boundary constraint resource two-level scheduling goal of rationality and high efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0042] Figure 1 It is a flow chart of an interactive two-level scheduling method for resource-constrained parallel machines with flexible boundary constraints disclosed in an embodiment of the present application;

[0043] Figure 2 is an interactive two-level scheduling solution flow chart in one embodiment;

[0044] Figure 3 It is a schematic diagram of a process for calculating an initial solution vector set according to boundary constraint parameters disclosed in an embodiment of the present application;

[0045] Figure 4 It is a schematic diagram of a process for obtaining an optimal flexible constraint parameter combination and an optimal constraint boundary parameter disclosed in an embodiment of the present application;

[0046] Figure 5 is a schematic diagram illustrating encoding and decoding in an embodiment;

[0047] Figure 6 is a schematic diagram of the first cycle neighborhood structure in an embodiment;

[0048] Figure 7is a schematic diagram of an intermediate period neighborhood structure in an embodiment;

[0049] Figure 8 is a schematic diagram of the neighborhood structure of the end period in one embodiment;

[0050] Fig. 9 A schematic diagram of a neighborhood structure for optimizing the number of extreme mold types and shifts in one embodiment. DETAILED DESCRIPTION

[0051] The following will be combined with the drawings in the embodiments of the present application to clearly and completely describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0052] It should be noted that the terms "including" and "having" and any variations thereof in the embodiments of the present application and the accompanying drawings are intended to cover non-exclusive inclusions. For example, a process, method, system, product or device including a series of steps or units is not limited to the listed steps or units, but may optionally include steps or units not listed, or may optionally include other steps or units inherent to these processes, methods, products or devices.

[0053] In the prior art, most studies solve RCPMS problems by obtaining constraints and objective functions based on problem analysis and then establishing integer programming models for single-objective solutions. For multi-objective and more complex scenarios, heuristic algorithms are more often used. However, when faced with RCPMS problems with complex decision variables and constraints, these algorithms have the disadvantages of being difficult to model and difficult to implement.

[0054] As real manufacturing scenarios become more and more complex, the RCPMS problem also has flexible constraints with adjustable boundaries. When using conventional solution methods, if the flexible constraints are set to the most relaxed and converted to hard constraints, integer programming methods and heuristic algorithms are prone to difficulties in generating feasible solutions, low solution efficiency, and slow convergence due to the large search space under large-scale scheduling. If multiple flexible constraints are converted into multiple optimization objectives, various heuristic algorithms will face problems such as difficulty in encoding decision variables, high complexity in constraint implementation, and slow convergence.

[0055] The embodiment of the present application discloses an interactive two-level scheduling method for resource-constrained parallel machines with flexible boundary constraints, which can achieve the goal of two-level scheduling of boundary-constrained resources with both rationality and efficiency.

[0056] Figure 11 is a flow chart of an interactive two-level scheduling method for resource-constrained parallel machines with flexible boundary constraints disclosed in an embodiment of the present application. Figure 1 As shown, the resource-constrained parallel machine interactive two-level scheduling method with flexible boundary constraints may include the following steps:

[0057] Step S102, obtaining boundary constraint parameters.

[0058] The present invention takes the production scheduling of foaming refrigerators of multiple varieties and small batches as the research object. The production process of refrigerator foaming is divided into: pre-assembling the box, the box foaming process, and the general assembly process. Pre-assembling the box refers to assembling various parts into a semi-finished box. The box foaming process refers to using the box mold in combination with the foaming machine to foam the semi-finished box into a finished box. The box foaming machine is a general equipment. All box molds can be foamed in any box foaming machine, but the foaming time of different molds in the same foaming machine may be different. Switching the box mold of the same foaming machine between adjacent shifts, including switching from mold A to mold B, removing the original mold or installing the mold on an empty machine, is called mold change. Mold change takes a long time and has a great impact on production capacity. The general assembly process refers to assembling the finished box and the corresponding parts into a finished refrigerator. In order to meet the market challenges of personalized demand, refrigerator production has shifted from a single variety and large-scale mode to a multi-variety and small-batch production mode. In order to meet the diversified production needs of final assembly, the production of refrigerator cabinets was separated out separately, transformed from the previous conventional long assembly line to a multi-stage production line, and a component buffer area was set up between the cabinet foaming process and the final assembly.

[0059] Description of the problem of scheduling the foaming production of refrigerators with multiple varieties and small batches: The foaming production of refrigerator cases is a bottleneck process, which determines the production efficiency of the entire refrigerator production line, and plays a role in driving the pre-assembly of cases and promoting the production of final assembly. Because the production of refrigerators requires the coordination of case foaming and final assembly to be completed, it is necessary to simultaneously decide on the production scheduling of the case mold and the production scheduling of the product model of the final assembly process. There needs to be a certain balance between production efficiency and delivery requirements, and the increasing fragmentation of orders makes it difficult to schedule production according to orders. Therefore, the monthly orders are aggregated to the model level, and scheduling is carried out from the perspective of the monthly demand for product models to meet the production capacity requirements and cycle delivery requirements at the model level. Since the time unit for mold change is shift, the time unit for refrigerator foaming production scheduling is shift, and scheduling is carried out based on the available production hours specified in the work calendar.

[0060] In some embodiments, the basic parameters for constructing a two-level scheduling model for boundary-constrained resources by an electronic device may be as shown in Table 1 below:

[0061] Table 1

[0062]

[0063]

[0064] In some embodiments, the boundary constraint parameters can be used to describe the constraints of the boundary constraint resource two-level scheduling problem. The boundary constraint parameters may include LC w 、TIS w 、TOS w , P, ES and decision variables. Among them, It can be used to describe that if the first product and the second product are mutually exclusive and cannot be produced in the same shift, the value is 1, otherwise it is 0, and the first product and the second product are different products. LC w It can be used to describe the upper limit of the number of mold types that can be scheduled for production in all shifts in the wth cycle of the box foam production part. TIS w It can be used to describe the domestic delivery schedule deviation ratio in the wth cycle. TOS w It can be used to describe the deviation ratio of overseas delivery schedule in the wth cycle, P can be used to describe the completion rate of demand schedule, and ES can be used to describe the capacity utilization constraint setting parameters.

[0065] The decision variables are as follows:

[0066] Due to the restrictions of many constraints, it is always difficult to complete the production of the summary orders of various products continuously, and usually they cannot be scheduled as a task. Therefore, this CP model does not use the interval variables in CP Optimizer as decision variables, but uses integer type variables. Based on the characteristics that the box mold is scheduled in shifts and one box mold uses one foaming machine, for the convenience of modeling, the number of shifts of the box mold is defined as the capacity base, and the decision variables of the CP model are constructed based on the number of foaming machines. The shift capacity is calculated based on the capacity base as shown in formula (1):

[0067] Powe i =Cd Num ×TM i #(1)

[0068] A total of 3 groups of integer decision variables are defined: salesF ij , fridge ij , mould ij , and use the efficient Element(Expr i ,Expr j ,Arry) function establishes the relationship between the three groups of decision variables, Expr i With Expr j are single decision variables, Arry is an array, and the array index is the same as Expr j The value range of Eleme(Expri ,Expr j ,Arry) is used to establish constraints: Expr i The value of is equal to the index Expr in Arry j The value of .

[0069] 1)salesF ij is the capacity decision variable, salesF ij Decision on the delivery product number f of the jth foaming machine capacity supply in the i-th shift s , the value range is: salesF ij ∈{f s |f s =f×10+s}; Using formula (1), calculate the supply f s The number of foaming machines is Cd Num ,TM i Given this, the shift capacity for delivery type s of product f can be calculated.

[0070] 2) Fridge ij is the product model decision variable, which indicates the product number supplied by the jth foaming machine in the i-th shift, and its value range is: 1≤fridge ij ≤f. Formula (2) shows that the constraint is established: for any foaming machine j in shift i, the decision variable fridge ij The value is equal to Arr sf The index in salesF ij The value of .

[0071]

[0072] 3) Mould ij is the decision variable for the box mold, indicating the box mold number scheduled for production by the jth foaming machine in the i-th shift, and its value range is: 1≤mould ij ≤m, we can conveniently use the count and countdifferent functions in CP Optimizer; Formula (3) shows that the constraint is established: for any foaming machine j in shift i, the decision variable mould ij The value is equal to Array sm The index in salesF ij Value

[0073]

[0074] In fact, a foaming machine may be idle in a certain shift. In order to indicate the idle state of the machine, selesF ij , fridge ij , mouldij It is necessary to add a dummy variable value of 0. When the decision variable takes the value of 0, the machine is idle.

[0075] In some embodiments, after obtaining the boundary constraint parameters, corresponding constraint conditions can be generated according to the boundary constraint parameters; the constraint conditions include available quantity limit constraints for box molds, shift capacity limit constraints for door molds, production scheduling constraints for mutually exclusive product models in different assembly stages, quantity constraints for box mold types being foamed at the same time, production scheduling tolerance limits for domestic and foreign cycle delivery, production scheduling completion rate limits for each product demand, and capacity utilization constraints; the initial solution vector set is calculated according to the constraint conditions corresponding to the boundary constraint parameters.

[0076] The constraints generated for the edge constraint parameters are as follows:

[0077]

[0078] count(emptyVars i ,J)=ES#(13)

[0079] Among them, formula (4) represents the available quantity limit constraint of box molds; formula (5) represents the shift capacity limit constraint of door molds; formula (6) represents the scheduling constraint of mutually exclusive product models in different assembly stages; formula (7)(8) represents the quantity constraint of box mold types that are foaming at the same time; formula (9)(10) represents the tolerance limit of domestic and foreign periodic delivery scheduling; formula (11) represents the scheduling completion rate limit of each product demand; formula (12)(13) capacity utilization constraint setting.

[0080] As an optional implementation method, before obtaining the boundary constraint parameters, the electronic device may also obtain order data; extract features from the order data to obtain order data features; and set boundary constraint parameters based on the order data features. Based on the input order data, the summarized data features are: Total required production hours ratio Total T , used to describe the production hours required to produce all orders when only resource capacity is considered; the maximum proportion of production shifts required for each box mold Used to describe the ratio of the number of shifts required to produce the total order quantity of each mold at the maximum shift capacity to the total number of shifts, taking the maximum value; the ratio of the number of production shifts required for the bottleneck door mold It is used to describe the proportion of production shifts required for bottleneck box molds; the number of product model types CatF is used to describe the number of product types involved in all orders; the number of box mold types CatM is used to describe the number of box mold types used for all products; the proportion of domestic delivery orders SRIn is used to describe the proportion of domestic delivery orders to the total order volume; the proportion of foreign sales orders SRIut is used to describe the proportion of foreign delivery orders to the total order volume; the number of scheduling shifts is used to describe the number of available production shifts given by the work calendar; the minimum required scheduling shift number NShift, its calculation formula is Where Ceiling() refers to the smallest integer greater than or equal to the number and rounds it up.

[0081] Decision makers set the upper and lower limits of flexible constraint boundaries based on decision needs, combined with data characteristics and experience. In addition to setting the constraint value of each flexible constraint itself, the combination with other constraints must also be considered. For each flexible constraint, first determine its upper and lower limits, then set the required number of groups, and finally set the parameters of each group according to the number of groups. The setting based on flexible constraints is oriented to balance the constraints of production and demand matching and the constraints of coordinated delivery and efficiency. The production completion rate constraint and the capacity utilization constraint are combined and set, and the upper limit of the number of box mold types that are foaming at the same time and the domestic and foreign cycle delivery production deviation ratio are combined and set. Among them, the upper and lower limits of the flexible constraint boundaries may include: the upper limit of the number of box mold types that are foaming at the same time LC, and its upper line value LC max The lower limit is set by default. The domestic and foreign cycle delivery production deviation ratio is TIO, and its upper limit is TIO max =Max(SRIn,SROut)*25%, the lower limit is determined by the decision maker; the capacity utilization constraint ES, its upper limit is The lower limit is Total T ×P; the order scheduling completion rate P, its upper limit is determined by the CP solver, and the lower limit is determined by the decision maker.

[0082] In some embodiments, the electronic device may include preset result evaluation indicators for evaluating the rationality of the upper and lower limits of the flexible constraint boundaries set above. The result evaluation indicators may include: the average deviation of the domestic delivery capacity cycle TR in , which is calculated as Average deviation of foreign delivery capacity cycle TR out , which is calculated as The actual production completion rate of total demand Sat is calculated as The actual capacity utilization rate URate is calculated as follows: Total number of mold changes for box mold ST num , which is calculated as Limit mold type shift number MC num , which is calculated as count(countdifferent(mould i＝1…i,j＝1…j ),LC max ),mould i,j＝1…j ≠0.

[0083] Step S104, calculating an initial solution vector set according to the boundary constraint parameters.

[0084] In some embodiments, after calculating the initial solution vector set according to the boundary constraint parameters, the electronic device can determine whether the initial solution vector set contains at least one initial solution vector. If it is determined that the initial solution vector set contains at least one initial solution vector, the initial solution vector contained in the initial solution vector set is optimized according to the dual-neighborhood serial search strategy to obtain the target solution vector. If it is determined that the initial solution vector set does not contain at least one initial solution vector, the boundary constraint parameters can be reset, and the calculation is performed according to the boundary constraint parameters to obtain a new initial solution vector set.

[0085] Step S106, optimizing the initial solution vectors included in the initial solution vector set according to a dual-neighborhood serial search strategy to obtain an optimal flexible constraint parameter combination and an optimal constraint boundary parameter.

[0086] In the process of calculating the initial solution vector set, the requirement for the number of mold changes is not reflected in the constraint parameter setting. Since the solver does not have a search direction when searching for feasible solutions to the constraint satisfaction problem, after the decision maker screens out the constraint boundary parameters and feasible solutions through the first-level scheduling, it is necessary to further optimize the mold change number indicator in the second-level scheduling. And the indicator of the number of types of molds in production at the same time is also further optimized to improve the decision maker's satisfaction with the production efficiency indicator. In the second-level scheduling optimization, since the constructed constraint programming model groups the decision variables, it makes it possible to carry out targeted optimization of decision variables related to production efficiency. At the same time, in order to fully meet the interactive constraints in the first-level scheduling, a stable and efficient search algorithm is selected. Since here a part of the decision variables is optimized, a neighborhood search algorithm is selected. The present invention will design a neighborhood structure based on the problem domain knowledge and the characteristics of the decision variables to efficiently optimize the production capacity and efficiency indicators.

[0087] In some embodiments, a specific neighborhood search algorithm can be designed to optimize the mold change index and the limit mold type shift number index. Since the bottom line satisfaction of the number of mold types in production at the same time has been guaranteed through constraint setting in the first-level scheduling, the main goal of the second-level scheduling is to optimize the mold change number index that is not reflected by the constraint setting in the first-level scheduling. If the optimization result is not satisfactory, the decision maker can return to the first-level scheduling to adjust the constraint parameters and perform two-level scheduling optimization again until a satisfactory solution is obtained, thereby obtaining the optimal flexible constraint parameter combination and the optimal constraint boundary parameter.

[0088] Figure 2 is an interactive two-level scheduling solution flow chart in one embodiment, such as Figure 2 As shown in the figure, it is determined that the flexible constraint boundary of the scheduling problem is uncertain. Then the order data feature calculation can be scheduled, and the decision maker sets the flexible constraint parameter combination, and solves the feasible solution set of each flexible constraint parameter combination according to the constraint planning. Obtain the Pareto non-dominated solution set, normalize the performance indicators, and select a satisfactory feasible solution based on the specific performance indicators. At the same time, the corresponding constraint boundary parameters are obtained, and it is judged whether a satisfactory flexible constraint parameter setting and a satisfactory solution are obtained. If a satisfactory flexible constraint parameter setting and a satisfactory solution are not obtained, the flexible constraint parameters are readjusted. If it is determined that a satisfactory flexible constraint parameter setting and a satisfactory solution are obtained, the optimization problem with a determined constraint boundary is determined, and the capacity and efficiency indicators are optimized according to the neighborhood search algorithm. The decision maker determines whether the optimization result is satisfied. If not, the flexible constraint parameters can be readjusted. If satisfied, the final solution result is obtained.

[0089] In an embodiment of the present application, boundary constraint parameters are obtained, an initial solution vector set is calculated according to the boundary constraint parameters, and the initial solution vectors contained in the initial solution vector set are optimized according to the dual-neighborhood serial search strategy to obtain the optimal flexible constraint parameter combination and the optimal constraint boundary parameter. In the implementation of the embodiment of the present application, the initial solution vector set is calculated according to the obtained boundary constraint parameters, and the target solution vector can be optimized in the initial solution vector set, thereby reducing the search space for the target solution vector and improving the efficiency of solving the boundary constraint resource two-level scheduling problem. The initial solution vector contained in the initial solution vector set is optimized according to the dual-neighborhood serial search strategy to obtain the optimal flexible constraint parameter combination and the optimal constraint boundary parameter. The initial solution vector set can be further optimized through the dual-neighborhood serial search strategy to obtain the optimal flexible constraint parameter combination and the optimal constraint boundary parameter, which can effectively improve the production efficiency of the implementation of the production plan, and ensure the rationality of production, balance various production constraints and resource allocation, and improve data production, thereby achieving the boundary constraint resource two-level scheduling goal of rationality and high efficiency.

[0090] Figure 3is a schematic diagram of a process for calculating an initial solution vector set according to boundary constraint parameters disclosed in an embodiment of the present application. Figure 3 As shown, the method comprises the following steps:

[0091] Step S302: Calculate multiple feasible solution vectors according to boundary constraint parameters.

[0092] Step S304: Screen multiple feasible solution vectors to obtain an initial solution vector set.

[0093] The feasible solution screening method is as follows: Assuming that the multi-objective problem needs to find the minimum value, it is defined as follows:

[0094]

[0095] Among them, F(x) is the n-dimensional objective function, f i (x) is one of the targets; x=(x1,x1,…,x m ) T is an m-dimensional decision variable. Let vector u=(u1,u2,…,u m ) T and v=(v1,v2,…,v m ) T are two solutions in the decision variable space, if and Then it means that vector u dominates v, which is recorded as u<v. If solution u dominates v, it means that solution u is better than solution v. Pareto non-dominated solution screening refers to screening out a set of solutions that are not dominated by any solution through comparative calculation, that is, the Pareto frontier solution set.

[0096] The performance index dimension normalization evaluation method refers to the evaluation index ST num For example, is the index of solving x, is the mean value of the index in the solution space, then the dimensionally normalized value of the index The calculation formula of is shown in formula (15), which is consistent with the idea of ​​the general dimensional normalization method. The calculation formula of the total score of the dimensional normalization evaluation of the indicator x is shown in formula (16).

[0097]

[0098] In an embodiment of the present application, the electronic device calculates multiple feasible solution vectors according to the boundary constraint parameters, screens the multiple feasible solution vectors, and obtains an initial solution vector set, which can improve the rationality of calculating the initial solution vector set.

[0099] See also Figure 4 , Figure 4The present invention discloses a flow chart of obtaining the optimal flexible constraint parameter combination and the optimal constraint boundary parameter. In one embodiment, the steps include optimizing the initial solution vectors contained in the initial solution vector set according to the dual-neighborhood serial search strategy to obtain the optimal flexible constraint parameter combination and the optimal constraint boundary parameter, and further including the following steps:

[0100] Step S402: optimizing the configuration parameters corresponding to the initial solution vector according to the dual-neighborhood serial search strategy to obtain optimized configuration parameters.

[0101] Step S404: obtaining an optimal flexible constraint parameter combination and an optimal constraint boundary parameter according to the optimized configuration parameters and the initial solution vector corresponding to the optimized configuration parameters.

[0102] To illustrate the coding and iteration process, assume that there are 6 shifts in a cycle and a total of 10 machines. According to the decision variable structure of the box mold in the constraint programming modeling, the solution of the decision variable is as follows: Figure 5 As shown in the actual decision variable table, the rows represent the shift numbers, the columns represent the machine numbers, and the values ​​in the table are the box mold numbers. This table accurately expresses the production schedule of box molds on each machine in each shift, but this representation method cannot directly express the changes in the number of box molds between shifts. Therefore, the production schedule of box molds in each shift is counted and converted into Figure 5 In the format shown in the coding table, the rows are still shifts and the columns are mold numbers. When decoding, they will be converted back to output the production scheduling results according to the machine position.

[0103] Neighborhood structure design for optimization of mold change times: Based on the connection characteristics between the first cycle, the middle cycle, and the last cycle and other cycles, three specific neighborhood structures are designed for the first cycle, the middle cycle, and the last cycle. The first cycle neighborhood structure is described as follows: Figure 6 As shown in the figure, based on the connection point of view, the first shift of the next cycle needs to be considered. The shifts of the second cycle are replaced with the first shift of the cycle in turn, and included in the calculation range of the module change. The neighborhood search is only performed for the shifts of the first cycle. The search range is as follows: Figure 6 As shown in , the connection between the first cycle and the second cycle is considered. The neighborhood structure of the intermediate cycle is shown in Figure 7 As shown in the figure, the connection processing with the next cycle is the same as the first cycle, but the middle cycle only participates in the calculation of the number of mold changes and does not participate in the search range because its first shift has been locked by the previous cycle search. The last cycle locks the first shift determined by the previous cycle search and only searches the remaining shifts. Through these three types of neighborhood structures, the purpose of not destroying other evaluation indicators within the cycle and shift is achieved, and the evaluation indicators that have been met in the first-level scheduling are effectively protected.

[0104] The search ranges of the three types of periodic neighborhood structures are different from the calculation ranges of the mold change times, but the neighborhood search action process for the search range is the same. The pseudo code of the neighborhood action algorithm for the set search range is as follows:

[0105]

[0106] The neighborhood structure for optimizing the number of shifts for extreme mold types is as follows: Figure 8 As shown: The pseudo code of the domain action is as follows:

[0107]

[0108]

[0109] From a single dimension, the number of mold changes and the number of mold types are considered for optimization. In the actual production environment, in order to maximize production efficiency and ensure production rationality, both need to be taken into account. A dual-neighborhood serial search strategy is proposed to take into account the synergy of the two. The specific implementation steps are shown in the following pseudo code:

[0110]

[0111]

[0112] In an embodiment of the present application, the configuration parameters corresponding to the initial solution vector are optimized according to the dual-neighborhood serial search strategy to obtain the optimized configuration parameters. According to the optimized configuration parameters and the initial solution vector corresponding to the optimized configuration parameters, the optimal flexible constraint parameter combination and the optimal constraint boundary parameters are obtained. A fast and effective dual-neighborhood serial search strategy can be designed, which can further optimize the scheduling scheme, effectively improve the production efficiency of the implementation of the scheme, ensure the rationality of production, balance various production constraints and resource allocation, and thus achieve the scheduling goal of both high efficiency and rationality.

[0113] It should be understood that the "one embodiment" or "an embodiment" mentioned throughout the specification means that the specific features, structures or characteristics related to the embodiment are included in at least one embodiment of the present application. Therefore, "in one embodiment" or "in an embodiment" appearing throughout the specification does not necessarily refer to the same embodiment. In addition, these specific features, structures or characteristics can be combined in one or more embodiments in any suitable manner. Those skilled in the art should also be aware that the embodiments described in the specification are all optional embodiments, and the actions and modules involved are not necessarily required for the present application.

[0114] In the various embodiments of the present application, it should be understood that the size of the serial numbers of the above-mentioned processes does not necessarily mean the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present application.

[0115] The units described above as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed on multiple network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0116] In addition, each functional unit in each embodiment of the present application may be integrated into one processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit. The above-mentioned integrated unit may be implemented in the form of hardware or in the form of software functional units.

[0117] If the above-mentioned integrated unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-accessible memory. Based on this understanding, the technical solution of the present application, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product, which is stored in a memory and includes several requests for a computer device (which can be a personal computer, a server or a network device, etc., specifically a processor in a computer device) to perform some or all of the steps of the above-mentioned methods of various embodiments of the present application.

[0118] Those skilled in the art can understand that all or part of the steps in the various methods of the above embodiments can be completed by instructing related hardware through a program, and the program can be stored in a computer-readable storage medium, and the storage medium includes a read-only memory (ROM), a random access memory (RAM), a programmable read-only memory (PROM), an erasable programmable read-only memory (EPROM), a one-time programmable read-only memory (OTPROM), an electronically erasable programmable read-only memory (EEPROM), a compact disc read-only memory (CD-ROM) or other optical disc storage, magnetic disk storage, magnetic tape storage, or any other computer-readable medium that can be used to carry or store data.

[0119] The above is a detailed introduction to a resource-constrained parallel machine interactive two-level scheduling method with flexible boundary constraints disclosed in the embodiment of the present application. This article uses specific examples to illustrate the principles and implementation methods of the present application. The description of the above embodiments is only used to help understand the method and core ideas of the present application. At the same time, for those of ordinary skill in the art, according to the ideas of the present application, there will be changes in the specific implementation methods and application scopes. In summary, the content of this specification should not be understood as limiting the present application.

Claims

1. An interactive two-level scheduling method for resource-constrained parallel machines with flexible boundary constraints, characterized in that: The method comprises: Get boundary constraint parameters; Calculating an initial solution vector set according to the boundary constraint parameters; The initial solution vectors contained in the initial solution vector set are optimized according to a dual-neighborhood serial search strategy to obtain an optimal flexible constraint parameter combination and an optimal constraint boundary parameter.

2. The method according to claim 1, characterized in that Before obtaining the boundary constraint parameters, the method further includes: Get order data; Extracting features from the order data to obtain order data features; Boundary constraint parameters are set according to the order data characteristics.

3. The method according to claim 1, characterized in that After obtaining the boundary constraint parameters, the method further includes: Generate corresponding constraint conditions according to the boundary constraint parameters; the constraint conditions include available quantity limit constraint for box body molds, shift capacity limit constraint for door body molds, production scheduling constraints for mutually exclusive product models that are not scheduled at the same time during the general assembly phase, quantity constraint for box body mold types that are foaming at the same time, production scheduling tolerance limit for domestic and foreign periodic delivery, production scheduling completion rate limit for each product demand, and capacity utilization rate constraint; The step of calculating an initial solution vector set according to the boundary constraint parameters comprises: An initial solution vector set is calculated according to the constraint conditions corresponding to the boundary constraint parameters.

4. The method according to claim 1, characterized in that: The step of calculating an initial solution vector set according to the boundary constraint parameters comprises: Calculating a plurality of feasible solution vectors according to the boundary constraint parameters; The multiple feasible solution vectors are screened to obtain the initial solution vector set.

5. The method according to claim 4, characterized in that The screening of the multiple feasible solution vectors to obtain the initial solution vector set includes: Substituting the multiple feasible solutions into a preset objective function for calculation, to obtain objective function values ​​corresponding to the multiple feasible solutions respectively; An initial solution vector is screened out according to the objective function values ​​respectively corresponding to the multiple feasible solutions.

6. The method according to claim 1, characterized in that After calculating the initial solution vector set according to the boundary constraint parameters, the method further includes: Determining whether the initial solution vector set includes at least one initial solution vector; The step of optimizing the initial solution vectors contained in the initial solution vector set according to the dual-neighborhood serial search strategy to obtain an optimal flexible constraint parameter combination and an optimal constraint boundary parameter includes: If it is determined that the initial solution vector set includes at least one initial solution vector, the initial solution vectors included in the initial solution vector set are optimized according to a dual-neighborhood serial search strategy to obtain an optimal flexible constraint parameter combination and an optimal constraint boundary parameter.

7. The method according to claim 1, characterized in that The step of optimizing the initial solution vectors contained in the initial solution vector set according to the dual-neighborhood serial search strategy to obtain an optimal flexible constraint parameter combination and an optimal constraint boundary parameter includes: Optimizing the configuration parameters corresponding to the initial solution vector according to a dual-neighborhood serial search strategy to obtain optimized configuration parameters; According to the optimized configuration parameters and the initial solution vectors corresponding to the optimized configuration parameters, an optimal flexible constraint parameter combination and an optimal constraint boundary parameter are obtained.

8. The method according to claim 7, characterized in that The step of optimizing the configuration parameters corresponding to the initial solution vector according to the dual-neighborhood serial search strategy to obtain the optimized configuration parameters includes: Calculating process parameters corresponding to each initial solution vector; the process parameters are used to describe the complexity of the resource production process; The process parameters corresponding to the initial solution vectors are compared, and the configuration parameters corresponding to the initial solution vector with the smallest process parameters are selected as the optimized configuration parameters.

9. The method according to claim 1, characterized in that: The method further comprises: The number of box molds scheduled for production in shifts is defined as the capacity base, and the decision variables of the CP model are constructed based on the number of foaming machines. The method for calculating the shift capacity based on the capacity base is: Power i =Cd Num ×TM i .

10. The method according to claim 9, characterized in that The method further comprises: Using the efficient El(Expr i ,Expr j ,Arry) function to establish the decision variable salesF ij , fridge ij , mould ij The relationship between them, Expr i With Expr j are single decision variables, Arry is an array, and the array index is the same as Expr j The value range of Eleme(Expr i ,Expr j ,Arry) is used to establish constraints: Expr i The value of is equal to the index Expr in Arry j The value of .

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