Intelligent scheduling multi-objective optimization method based on pulse propagation algorithm

Abstract

The application discloses an intelligent scheduling multi-objective optimization method based on a pulse propagation algorithm, relates to the field of manufacturing scheduling, and comprises the following steps: a scheduling data preparation stage, which is used for making a pre-decision for the schedulable resources in a pool and generating data of an input model; a multi-objective model establishment stage, which describes scheduling rules and optimization targets in a mathematical modeling mode; and a pulse propagation algorithm stage, which solves the above multi-objective model by designing an epsilon-constraint and a pulse propagation algorithm. The application greatly reduces the work burden of a planner, and the batch decision and specific scheduling details can be automatically completed by an embedded advanced model and intelligent algorithm. The intelligent decision mechanism not only improves work efficiency, but also ensures the accuracy and rationality of the scheduling plan.

Description

Technical Field

[0001] This invention relates to the field of manufacturing scheduling, specifically an intelligent scheduling multi-objective optimization method based on the pulse propagation algorithm. It is applied to scenarios requiring continuous production, such as steel cold rolling / hot rolling workshops and non-ferrous metal (aluminum / copper) rolling workshops. The target workpieces are plate and strip workpieces with continuous rolling conditions (such as cold-rolled steel plates and aluminum foil billets). It is suitable for scenarios with continuous production scheduling of multiple workpieces on a single production line, and is especially suitable for production modes with urgent material supply needs and high thickness accuracy requirements in downstream processes (such as automotive sheet cold rolling scheduling and power battery aluminum foil scheduling). Background Technology

[0002] Workpiece scheduling is a crucial step in the workpiece production process, characterized by its high importance and complexity. This process encompasses a series of meticulous technological steps, from raw material preparation to finished product delivery, each requiring strict time planning and resource allocation. In particular, when formulating the production sequence plan, it is necessary to comprehensively examine multiple factors such as workpiece resource distribution, production concentration, and equipment utilization rate to ensure the efficiency and smoothness of the production process. In the past, a common approach to multi-objective scheduling problems was to transform them into single-objective problems using a weighted approach. While this simplified the problem operationally, determining the appropriate weights became a challenging task due to the significant differences in the dimensions and numerical ranges of the objectives. Inadequate weight selection could easily lead to scheduling results deviating from the optimal state, failing to meet expectations and needs, and potentially causing a series of negative effects such as uneven resource allocation and low productivity. Given the limitations of the weighted approach, it is crucial to explore multi-objective optimization strategies for scheduling problems. Multi-objective optimization aims to simultaneously consider and balance multiple conflicting or mutually restrictive objectives to effectively explore and find a solution set close to the Pareto optimal front in a complex search space, providing decision-makers with diverse options. Furthermore, by combining domain knowledge and practical needs, appropriate improvements and customizations to the algorithm can further enhance optimization performance, ensuring that the scheduling solution is both efficient and practical.

[0003] There are three main problems with using the weighted method to handle multi-objective problems: First, it is difficult to determine the weights. The primary challenge in using the weighted method to handle multi-objective scheduling problems is determining the weights. This is because the multiple objectives involved in the scheduling process often have different dimensions and orders of magnitude. For example, the significant difference between the two objectives of workpiece quantity and specification fluctuation makes the reasonable allocation of weights complicated. An unreasonable weight allocation may lead to the scheduling results deviating from the actual needs. For instance, a steel plant once experienced a situation where the downstream process was waiting for materials for an average of 2 hours per day due to weight deviation. The traditional weighted method for multi-objective problems often only outputs a single solution that is optimal for the overall weighted objective, leading to a limited range of output solutions. This single-solution output mode greatly restricts the flexibility and diversity of scheduling. If the solution performs poorly in practical applications, planners need to spend time and effort making manual adjustments or have to rebuild and solve the model again, which undoubtedly reduces the efficiency of scheduling work significantly. For example, if the solution does not conform to the real-time state of the equipment (such as sudden wear of the rolls), planners need to remodel, which takes more than 2 hours. The reliance on general-purpose solvers (such as Gurobi, CPLEX, etc.) results in low efficiency and high cost. Existing scheduling technologies still heavily rely on general-purpose solvers. Although these solvers are powerful, they are not specifically optimized for the characteristics of scheduling problems. Therefore, the solution process is often time-consuming and inefficient. Scheduling 500+ workpieces takes more than 2 hours, which cannot meet the real-time requirement of generating adjustment solutions within half an hour in the cold rolling workshop. Summary of the Invention

[0004] The purpose of this invention is to provide an intelligent scheduling multi-objective optimization method based on the pulse propagation algorithm to solve the problems raised in the prior art.

[0005] To achieve the above objectives, the present invention provides the following technical solution: an intelligent scheduling multi-objective optimization method based on pulse propagation algorithm, the method comprising the following steps:

[0006] S01: Scheduling data preparation stage, used to make pre-decision for the resources that can be scheduled in the collection pool and generate data for the input model; the collection pool refers to the set of workpieces that have the conditions for production scheduling; the pre-decision includes: assigning material matching degree parameters to the workpieces, deciding on production batches, and pre-processing workpieces of the same specification.

[0007] S02: In the multi-objective model establishment stage, mathematical modeling is used to characterize the production scheduling rules and optimization objectives; the optimization objectives include maximizing the material supply matching degree, minimizing the inlet thickness fluctuation, and minimizing the order thickness fluctuation; the production scheduling rules include specification transition constraints, specific workpiece sequential constraints, and rolling period upper limit constraints, etc.

[0008] S03: Pulse propagation algorithm stage, the multi-objective model is solved by designing a method based on ε-constraints and pulse propagation algorithm; the ε-constraints specifically involve introducing parameters. and Minimizing inlet thickness fluctuation and minimizing order thickness fluctuation are transformed into constraints. Maximizing the material supply matching degree is transformed into a single-objective model that minimizes the negative value of the material supply matching degree. This single-objective model is then solved using the pulse propagation algorithm. Where: parameters This is the upper limit for inlet thickness fluctuation; parameter This is the upper limit for fluctuations in order thickness.

[0009] Furthermore, in step S01: for the resources available for scheduling in the collection pool, a pre-decision is made and data for the input model is generated, thereby preparing scheduling data; the scheduling data preparation process includes the following steps:

[0010] S101. Assign material supply matching degree parameters to workpieces; by constructing a scoring system for workpiece material supply matching degree, assign material supply matching degree parameters to each workpiece; the scoring system is divided into two items: basic score and correction score; the basic score is assigned different scores according to the priority of the subsequent process supply corresponding to the workpiece; the higher the score, the higher the material supply demand of the subsequent process corresponding to the workpiece; the correction score is adjusted according to special workpieces and special situations; for example, urgent workpieces and workpieces that must be scheduled are given greater correction weight.

[0011] The base score is assigned based on the priority of the subsequent process supplying the workpiece. For example, a workpiece whose subsequent process is 'automotive sheet stamping' (delivery time ≤ 3 days) is assigned 80-100 points, and a workpiece whose subsequent process is 'ordinary civil sheet' (delivery time ≥ 7 days) is assigned 40-60 points. The correction score is adjusted based on 'urgency level and must-order attribute': urgent orders (must be delivered within 48 hours) add 20-30 points, must-order workpieces (subsequent processes have run out of materials) add 30-50 points, and no points are added in the absence of special circumstances.

[0012] S102. Decision on production batches and corresponding workpieces; determine the next production batch based on the production line status, and select the workpieces that can be included in each batch; calculate the sum of the material matching degrees of the workpieces in each batch based on the material matching degree of each workpiece determined in step S101; select the batch with the largest sum of material matching degrees as the next batch to be arranged, and the workpieces in this batch are the selected workpieces to be arranged.

[0013] S103. Preprocessing of workpieces of the same specification: Since the objective includes minimizing the total specification fluctuation value, it is generally desirable for workpieces of the same specification to form a local "small batch" for production, thereby reducing specification fluctuation; In order to reduce the problem size, it is necessary to identify workpieces of the same specification; The specifications of the workpieces are detected and identified. For workpieces of the same specification, only at most N pieces are retained, where N is a configurable parameter, and the remaining workpieces are deleted from the workpieces to be scheduled; After the subsequent algorithm steps form a plan, the deleted workpieces of the same specification are inserted into feasible positions while ensuring that all constraints are met.

[0014] The scheduling object is the workpiece. Each workpiece has multiple known attributes, such as: inlet thickness, order thickness, material supply matching degree, weight in tons, etc. Multiple workpieces that meet the production and manufacturing conditions form a collection pool to be scheduled.

[0015] A receiving pool refers to a collection of workpieces that meet the conditions for production scheduling. The workpieces in the receiving pool must meet the following conditions: 1. The previous process (such as hot rolling and leveling) has been completed and the quality inspection is qualified; 2. The workpieces have the process parameters required for rolling (such as material, width, and initial hardness); 3. The workpieces have been entered into the production system and the subsequent process has confirmed the material supply requirements to avoid the situation where there is no receiving process after production scheduling.

[0016] The entry thickness is the material thickness of the workpiece before production rolling (the workpiece thickness may change during the production rolling process).

[0017] The order thickness refers to the material thickness when the workpiece is manufactured into a finished product.

[0018] The same type of workpiece refers to workpieces with the same "entrance width, entrance thickness, order thickness, and steel grade". The core purpose of identifying workpieces of the same specification is to reduce specification transition fluctuations: when workpieces of the same specification are connected, the rolling mill does not need to adjust parameters such as roll gap and pressure, which can reduce equipment adjustment time (a single adjustment takes 5-8 minutes) and avoid thickness deviations during the adjustment process (the fluctuation value can be reduced by more than 60%).

[0019] Even if the workpiece meets the core specifications of "the same entry thickness, order thickness, and material grade", there are still differences. These differences are important bases for scheduling decisions (such as material supply priority and insertion timing). These differences include material supply matching parameters, urgency and delivery requirements, completion time and status of the previous process, and receiving capacity of the subsequent process.

[0020] Regarding the statement "for workpieces of the same specification, only retain a maximum of N pieces," N pieces are dynamically configured and adjustable. This is mainly because some workpieces can be connected to other workpieces in any position. For these more "versatile" workpieces, N pieces can be reserved during production scheduling to be added to production later. Not all workpieces need to be scheduled at the current time; they can be scheduled according to a certain quantity or time interval. Therefore, it is not necessary to insert deleted but retained workpieces of the same specification into a certain position in the current scheduling. The reason for retaining a maximum of N workpieces is to control the initial problem size: if there are more than 10 workpieces of the same specification in the pool, the number of path combinations in the scheduling will increase exponentially (e.g., the number of combinations for 15 workpieces exceeds 10). 8 This causes the algorithm to take twice as long; keeping N pieces (usually set to 2-5 pieces, which can be dynamically adjusted according to the total number of pieces) can reduce the initial number of combinations by more than 50%. At the same time, when the temporarily stored pieces are inserted later, they can be directly connected because they are consistent with the specifications of the already arranged pieces, without affecting the overall fluctuation constraints and material supply matching degree.

[0021] Furthermore, in step S02: mathematical modeling is used to characterize the production scheduling rules and optimization objectives for establishing a multi-objective model; the process of establishing the multi-objective model includes the following steps:

[0022] S201: Establish a mathematical model to represent maximizing the material supply matching degree, minimizing the inlet thickness fluctuation, and minimizing the order thickness fluctuation; and characterize the constraints and objective function; the mathematical model is as follows:

[0023] ;

[0024] ;

[0025] ;

[0026] in, This indicates maximizing the matching degree of material supply. This indicates minimizing inlet thickness fluctuation. This represents minimizing order thickness fluctuation; I represents the set of all candidate workpieces, I={0,1,…,n}, where 0 is the starting point and n is the ending point; c i Indicates the material feeding matching degree of workpiece i; y i Indicates whether workpiece i is used; This refers to the workpiece that follows workpiece i and meets all specification transition requirements; r i,j This indicates the inlet thickness fluctuation at the junction of workpieces i and j; t i,j This indicates the order thickness fluctuation at the junction of workpiece i and workpiece j;

[0027] The optimization objectives are 'maximizing material supply matching, minimizing inlet thickness fluctuation, and minimizing order thickness fluctuation', based on the following:

[0028] Material supply matching degree is directly related to the connection between subsequent processes and the availability of materials for the current process: if the material supply matching degree is low (such as the urgent workpieces for the subsequent automotive sheet stamping process not being scheduled for production), it will lead to the subsequent processes waiting for materials;

[0029] Fluctuations in entry thickness affect the stability of rolling mill processing: when the fluctuation exceeds 0.5mm, the rolling mill is prone to 'bouncing', resulting in local thickness deviations in the workpiece and an increase in scrap rate of 3%-5%.

[0030] Fluctuations in order thickness affect finished product pass rate: The order thickness is the final thickness required by the customer. A fluctuation of more than 0.1mm will cause the product to fail to meet the order requirements, and the rework rate will exceed 10%.

[0031] The constraints are as follows: constraint groups A1, A2 and A3 are specification transition constraints, used to ensure that the sorted workpieces can be welded to adjacent workpieces; constraint A4 is a specific workpiece sequential constraint; constraint A5 is a rolling period upper limit constraint.

[0032] A1: Each selected workpiece has one and only one predecessor and one successor;

[0033] (1) For any workpiece i in the candidate set I, it cannot be adjacent to any workpiece j in the set of workpieces that cannot be arranged before workpiece i and satisfy the specification transition constraint. That is, the sum of whether workpiece j and workpiece i are adjacent in production is 0.

[0034] ;

[0035] in, This indicates that a workpiece that can be placed before workpiece i must satisfy all specification transition constraints with workpiece i. This represents the set of workpieces removed from the entire set of selectable workpieces I that can be ranked before workpiece i and satisfy all specification transitions; that is, the set of workpieces ranked before workpiece i that cannot satisfy the specification transition constraints with workpiece i. j,i Indicates whether workpiece i is scheduled for production immediately following workpiece j, with a value of 1 or 0. j,i =1 indicates that workpiece i is immediately following workpiece j, x j,i =0 indicates that workpiece i is not immediately after workpiece j;

[0036] (2) For any workpiece i in the candidate set I, it cannot be adjacent to any workpiece j in the set of workpieces that cannot be arranged after workpiece i and satisfy the specification transition constraint. That is, the sum of whether workpiece i and workpiece j are adjacent in production is 0.

[0037] ;

[0038] in, This indicates a workpiece that can be placed after workpiece i, and that satisfies all specification transition constraints with workpiece i. This represents the set of workpieces removed from the entire set of candidate workpieces I that can be placed after workpiece i and satisfy all specification transitions; that is, the set of workpieces placed after workpiece i that cannot satisfy the specification transition constraints with workpiece i; x i,j Indicates whether workpiece j is scheduled for production immediately following workpiece i, with a value of 1 or 0. i,j =1 indicates that workpiece j is immediately following workpiece i, x i,j =0 indicates that workpiece j is not immediately following workpiece i;

[0039] (3) For any workpiece i starting from the first position, if workpiece i is included, then workpiece i can only be adjacent to one of the workpieces j that can be included in the production of workpiece i, that is, the left and right sides of the equal sign are both 1; if workpiece i is not included, then workpiece i cannot be adjacent to any of the workpieces j that can be included in the production of workpiece i, that is, the left and right sides of the equal sign are both 0.

[0040] ;

[0041] in, This indicates a workpiece that can be placed before workpiece i, satisfying all specification transition constraints with workpiece i. i Indicates whether workpiece i is used, y i =1 indicates that workpiece i is discharged, y i =0 means that workpiece i is not included, and I\{0} means that the set of workpieces after the first position 0 is removed from the set of all available workpieces.

[0042] (4) For any workpiece i, if workpiece i is included, then workpiece i can only be adjacent to one of the workpieces j that can be included after workpiece i, that is, the left and right sides of the equal sign are both 1; if workpiece i is not included, then workpiece i cannot be adjacent to any of the workpieces j that can be included after workpiece i, that is, the left and right sides of the equal sign are both 0.

[0043] ;

[0044] in, This indicates a workpiece that can be placed after workpiece i, satisfying all specification transition constraints with workpiece i. i Indicates whether workpiece i is used, y i =1 indicates that workpiece i is discharged, y i =0 indicates that workpiece i is not included;

[0045] A2: The conditions for using the first and last items are:

[0046] ;

[0047] Workpiece 0 at the starting position and workpiece n at the ending position must be loaded. This indicates that the last workpiece already placed in the production line must be placed in the next production line. This indicates the point from the end of the current production schedule to a specific virtual workpiece n.

[0048] Starting point 0 is not a "virtual empty node," but rather the final workpiece of the previous batch of production. Forcing selection of 0 ensures seamless connection between the current production schedule and the preceding production, avoiding interruptions in the rolling process (e.g., the rolling mill does not need to readjust the roll gap and pressure due to "no starting workpiece," reducing equipment downtime).

[0049] The endpoint n is the "virtual endpoint workpiece" of the current batch. Its core function is to "define the production boundary of the current batch" to form a production closed loop: after the current batch ends at n, the next batch can use n as the new "starting point 0" to realize the continuous production cycle.

[0050] A3: The condition for eliminating sub-loop constraints is:

[0051] ;

[0052] Among them, u i and u j As an auxiliary variable, it represents the sequence number of workpiece i and workpiece j after they are placed in the production process, ensuring that when workpiece i and workpiece j are arranged adjacently, the sequence number of workpiece j and workpiece i does not decrease.

[0053] A4: Set specific workpiece order constraints. If placing j before i would affect production quality, then place j after i.

[0054] ;

[0055] in Let represent the set of workpieces that affect the quality of workpiece i before and after workpiece i. The formula means that for any workpiece i, any workpiece j that affects the quality of workpiece i before workpiece i must have a higher sequence number than workpiece i.

[0056] A5: Rolling period upper limit constraint:

[0057] ;

[0058] Among them, w i W represents the tonnage of workpiece i; W represents the upper limit constraint of the rolling period; for all workpiece i included in this roll, the sum of their weight in tons shall not exceed the upper limit of the rolling period W.

[0059] The upper limit constraint W for the roll life is set based on the wear cycle of core equipment such as rolls. Taking a four-high rolling mill in a cold rolling workshop as an example, the surface hardness of the rolls decreases as the rolling weight increases. When the total weight of a single production run exceeds the upper limit (e.g., 10 tons), the roll wear will exceed 0.02mm, resulting in a thickness deviation of subsequent workpieces exceeding ±0.01mm (exceeding the requirements of national standard GB / T 708-2019). In addition, exceeding the upper limit will shorten the roll replacement cycle (from the original 3 days to 1 day), increasing equipment maintenance costs. Therefore, setting the upper limit W for the roll life is a key constraint for balancing production efficiency with equipment life and product accuracy.

[0060] A6: Set constraints on the range of variable values: Let represent the natural number from 0 to n corresponding to any workpiece i.

[0061] Furthermore, step S03 includes the following steps:

[0062] S301: Perform ε-constraint-based multi-objective model transformation;

[0063] S302: Establish the solution model M(ε) based on the pulse propagation algorithm;

[0064] S303: Implementation of the bounding phase algorithm flow;

[0065] S304: Implementation flow of the pulse phase algorithm;

[0066] S305: Set the acceleration strategy for the pulse propagation algorithm.

[0067] Furthermore, in step S301: the above multi-objective model is a multi-objective optimization model, and parameters are introduced into the multi-objective optimization model. and Transform the second and third objectives into ε-constraints:

[0068] ;

[0069] ;

[0070] Setting parameters and parameters Let the value sets be V1 and V2, and let Simultaneously, the first objective is transformed into a minimization problem, for any Establish the following single-objective model with ε-constraints, denoted as model M(ε):

[0071] : ;

[0072] in This represents a negative value that minimizes the material supply matching degree.

[0073] The first objective is to "maximize the material supply matching degree"; the second objective is to "minimize the inlet thickness fluctuation"; and the third objective is to "minimize the order thickness fluctuation". These three objectives correspond to the core optimization directions of the multi-objective model specified in claim 3. The transformation from a multi-objective problem to a single-objective problem is achieved through ε-constraint transformation, so that it can be solved by the pulse propagation algorithm.

[0074] Furthermore, in step S302: firstly, M(ε) is transformed into a network flow problem, and then a pulse propagation algorithm is designed to solve the network flow problem. Finally, the overall algorithm flow is obtained.

[0075] The model M(ε) is reconstructed as a network flow problem; the workpiece is regarded as a node in the network graph, and the connection relationship of the workpiece is described as an arc segment; a network graph G(N, E) is established, where N is the set of nodes satisfying N=I, and E is the set of arc segments; any arc segment (i, j)∈E has three key properties: first, the thickness fluctuation r of the entrance corresponding to the connection. i,j Secondly, the corresponding order thickness fluctuation t i,j Thirdly, the distance d traversed by the connection. i,j The d i,j The value is -c j Both the entry thickness fluctuation and the order thickness fluctuation are considered as resource consumption through the arc segment. Based on this, the problem is transformed into finding the shortest path from the starting point 0 to the ending point n in the network, satisfying that the resource consumption does not exceed ε, and requiring that each node in the path is visited at most once. The problem is thus transformed into the Elementary Shortest Path Problem with Resource Constraints (ESPPRC). In addition, the order constraint of specific workpieces is an additional constraint that needs to be considered in ESPPRC.

[0076] Then, the pulse propagation algorithm is designed. In order to efficiently solve ESPPRC and adapt to the fast solution requirements under different parameter ε settings, the pulse propagation algorithm is introduced. The pulse propagation algorithm consists of two core stages: the bounding stage and the pulse stage.

[0077] The boundary phase is used to determine the shortest distance from each node to the endpoint under different resource consumption conditions; the different resource consumption conditions refer to two types of resource consumption: inlet thickness fluctuation and order thickness fluctuation, which are introduced by parameters. and parameters Subsequent constraints;

[0078] The pulse phase is based on an implicit enumeration strategy of the solution space, that is, invalid paths are eliminated in advance by mathematical rules to avoid explicitly traversing all possible path sets and exploring potential subspaces. A pulse signal is emitted from the starting node 0∈I and propagates along the arcs in the network to explore all paths. At each node, the pulse signal records partial path information p, the accumulated distance d(p), and the amount of resources consumed r(p). In order to optimize the search efficiency, a pruning strategy is adopted to limit the further propagation of the pulse and reduce the search space. Whenever the pulse successfully reaches the final node, it can carry a complete and feasible path information from the starting point to the end point.

[0079] Finally, obtain the overall algorithm flow; parameters in the algorithm input. From the largest Value and maximum Value composition, i.e. Boundary step size ,in and These are the bounding step sizes for the inlet thickness and the order thickness in the pulse algorithm, respectively. , The overall algorithm flow is explained in detail below:

[0080] The first line is responsible for initialization, including setting the initial state of partial paths, cumulative distance, resource consumption, and the optimal path set;

[0081] The second line performs the bounding process, calculating and determining the lower bound of the shortest distance for each node in the network;

[0082] Lines 3 through 5 generate the resulting path; iterate through V, and for each ε, call the recursive function pulse, storing the optimal path generated each time into set P;

[0083] Line 6 returns the set of optimal paths P found during the recursive search.

[0084] Furthermore, in step S303: in the bounding phase algorithm flow, let This represents the length of the shortest path that satisfies the resource constraints found during the bounding process, and... As an upper bound in the iterative process, the bounding process can find the shortest distance to the destination for each node i∈I under the condition of resource consumption r. When a path p reaches node i, if the following conditions are met... If the node i ∈ I is not found in the bounding phase, then pruning is performed and propagation is stopped. The working principle of the bounding phase is as follows: for each node i ∈ I, given the resource consumption... Solving ESPPRC under the following conditions; initial settings Since both resources have been exhausted, leaving 0 resource units available, there are few feasible solutions. Therefore, the impulse process can quickly find the optimal solution; each optimal solution found is based on a given resource consumption. Below, find the lower bound of the minimum distance achievable by any partial path to node n∈I; after finding the bound, for each node i∈I, given the resource consumption... Solve an ESPPRC under the following circumstances; the current problem has few constraints, but the resource consumption is... The lower bound of the path distance has been obtained; using the previously calculated information, continue repeating the same process in reverse order; this process will produce a lower bound matrix, denoted as... This includes the lower bound computed for each node i∈I at each discrete bounding step size between 0 and ε. , Similarly, as available resources increase, the bounding scheme addresses problems with fewer constraints that are more difficult to solve, but the number of known bounds also increases, thus increasing the opportunity to use the bounding pruning strategy to prune parts of the path; in the specific implementation of Algorithm 2:

[0085] The first line is responsible for initializing the resource consumption value;

[0086] Lines 2 through 6 initiate the bounding scheme, traversing each node for every possible resource consumption;

[0087] Lines 7 and 8 use the pulse algorithm to solve an ESPPRC problem for each node given the current resource consumption.

[0088] Lines 9 through 13 store the optimal solution for each node, i.e., the lower bound of the shortest path length, in the corresponding position of the lower bound matrix; if a particular problem is infeasible under a given resource consumption, the lower bound is set to positive infinity.

[0089] Furthermore, in step S304: the recursive process pulse in the pulse phase algorithm flow targets the set of head nodes for each outgoing arc starting from a given node i. The operation involves implementing a pruning strategy. First, infeasibility and bounding checks are performed. Infeasibility pruning ensures path uniqueness (each node is visited at most once) and correctness (avoiding production quality issues caused by incorrect node order). Then, it determines whether to prune incoming pulses. If a pulse is not pruned, the current node is added to the partially constructed path. Next, the algorithm iterates through all outgoing arc nodes of the current node and recursively calls the `pulse` process for each node to propagate the pulse. When the `pulse` process is called at the final node, it updates the known optimal path information as needed and stops further pulse propagation. Afterward, the algorithm recursively continues propagating other potential pulses through a backtracking mechanism.

[0090] Furthermore, in step S305: the pulse propagation algorithm acceleration strategy is used to combine the characteristics of the scheduling problem and propose two strategies to accelerate the pulse algorithm: storing the optimal path in the bounding stage and improving the optimal path through the insertion algorithm.

[0091] The boundary phase stores the optimal path, thereby improving search efficiency by storing the optimal path in A. For workpieces i and j, if workpiece j can be both ranked before and after i, then workpiece j is called a neighbor of workpiece i. In the boundary phase, starting from node i, given a resource consumption of... Under the given conditions, when solving ESPPRC, nodes that simultaneously satisfy the following two conditions are excluded from the search path: a. They are adjacent to workpiece i; b. Their entrance width is greater than that of workpiece i. The optimal path obtained is denoted as... Save it to A, that is During the pulse process, for path p to reach node i, and given the resource consumption is... When, determine p and If the sets of nodes do not intersect, then directly connect path p and path... The concatenation is performed to return the optimal path; if it exists, the terminated path p is propagated to node i.

[0092] The insertion algorithm improves the optimal path by refining the already searched partial paths and checking for possible insertion points and nodes like B′ that can further reduce the target value. During the pulse search, a depth-first traversal is used to explore the path. Each time the endpoint is reached, a partial path is obtained. Consider a specific scenario: traversing along the red line yields a partial path {A, B, C}. However, in practice, it might be possible to insert a new node B′ into the existing path to optimize it. B′ represents the new node inserted into the existing path. For example, node B′ can be reasonably inserted between B and C, forming a potentially better path {A, B, B′, C}.

[0093] Compared with the prior art, the beneficial effects of the present invention are:

[0094] The introduction of this invention greatly reduces the workload of planners; batch decision-making and specific scheduling details can be fully automated by the embedded advanced model and intelligent algorithm. This intelligent decision-making mechanism not only improves work efficiency but also ensures the accuracy and rationality of production scheduling plans. The core of this invention lies in constructing a multi-objective optimization model and cleverly transforming the constraints of specification fluctuation type into ε-constraints. By adjusting different ε values, the model can automatically generate a variety of feasible decision-making schemes. The algorithm automatically traverses multiple preset ε value ranges, providing decision-makers with a rich variety of scheduling strategy choices, thereby meeting the needs of different scenarios and enhancing the flexibility and adaptability of decision-making. At the algorithm implementation level, this invention innovatively introduces the pulse propagation algorithm, which can be divided into two steps: a bounding stage and a pulse stage, with the algorithm's time consumption concentrated in the bounding stage. It is worth noting that the bounding matrix generated in the bounding stage has high reusability, and the bounding stage does not need to be executed repeatedly under different ε value conditions. This characteristic greatly reduces the workload of repeated calculations, effectively shortens the overall running time of the algorithm, and achieves a significant improvement in computational efficiency. Attached Figure Description

[0095] Figure 1 This is a schematic diagram of the overall process of an intelligent scheduling multi-objective optimization method based on the pulse propagation algorithm of the present invention;

[0096] Figure 2 This is a schematic diagram of the overall algorithm flow of the intelligent scheduling multi-objective optimization method based on the pulse propagation algorithm of the present invention;

[0097] Figure 3 This is a schematic diagram of the bounding process of an intelligent scheduling multi-objective optimization method based on the pulse propagation algorithm of the present invention;

[0098] Figure 4 This is a schematic diagram of the pulse process in the intelligent scheduling multi-objective optimization method based on the pulse propagation algorithm of the present invention;

[0099] Figure 5 This is a schematic diagram illustrating the improved path generation method of the depth-first search in the intelligent scheduling multi-objective optimization method based on the pulse propagation algorithm of the present invention.

[0100] Figure 6 This is a schematic diagram of the insertion algorithm of the intelligent scheduling multi-objective optimization method based on the pulse propagation algorithm of the present invention. Detailed Implementation

[0101] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0102] Example: This invention provides a technical solution, an intelligent scheduling multi-objective optimization method based on the pulse propagation algorithm, such as... Figure 1 As shown, the method includes the following steps:

[0103] S01: Scheduling data preparation stage, used to make pre-decision decisions on the available resources in the receiving pool and generate data for the input model; the receiving pool refers to the set of workpieces that meet the conditions for production scheduling; the pre-decision includes: assigning material matching parameters to workpieces, deciding on production batches, and pre-processing workpieces of the same specifications.

[0104] S02: In the multi-objective model establishment stage, mathematical modeling is used to characterize the production scheduling rules and optimization objectives; the optimization objectives include maximizing the material supply matching degree, minimizing the inlet thickness fluctuation, and minimizing the order thickness fluctuation; the production scheduling rules include specification transition constraints, specific workpiece sequential constraints, and rolling period upper limit constraints, etc.

[0105] S03: Pulse propagation algorithm stage, the multi-objective model is solved by designing a method based on ε-constraints and pulse propagation algorithm; the ε-constraints specifically involve introducing parameters. and Minimizing inlet thickness fluctuation and minimizing order thickness fluctuation are transformed into constraints. Maximizing the material supply matching degree is transformed into a single-objective model that minimizes the negative value of the material supply matching degree. This single-objective model is then solved using the pulse propagation algorithm. Where: parameters This is the upper limit for inlet thickness fluctuation; parameter This is the upper limit for fluctuations in order thickness.

[0106] In step S01: For the resources in the collection pool that can be scheduled, a preliminary decision is made and data for input to the model is generated, thereby preparing scheduling data; the scheduling data preparation process includes the following steps:

[0107] S101. Assign material supply matching parameters to workpieces; by constructing a scoring system for workpiece material supply matching, assign material supply matching parameters to each workpiece; the scoring system is divided into two parts: basic score and correction score; the basic score is assigned different values ​​according to the priority of the subsequent process supplying the workpiece, with higher scores reflecting higher material supply requirements of the subsequent process corresponding to the workpiece; the correction score is adjusted based on special workpieces and special circumstances; for example, urgent workpieces and workpieces that must be scheduled are given greater correction weight.

[0108] The base score is assigned based on the priority of the subsequent process supplying the workpiece. For example, a workpiece whose subsequent process is 'automotive sheet stamping' (delivery time ≤ 3 days) is assigned 80-100 points, and a workpiece whose subsequent process is 'ordinary civilian sheet metal' (delivery time ≥ 7 days) is assigned 40-60 points. The correction score is adjusted based on 'urgency level and must-order attribute': urgent orders (must be delivered within 48 hours) add 20-30 points, must-order workpieces (subsequent processes have run out of materials) add 30-50 points, and no points are added unless there are special circumstances.

[0109] S102. Decision on production batches and corresponding workpieces; determine the next production batch based on the production line status, and select the workpieces that can be included in each batch; calculate the sum of the material matching degrees of the workpieces in each batch based on the material matching degree of each workpiece determined in step S101; select the batch with the largest sum of material matching degrees as the next batch to be arranged, and the workpieces in this batch are the selected workpieces to be arranged.

[0110] S103. Preprocessing of workpieces of the same specification: Since the objective includes minimizing the total specification fluctuation value, it is generally desirable for workpieces of the same specification to form a local "small batch" for production, thereby reducing specification fluctuation; In order to reduce the problem size, it is necessary to identify workpieces of the same specification; The specifications of the workpieces are detected and identified. For workpieces of the same specification, only at most N pieces are retained, where N is a configurable parameter, and the remaining workpieces are deleted from the workpieces to be scheduled; After the subsequent algorithm steps form a plan, the deleted workpieces of the same specification are inserted into feasible positions while ensuring that all constraints are met.

[0111] The scheduling object is the workpiece. Each workpiece has multiple known attributes, such as: inlet thickness, order thickness, material supply matching degree, weight in tons, etc. Multiple workpieces that meet the production and manufacturing conditions form a collection pool to be scheduled.

[0112] A receiving pool refers to a collection of workpieces that meet the conditions for production scheduling. The workpieces in the receiving pool must meet the following conditions: 1. The previous process (such as hot rolling and leveling) has been completed and the quality inspection is qualified; 2. The workpieces have the process parameters required for rolling (such as material, width, and initial hardness); 3. The workpieces have been entered into the production system and the subsequent process has confirmed the material supply requirements to avoid the situation where there is no receiving process after production scheduling.

[0113] The entry thickness is the material thickness of the workpiece before production rolling (the workpiece thickness may change during the production rolling process).

[0114] The order thickness refers to the material thickness when the workpiece is manufactured into a finished product.

[0115] The same type of workpiece refers to workpieces with the same "entrance width, entrance thickness, order thickness, and steel grade". The core purpose of identifying workpieces of the same specification is to reduce specification transition fluctuations: when workpieces of the same specification are connected, the rolling mill does not need to adjust parameters such as roll gap and pressure, which can reduce equipment adjustment time (a single adjustment takes 5-8 minutes) and avoid thickness deviations during the adjustment process (the fluctuation value can be reduced by more than 60%).

[0116] Even if the workpiece meets the core specifications of "the same entry thickness, order thickness, and material grade", there are still differences. These differences are important bases for scheduling decisions (such as material supply priority and insertion timing). These differences include material supply matching parameters, urgency and delivery requirements, completion time and status of the previous process, and receiving capacity of the subsequent process.

[0117] Regarding the statement "for workpieces of the same specification, only retain a maximum of N pieces," N pieces are dynamically configured and adjustable. This is mainly because some workpieces can be connected to other workpieces in any position. For these more "versatile" workpieces, N pieces can be reserved during production scheduling to be added to production later. Not all workpieces need to be scheduled at the current time; they can be scheduled according to a certain quantity or time interval. Therefore, it is not necessary to insert deleted but retained workpieces of the same specification into a certain position in the current scheduling. The reason for retaining a maximum of N workpieces is to control the initial problem size: if there are more than 10 workpieces of the same specification in the pool, the number of path combinations in the scheduling will increase exponentially (e.g., the number of combinations for 15 workpieces exceeds 10). 8 This causes the algorithm to take twice as long; keeping N pieces (usually set to 2-5 pieces, which can be dynamically adjusted according to the total number of pieces) can reduce the initial number of combinations by more than 50%. At the same time, when the temporarily stored pieces are inserted later, they can be directly connected because they are consistent with the specifications of the already arranged pieces, without affecting the overall fluctuation constraints and material supply matching degree.

[0118] In step S02: Mathematical modeling is used to characterize the scheduling rules and optimization objectives for establishing a multi-objective model; the process of establishing the multi-objective model includes the following steps:

[0119] S201: Establish mathematical models to represent maximizing the material supply matching degree, minimizing the inlet thickness fluctuation, and minimizing the order thickness fluctuation; and characterize the constraints and objective functions; the mathematical model is as follows:

[0120] ;

[0121] ;

[0122] ;

[0123] in, This indicates maximizing the matching degree of material supply. This indicates minimizing inlet thickness fluctuation. This represents minimizing order thickness fluctuation; I represents the set of all candidate workpieces, I={0,1,…,n}, where 0 is the starting point and n is the ending point; c i Indicates the material feeding matching degree of workpiece i; y i Indicates whether workpiece i is used; This refers to the workpiece that follows workpiece i and meets all specification transition requirements; r i,j This indicates the inlet thickness fluctuation at the junction of workpieces i and j; t i,j This indicates the order thickness fluctuation at the junction of workpiece i and workpiece j;

[0124] The optimization objectives are 'maximizing material supply matching, minimizing inlet thickness fluctuation, and minimizing order thickness fluctuation', based on the following:

[0125] Material supply matching degree is directly related to the connection between subsequent processes and the availability of materials for the current process: if the material supply matching degree is low (such as the urgent workpieces for the subsequent automotive sheet stamping process not being scheduled for production), it will lead to the subsequent processes waiting for materials;

[0126] Fluctuations in entry thickness affect the stability of rolling mill processing: when the fluctuation exceeds 0.5mm, the rolling mill is prone to 'bouncing', resulting in local thickness deviations in the workpiece and an increase in scrap rate of 3%-5%.

[0127] Fluctuations in order thickness affect finished product pass rate: The order thickness is the final thickness required by the customer. A fluctuation of more than 0.1mm will cause the product to fail to meet the order requirements, and the rework rate will exceed 10%.

[0128] The constraints are as follows, where constraint groups A1, A2 and A3 are specification transition constraints, used to ensure that the sorted workpieces can be welded to adjacent workpieces; constraint A4 is a specific workpiece sequential constraint; constraint A5 is a rolling period upper limit constraint.

[0129] A1: Each selected workpiece has one and only one predecessor and one successor;

[0130] (1) For any workpiece i in the candidate set I, it cannot be adjacent to any workpiece j in the set of workpieces that cannot be arranged before workpiece i and satisfy the specification transition constraint. That is, the sum of whether workpiece j and workpiece i are adjacent in production is 0.

[0131] ;

[0132] in, This indicates that a workpiece that can be placed before workpiece i must satisfy all specification transition constraints with workpiece i. This represents the set of workpieces removed from the entire set of selectable workpieces I that can be ranked before workpiece i and satisfy all specification transitions; that is, the set of workpieces ranked before workpiece i that cannot satisfy the specification transition constraints with workpiece i. j,i Indicates whether workpiece i is scheduled for production immediately following workpiece j, with a value of 1 or 0. j,i =1 indicates that workpiece i is immediately following workpiece j, x j,i =0 indicates that workpiece i is not immediately after workpiece j;

[0133] (2) For any workpiece i in the candidate set I, it cannot be adjacent to any workpiece j in the set of workpieces that cannot be arranged after workpiece i and satisfy the specification transition constraint. That is, the sum of whether workpiece i and workpiece j are adjacent in production is 0.

[0134] ;

[0135] in, This indicates a workpiece that can be placed after workpiece i, and that satisfies all specification transition constraints with workpiece i. This represents the set of workpieces removed from the entire set of candidate workpieces I that can be placed after workpiece i and satisfy all specification transitions; that is, the set of workpieces placed after workpiece i that cannot satisfy the specification transition constraints with workpiece i; x i,j Indicates whether workpiece j is scheduled for production immediately following workpiece i, with a value of 1 or 0. i,j =1 indicates that workpiece j is immediately following workpiece i, x i,j =0 indicates that workpiece j is not immediately following workpiece i;

[0136] (3) For any workpiece i starting from the first position, if workpiece i is included, then workpiece i can only be adjacent to one of the workpieces j that can be included in the production of workpiece i, that is, the left and right sides of the equal sign are both 1; if workpiece i is not included, then workpiece i cannot be adjacent to any of the workpieces j that can be included in the production of workpiece i, that is, the left and right sides of the equal sign are both 0.

[0137] ;

[0138] in, This indicates a workpiece that can be placed before workpiece i, satisfying all specification transition constraints with workpiece i. i Indicates whether workpiece i is used, y i =1 indicates that workpiece i is discharged, y i =0 means that workpiece i is not included, and I\{0} means that the set of workpieces after the first position 0 is removed from the set of all available workpieces.

[0139] (4) For any workpiece i, if workpiece i is included, then workpiece i can only be adjacent to one of the workpieces j that can be included after workpiece i, that is, the left and right sides of the equal sign are both 1; if workpiece i is not included, then workpiece i cannot be adjacent to any of the workpieces j that can be included after workpiece i, that is, the left and right sides of the equal sign are both 0.

[0140] ;

[0141] in, This indicates a workpiece that can be placed after workpiece i, satisfying all specification transition constraints with workpiece i. i Indicates whether workpiece i is used, y i =1 indicates that workpiece i is discharged, y i =0 indicates that workpiece i is not included;

[0142] A2: The conditions for using the first and last items are:

[0143] ;

[0144] Workpiece 0 at the starting position and workpiece n at the ending position must be loaded. This indicates that the last workpiece already placed in the production line must be placed in the next production line. This indicates the point from the end of the current production schedule to a specific virtual workpiece n.

[0145] Starting point 0 is not a "virtual empty node," but rather the final workpiece of the previous batch of production. Forcing selection of 0 ensures seamless connection between the current production schedule and the preceding production, avoiding interruptions in the rolling process (e.g., the rolling mill does not need to readjust the roll gap and pressure due to "no starting workpiece," reducing equipment downtime).

[0146] The endpoint n is the "virtual endpoint workpiece" of the current batch. Its core function is to "define the production boundary of the current batch" to form a production closed loop: after the current batch ends at n, the next batch can use n as the new "starting point 0" to realize the continuous production cycle.

[0147] A3: The condition for eliminating sub-loop constraints is:

[0148] ;

[0149] Among them, u i and u j As an auxiliary variable, it represents the sequence number of workpiece i and workpiece j after they are placed in the production process, ensuring that when workpiece i and workpiece j are arranged adjacently, the sequence number of workpiece j and workpiece i does not decrease.

[0150] A4: Set specific workpiece order constraints. If placing j before i would affect production quality, then place j after i.

[0151] ;

[0152] in Let represent the set of workpieces that affect the quality of workpiece i before and after workpiece i. The formula means that for any workpiece i, any workpiece j that affects the quality of workpiece i before workpiece i must have a higher sequence number than workpiece i.

[0153] A5: Rolling period upper limit constraint:

[0154] ;

[0155] Among them, w i W represents the tonnage of workpiece i; W represents the upper limit constraint of the rolling period; for all workpiece i included in this roll, the sum of their weight in tons shall not exceed the upper limit of the rolling period W.

[0156] The upper limit constraint W for the roll life is set based on the wear cycle of core equipment such as rolls. Taking a four-high rolling mill in a cold rolling workshop as an example, the surface hardness of the rolls decreases as the rolling weight increases. When the total weight of a single production run exceeds the upper limit (e.g., 10 tons), the roll wear will exceed 0.02mm, resulting in a thickness deviation of subsequent workpieces exceeding ±0.01mm (exceeding the requirements of national standard GB / T 708-2019). In addition, exceeding the upper limit will shorten the roll replacement cycle (from the original 3 days to 1 day), increasing equipment maintenance costs. Therefore, setting the upper limit W for the roll life is a key constraint for balancing production efficiency with equipment life and product accuracy.

[0157] A6: Set constraints on the range of variable values: Let represent the natural number from 0 to n corresponding to any workpiece i.

[0158] Step S03 includes the following steps:

[0159] S301: Perform ε-constraint-based multi-objective model transformation;

[0160] S302: Establish the solution model M(ε) based on the pulse propagation algorithm;

[0161] S303: Implementation of the bounding phase algorithm flow;

[0162] S304: Implementation flow of the pulse phase algorithm;

[0163] S305: Set the acceleration strategy for the pulse propagation algorithm.

[0164] In step S301: The above multi-objective model is a multi-objective optimization model, and parameters are introduced into the multi-objective optimization model. and Transform the second and third objectives into ε-constraints:

[0165] ;

[0166] ;

[0167] Setting parameters and parameters Let the value sets be V1 and V2, and let Simultaneously, the first objective is transformed into a minimization problem, for any Establish the following single-objective model with ε-constraints, denoted as model M(ε):

[0168] : ;

[0169] in This represents a negative value that minimizes the material supply matching degree.

[0170] In step S302: First, M(ε) is transformed into a network flow problem, and a pulse propagation algorithm is designed to solve the network flow problem. Finally, the overall algorithm flow is obtained.

[0171] The model M(ε) is reconstructed as a network flow problem; the workpiece is regarded as a node in the network graph, and the connection relationship of the workpiece is described as an arc segment; a network graph G(N, E) is established, where N is the set of nodes satisfying N=I, and E is the set of arc segments; any arc segment (i, j)∈E has three key properties: first, the thickness fluctuation r of the entrance corresponding to the connection. i,j Secondly, the corresponding order thickness fluctuation t i,j Thirdly, the distance d traversed by the connection. i,j The d i,j The value is -c jBoth the entry thickness fluctuation and the order thickness fluctuation are considered as resource consumption through the arc segment. Based on this, the problem is transformed into finding the shortest path from the starting point 0 to the ending point n in the network, satisfying that the resource consumption does not exceed ε, and requiring that each node in the path is visited at most once. The problem is thus transformed into the Elementary Shortest Path Problem with Resource Constraints (ESPPRC). In addition, the order constraint of specific workpieces is an additional constraint that needs to be considered in ESPPRC.

[0172] Then, the pulse propagation algorithm is designed. In order to efficiently solve ESPPRC and adapt to the fast solution requirements under different parameter ε settings, the pulse propagation algorithm is introduced. The pulse propagation algorithm consists of two core stages: the bounding stage and the pulse stage.

[0173] The boundary phase is used to determine the shortest distance from each node to the endpoint under different resource consumption conditions; the different resource consumption conditions refer to two types of resource consumption: inlet thickness fluctuation and order thickness fluctuation, which are introduced by parameters. and parameters Subsequent constraints;

[0174] The pulse phase is based on an implicit enumeration strategy of the solution space, that is, invalid paths are eliminated in advance by mathematical rules to avoid explicitly traversing all possible path sets and exploring potential subspaces. A pulse signal is emitted from the starting node 0∈I and propagates along the arcs in the network to explore all paths. At each node, the pulse signal records partial path information p, the accumulated distance d(p), and the amount of resources consumed r(p). In order to optimize the search efficiency, a pruning strategy is adopted to limit the further propagation of the pulse and reduce the search space. Whenever the pulse successfully reaches the final node, it can carry a complete and feasible path information from the starting point to the end point.

[0175] Finally, obtain the overall algorithm flow, such as... Figure 2 As shown; parameters in the algorithm input From the largest Value and maximum Value composition, i.e. Boundary step size ,in and These are the bounding step sizes for the inlet thickness and the order thickness in the pulse algorithm, respectively. , The overall algorithm flow is explained in detail below:

[0176] The first line is responsible for initialization, including setting the initial state of partial paths, cumulative distance, resource consumption, and the optimal path set;

[0177] The second line performs the bounding process, calculating and determining the lower bound of the shortest distance for each node in the network (see Algorithm 3 for details).

[0178] Lines 3 through 5 generate the resulting path; iterate through V, and for each ε, call the recursive function pulse, storing the optimal path generated each time into set P;

[0179] Line 6 returns the set of optimal paths P found during the recursive search.

[0180] In step S303: as Figure 3 As shown, in the bounding phase algorithm flow, let This represents the length of the shortest path that satisfies the resource constraints found during the bounding process, and... As an upper bound in the iterative process, the bounding process can find the shortest distance to the destination for each node i∈I under the condition of resource consumption r. When a path p reaches node i, if the following conditions are met... If the node i ∈ I is not found in the bounding phase, then pruning is performed and propagation is stopped. The working principle of the bounding phase is as follows: for each node i ∈ I, given the resource consumption... Solving ESPPRC under the following conditions; initial settings Since both resources have been exhausted, leaving 0 resource units available, there are few feasible solutions. Therefore, the impulse process can quickly find the optimal solution; each optimal solution found is based on a given resource consumption. Below, find the lower bound of the minimum distance achievable by any partial path to node n∈I; after finding the bound, for each node i∈I, given the resource consumption... Solve an ESPPRC under the following circumstances; the current problem has few constraints, but the resource consumption is... The lower bound of the path distance has been obtained; using the previously calculated information, continue repeating the same process in reverse order; this process will produce a lower bound matrix, denoted as... This includes the lower bound computed for each node i∈I at each discrete bounding step size between 0 and ε. , Similarly, as available resources increase, the bounding scheme addresses problems with fewer constraints that are more difficult to solve, but the number of known bounds also increases, thus increasing the opportunity to use the bounding pruning strategy to prune parts of the path; in the specific implementation of Algorithm 2:

[0181] The first line is responsible for initializing the resource consumption value;

[0182] Lines 2 through 6 initiate the bounding scheme, traversing each node for every possible resource consumption;

[0183] Lines 7 and 8 use the pulse algorithm to solve an ESPPRC problem for each node given the current resource consumption.

[0184] Lines 9 through 13 store the optimal solution for each node, i.e., the lower bound of the shortest path length, in the corresponding position of the lower bound matrix; if a particular problem is infeasible under a given resource consumption, the lower bound is set to positive infinity.

[0185] In step S304: as Figure 4 As shown, the recursive process `pulse` in the pulse phase algorithm handles the set of head nodes for each outgoing arc starting from a given node `i`. The operation involves implementing a pruning strategy. First, infeasibility and bounding checks are performed. Infeasibility pruning ensures path uniqueness (each node is visited at most once) and correctness (avoiding production quality issues caused by incorrect node order). Then, it determines whether to prune incoming pulses. If a pulse is not pruned, the current node is added to the partially constructed path. Next, the algorithm iterates through all outgoing arc nodes of the current node and recursively calls the `pulse` process for each node to propagate the pulse. When the `pulse` process is called at the final node, it updates the known optimal path information as needed and stops further pulse propagation. Afterward, the algorithm recursively continues propagating other potential pulses through a backtracking mechanism.

[0186] In step S305: The pulse propagation algorithm acceleration strategy is used to combine the characteristics of the scheduling problem and propose two strategies to accelerate the pulse algorithm: storing the optimal path in the bounding stage and improving the optimal path by inserting the algorithm.

[0187] The bounding phase stores the optimal path, thereby improving search efficiency. For workpieces i and j, if workpiece j can be ranked both before and after i, then workpiece j is called a neighbor of workpiece i. In the bounding phase, starting from node i, given a resource consumption of... Under the given conditions, when solving ESPPRC, nodes that simultaneously satisfy the following two conditions are excluded from the search path: a. They are adjacent to workpiece i; b. Their entrance width is greater than that of workpiece i. The optimal path obtained is denoted as... Save it to A, that is During the pulse process, for path p to reach node i, and given the resource consumption is... When, determine p and If the sets of nodes do not intersect, then directly connect path p and path... The concatenation is performed to return the optimal path; if it exists, the terminated path p is propagated to node i.

[0188] The insertion algorithm improves the optimal path by refining the already searched partial path and checking for possible insertion points and nodes like B′ that can further reduce the target value. During the pulse search, a depth-first traversal is used to explore the path. Each time the endpoint is reached, a partial path is obtained. Consider a specific scenario: traversing along the red line yields a partial path {A, B, C}. However, in practice, it might be possible to insert a new node B′ into the existing path to optimize it. B′ represents the new node inserted into the existing path. For example, node B′ can be reasonably inserted between B and C, forming a potentially better path {A, B, B′, C}, as shown below. Figure 5 As shown, referencing Figure 6 Algorithm 4 in the paper introduces an insertion algorithm to improve the partially searched paths. This insertion algorithm checks whether there are possible insertion points and whether there are nodes such as B′ that can further reduce the target value.

[0189] The following example from a steel company illustrates the specific process of this invention:

[0190] During the scheduling data preparation phase, a steel company's cold rolling workshop has 5 workpieces (numbered 1-5) in its receiving pool that meet production requirements. Including the starting point 0 and the ending point 6, there are a total of 7 nodes requiring production scheduling. Each workpiece is assigned a material matching degree parameter: workpiece 1 has a material matching degree of 80 (base score 60 + emergency correction score 20), workpiece 2 has 70 (base score 50 + normal correction score 20), workpiece 3 has 60 (base score 60 + no correction score), workpiece 4 has 50 (base score 50 + no correction score), and workpiece 5 has 40 (base score 40 + no correction score). The material matching degree for starting point 0 and ending point 6 is fixed at 100. When deciding on a production batch, since the receiving pool only has one batch, its total material matching degree is calculated to be 80 + 70 + 60 + 50 + 40 = 300, thus determining this batch as a batch to be scheduled. When preprocessing workpieces of the same specification, specification A includes workpieces 1, 2, and 4, with 2 pieces (workpieces 1 and 2) retained and workpiece 4 temporarily stored; specification B includes workpieces 3 and 5, with 2 pieces retained and both included in the schedule.

[0191] According to step S103, the purpose of preprocessing workpieces of the same specification is to reduce the scale of the initial scheduling problem, rather than permanently excluding temporarily stored workpieces. The specific rule is: for workpieces of the same specification, initially only a maximum of N pieces (configurable parameter) are retained for scheduling calculation, and the remaining workpieces are temporarily removed from the "workpiece pool to be scheduled" (i.e., "temporarily stored"). After the initial scheduling plan is formed, the temporarily stored workpieces are inserted into feasible positions, provided that all constraints (such as specification transition, sequence, rolling period upper limit, etc.) are met. In this example, specification A includes workpieces 1, 2, and 4, and N=2 (2 pieces are retained). Therefore, initially only workpieces 1 and 2 are retained for scheduling calculation, and workpiece 4 is temporarily stored (removed from the initial pool to be scheduled). This step is to simplify the complexity of the initial model.

[0192] In the multi-objective model establishment phase, the constructed multi-objective model includes three optimization objectives: maximizing the material supply matching degree, minimizing the inlet thickness fluctuation, and minimizing the order thickness fluctuation. Regarding constraints, the upper limit constraint for the rolling period is that the total weight cannot exceed 10 tons; in the sequence constraint, if workpiece 5 is placed before 3, it will cause quality problems, therefore, u5≥u3 (u i (This is the sequence number); the starting point 0 and the ending point 6 must be used, i.e., y0=1 and y6=1. The entry thickness fluctuation and order thickness fluctuation are calculated by the attribute difference between adjacent workpieces. For example, the entry thickness fluctuation of workpiece 0 to 1 is 2.0mm and the order thickness fluctuation is 1.0mm, and the entry thickness fluctuation of workpiece 1 to 3 is 1.0mm and the order thickness fluctuation is 0.5mm.

[0193] In the pulse propagation algorithm stage, a multi-objective model transformation based on ε-constraints is first performed to set an upper limit for inlet thickness fluctuation. =2.0, upper limit of order thickness fluctuation =1.5, transforming the original multi-objective model into a single-objective model min-Σc i y i The boundary phase calculates the shortest distance from each node to the endpoint. For example, under resource conditions (entrance thickness fluctuation 0.5, order thickness fluctuation 0.3), the shortest distance from node 3 to endpoint 6 is 3.0. The pulse phase sends a pulse from starting point 0 to explore paths. The path 0→1→3→6 exceeds this limit because the total entrance thickness fluctuation of 3.0 exceeds the limit. The branch was pruned, and the path 0→2→4→6 was affected by a total inlet thickness fluctuation exceeding 3.0. The path was pruned, and the total entry thickness fluctuation of path 0→1→4→6 (2.0) and the total order thickness fluctuation of path 1.0 both met the constraints, resulting in a total supply matching degree of 130. Simultaneously, an acceleration strategy was applied, concatenating the optimal path 0→2→6 stored in the boundary phase with the exploration path to obtain a feasible path 0→1→4→2→6 with a total supply matching degree of 200.

[0194] After the initial scheduling algorithm generates the basic path (e.g., 0→1→2→6), a secondary insertion check is required for the temporarily stored workpieces (e.g., workpiece 4): This check examines the specification transition constraints between workpiece 4 and adjacent workpieces in the path (e.g., whether the entry thickness and order thickness fluctuations meet requirements); it checks whether the total weight after insertion still meets the rolling period limit (10 tons); and it confirms that insertion does not violate specific workpiece sequence constraints (e.g., the order requirement without quality impact). Ultimately, workpiece 4, satisfying all constraints, is inserted between paths 0→1 and 2, forming the optimized path 0→1→4→2→6, and thus appears in the final schedule.

[0195] The optimization results show that the optimal path 0→1→4→2→6 has a total material matching degree of 200, a total inlet thickness fluctuation of 2.5, a total order thickness fluctuation of 1.2, and a total weight of 7 tons (meeting the 10-ton limit constraint for the rolling period). Compared with the traditional weighted method, this method improves the material matching degree by 20% while meeting the thickness fluctuation constraint, reduces scheduling time from 2 hours to 15 minutes, and increases efficiency by 87.5%. Furthermore, by performing insertion operations after pre-processing workpieces of the same specification, the number of specification changes is reduced by 3, lowering production costs by approximately 12%.

[0196] Nodes 3 and 5, which were not included in the process, will be handled differently based on the "phased production scheduling + temporary insertion" mechanism and constraints. Their specific destinations are as follows:

[0197] (1) The feasible position to be inserted into the current batch after temporary storage is based on document S103 "Preprocessing rules for workpieces of the same specification": "Only a maximum of N workpieces of the same specification are retained, and the remaining workpieces are deleted from the workpieces to be scheduled; after the subsequent algorithm steps form a plan, the deleted workpieces of the same specification are inserted into the feasible position under the condition of satisfying all constraints." In the example, if nodes 3 and 5 belong to the category of "temporary storage of workpieces of the same specification" (e.g., specification B includes 3 and 5, N=1 is set, initially only 3 or 5 is retained in the schedule, and the other workpiece is temporarily stored), then after the optimal path 0→1→4→2→6 is generated, the feasibility of the connection between 3 and 5 and the adjacent nodes in the path will be checked: if the entrance thickness fluctuation of node 3 and workpiece 2 (segment 2→6 in the path) is 0.3mm≤ =2.0, Order thickness fluctuation ≤ 0.2mm =1.5, and the total weight after insertion (7 tons + the weight of 3) ≤ 10 tons, then insert 3 between "2→6" to form a new path 0→1→4→2→3→6; if the constraint is not met during temporary storage (such as exceeding the upper limit of the roll period after insertion), then continue to store it in the next batch.

[0198] (2) Inclusion in the next batch of production (due to current batch constraints) If nodes 3 and 5 are not temporarily stored, but are not included in the optimal path due to "current batch constraints not being met", they will automatically enter the "next batch collection pool" and participate in subsequent production: Constraint 1: Thickness fluctuation exceeds the upper limit - such as the connection fluctuation between node 3 and any node in the path (such as the entry thickness fluctuation of 0→3 3.0mm> =2.0), which does not meet the ε constraint of the current batch, and the ε value of the next batch needs to be adjusted (e.g., relaxed). =3.5) and then included; Constraint 2: Rolling period upper limit overrun - If the sum of the weights of nodes 3 and 5 is 4 tons, and the total weight of the optimal path in the current batch is 7 tons, after adding 7+4=11 tons>10 tons (rolling period upper limit), it needs to be included in the next batch (the starting point of the next batch is 6, and the total weight can be recalculated); Constraint 3: Order conflict - If node 5 needs to satisfy "not ranked before 3" (constraint condition A4), if 3 is not included in the current batch, 5 also needs to be postponed to the next batch to avoid order conflict affecting quality.

[0199] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other specific forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered in all respects as exemplary and non-limiting, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of equivalents of the claims are intended to be included within the present invention. No reference numerals in the claims should be construed as limiting the scope of the claims.

Claims

1. A smart scheduling multi-objective optimization method based on pulse propagation algorithm, characterized in that, Includes the following steps: S01: Scheduling data preparation stage, making pre-decision for the available resources in the receiving pool and generating data for the input model; the receiving pool refers to the set of workpieces that meet the production scheduling conditions; the pre-decision includes: assigning material matching parameters to the workpieces, deciding on production batches, and pre-processing workpieces of the same specification; step S01 includes the following sub-steps: S101. Assign a material supply matching parameter to each workpiece, wherein the matching parameter reflects the priority of workpiece supply; S102. Decision on production batches and corresponding workpieces; determine the next production batch based on the production line status, and select the workpieces that can be included in each batch; calculate the sum of the material matching degrees of the workpieces in each batch based on the material matching degree of each workpiece determined in step S101; select the batch with the largest sum of material matching degrees as the next batch to be arranged, and the workpieces in this batch are the workpieces to be arranged. S103. Perform preprocessing on workpieces of the same specification; the workpieces of the same specification refer to workpieces with the same specification attributes; identify workpieces of the same specification, retain at most N workpieces of the same specification, where N is a configurable parameter, and delete the remaining workpieces from the workpieces to be sorted; after the subsequent algorithm steps form a plan, insert the deleted workpieces of the same specification into feasible positions while ensuring that all constraints are met. S02: Multi-objective model establishment stage, mathematical modeling is used to characterize the production scheduling rules and optimization objectives. The optimization objectives include maximizing the material supply matching degree, minimizing the inlet thickness fluctuation, and minimizing the order thickness fluctuation. The production scheduling rules include specification transition constraints, specific workpiece front and back sequence constraints, and rolling period upper limit constraints. S03: In the pulse propagation algorithm stage, the multi-objective model is solved by designing a model based on ε-constraints and the pulse propagation algorithm. Specifically, the ε-constraints introduce parameters ε1 and ε2, transforming the minimization of inlet thickness fluctuation and the minimization of order thickness fluctuation into constraint conditions, and transforming the maximization of material supply matching degree into a single-objective model that minimizes the negative value of material supply matching degree. Then, the single-objective model is solved using the pulse propagation algorithm. Wherein: parameter ε1 is the upper limit of inlet thickness fluctuation; parameter ε2 is the upper limit of order thickness fluctuation. Step S03 includes: S302: Establish the solution model M(ε) based on the pulse propagation algorithm; S305: Set the acceleration strategy for the pulse propagation algorithm; In step S302, the solution model M(ε) based on the pulse propagation algorithm is established as follows: Reconstruct the model M(ε) as a network flow problem; treat the workpieces as nodes in the network graph, and describe the connection relationships of the workpieces as arc segments; establish a network graph G(N, E), where N is the set of nodes satisfying N=I, and E is the set of arc segments; any arc segment (i, j)∈E has three key properties: The inlet thickness fluctuation r corresponding to the connection i,j ; The corresponding order thickness fluctuation t i,j ; The distance d traversed by the connection i,j ; The d i,j The value is -c j , where c j The material supply matching degree for workpiece j; In step S305, the acceleration strategy for the pulse propagation algorithm includes two strategies: storing the optimal path during the bounding stage and inserting the optimal path to improve the algorithm. The boundary phase stores the optimal path to improve search efficiency by storing the optimal path in A; for workpieces i and j, if workpiece j can be both before and after i, then workpiece j is called a neighbor of workpiece i; in the boundary phase, starting from node i, given a resource consumption of... Under these conditions, when solving ESPPRC, nodes that simultaneously satisfy the following two conditions are excluded from the search path: a. A component adjacent to workpiece i; b. The entrance width attribute value is greater than the entrance width attribute value of workpiece i; The optimal path obtained by solving the problem is denoted as . Save it to A, that is During the pulse process, for path p to reach node i, and given the resource consumption is... When, determine p and If there is an intersection between the sets of nodes, and if not, then directly concatenate path p and path p* as the optimal path and return it; if there is an intersection, then terminate the propagation of path p to node i. The insertion algorithm improves the optimal path by checking for possible insertion points and nodes that can further reduce the target value. During the pulse search, a depth-first traversal method is used to explore the path. Whenever the destination is reached, a partial path is obtained. New nodes are inserted into the existing path to optimize it.

2. The method according to claim 1, characterized in that, In step S02, the process of establishing the multi-objective model includes the following steps: S201: Establish a mathematical model to represent maximizing the material supply matching degree, minimizing the inlet thickness fluctuation, and minimizing the order thickness fluctuation, and characterize the constraints and objective function; the mathematical model is as follows: ； ； ； in, This indicates maximizing the matching degree of material supply. This indicates minimizing inlet thickness fluctuation. This represents minimizing order thickness fluctuation; I represents the set of all candidate workpieces, I={0,1,…,n}, where 0 is the starting point and n is the ending point; c i Indicates the material feeding matching degree of workpiece i; y i This indicates whether workpiece i is used; yi=1 indicates that workpiece i is included, and yi=0 indicates that workpiece i is not included. This refers to the workpiece that follows workpiece i and meets all specification transition requirements; r i,j This indicates the inlet thickness fluctuation at the junction of workpieces i and j; t i,j This indicates the order thickness fluctuation at the junction of workpieces i and j; x i,j Indicates whether workpiece j is immediately following workpiece i, with a value of 1 or 0, x i,j =1 indicates that workpiece j is immediately after workpiece i, x i,j =0 indicates that workpiece j is not immediately adjacent to workpiece i; The constraints include specification transition constraints, specific workpiece sequence constraints, rolling period upper limit constraints, and variable value range constraints.

3. The method according to claim 2, characterized in that, The specific constraints are as follows: A1: Each selected workpiece has one and only one predecessor and one successor; (1) For any workpiece i in the candidate set I, it cannot be adjacent to any workpiece j in the set of workpieces that cannot be placed before workpiece i and satisfy the specification transition constraint, i.e. ； in, This indicates that a workpiece that can be placed before workpiece i must satisfy all specification transition constraints with workpiece i. This indicates removing workpieces from the set I of all candidate workpieces that can be ranked before workpiece i and meet all specification transition requirements; x j,i Indicates whether workpiece i is scheduled for production immediately following workpiece j, with a value of 1 or 0. j,i =1 indicates that workpiece i is immediately after workpiece j, x j,i =0 indicates that workpiece i is not immediately adjacent to workpiece j; (2) For any workpiece i in the candidate set I, it cannot be adjacent to any workpiece j in the set of workpieces that cannot be placed after workpiece i and satisfy the specification transition constraint, i.e. ； in, This indicates a workpiece that can be placed after workpiece i, and that satisfies all specification transition constraints with workpiece i. This means removing workpieces that can be ranked after workpiece i and meet all specification transition requirements from the set of all candidate workpieces I; (3) For any workpiece i starting from the first position, if workpiece i is included, then workpiece i can only be arranged adjacent to one of the workpieces j that can be arranged before workpiece i, i.e. ； (4) For any workpiece i, if workpiece i is arranged, then workpiece i can only be arranged adjacent to one of the workpieces j that can be arranged after workpiece i, that is... ； A2: Workpiece 0 at the starting position and workpiece n at the ending position must be inserted, that is... ； A3: The condition for eliminating sub-loop constraints is: ； Among them, u i and u j As an auxiliary variable, it represents the sequence number of workpiece i and workpiece j after they are placed in the workpiece; A4: For specific workpiece order constraints, if placing j before i would negatively impact production quality, then... ； in This represents the set of workpieces that precede workpiece i and will have a quality impact on workpiece i; A5: Rolling period upper limit constraint: ； Among them, w i Indicates the tonnage of workpiece i; W represents the upper limit constraint of the rolling period; A6: Variable value range constraints: 。 4. The method according to claim 1, characterized in that, Step S03 also includes the following sub-steps: S301: Perform ε-constraint-based multi-objective model transformation; S303: Implement the bounding phase algorithm process, which determines the shortest distance from each node to the destination under given resource consumption conditions; S304: Implement the pulse phase algorithm flow, which adopts an implicit enumeration strategy for the solution space, and performs a strategy of recursively exploring all possible paths but only retaining feasible paths to reduce the search space.

5. The method according to claim 4, characterized in that, In step S301, the multi-objective model transformation based on ε-constraints is specifically as follows: Introducing parameters into a multi-objective optimization model and Transform the second and third objectives into ε-constraints: ； ； Setting parameters and parameters Let the value sets of be V1 and V2 be respectively. Simultaneously, the first objective is transformed into a minimization problem. For any ε∈V, a single-objective model M(ε) with ε-constraints is established: ： ； in This represents a negative value that minimizes the material supply matching degree.

6. The method according to claim 1, characterized in that, In step S302, Both the entry thickness fluctuation and the order thickness fluctuation are considered as resource consumption through the arc segment; the problem is transformed into finding the shortest path from the starting point 0 to the ending point n in the network that satisfies the resource consumption not exceeding ε, requiring that each node in the path is visited at most once; The pulse propagation algorithm consists of two core phases: a bounding phase and a pulse phase. The bounding phase determines the shortest distance from each node to the endpoint under different resource consumption conditions. These different resource consumption conditions refer to two types of resource consumption: inlet thickness fluctuation and order thickness fluctuation, with constraints introduced by parameters ε1 and ε2. The pulse phase is based on an implicit enumeration strategy of the solution space, which eliminates invalid paths in advance through mathematical rules, avoiding explicit traversal of all possible path sets and exploring potential subspaces. A pulse signal is emitted from the starting node 0∈I, and the pulse signal propagates along the arcs in the network to explore all paths. At each node, the pulse signal records partial path information p, the accumulated distance d(p), and the amount of resources consumed r(p); a pruning strategy is used to limit the further propagation of the pulse and reduce the search space; when the pulse successfully reaches the final node, it carries a complete and feasible path information from the starting point to the end point.

7. The method according to claim 4, characterized in that, In step S303, the specific algorithm flow for the boundary determination stage is as follows: make This represents the length of the shortest path that satisfies the resource constraints found during the bounding process, and... As an upper limit in the iterative process; The bounding process finds the shortest distance to the destination for each node i∈I under the condition of resource consumption r. When a path p reaches node i, if the following conditions are met... If it does not spread, then pruning should be performed to prevent further propagation. Initial settings ,in =max(V1), =max(V2); For each node i∈I, given the resource consumption Solve ESPPRC under the given resource consumption conditions; after finding the boundary value, for each node i∈I, under the given resource consumption... Solve an ESPPRC in the following situation: The bounding step size for the order thickness in the pulse algorithm; By using the previously calculated information, the same process is repeated in reverse order to produce the lower bound matrix. This includes the information for each node i∈I in the range from 0 to... The lower bound calculated for each discrete bounding step size. , The inlet thickness is the bounding step size in the pulse algorithm. , This is the bounding step size for the order thickness in the pulse algorithm.

8. The method according to claim 4, characterized in that, In step S304, the pulse stage algorithm flow is specifically as follows: The recursive process pulse is for the set of head nodes of each outgoing arc starting from a given node i. When implementing a pruning strategy, first perform infeasibility checks and boundary checks. Infeasibility pruning ensures the uniqueness and correctness of the path. If the pulse is not pruned, add the current node to the part of the path that is being built; Iterate through all the outgoing arc nodes of the current node and recursively call the pulse procedure for each node to propagate the pulse; When the pulse process is invoked at the final node, the known optimal path information is updated, and further pulse propagation is stopped; The algorithm recursively continues to propagate other potential pulses through a backtracking mechanism.

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