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

Abstract

The invention discloses an intelligent scheduling multi-objective optimization method based on a pulse propagation algorithm, and relates to the field of scheduling in the manufacturing industry, and the method comprises the following steps: a scheduling data preparation stage, which is used for carrying out pre-decision making on schedulable resources in a receiving pool and generating data of an input model; in the multi-target model establishment stage, a mathematical modeling mode is adopted to describe production scheduling rules and optimization targets; in the pulse propagation algorithm stage, the multi-target model is solved by designing an epsilon-constraint and pulse propagation algorithm; according to the invention, the workload of a planner is greatly reduced; the batch decision and the specific scheduling details can be fully automatically completed by an embedded advanced model and an intelligent algorithm; the intelligent decision-making mechanism not only improves the working efficiency, but also ensures the accuracy and rationality of the production scheduling plan.

Description

Technical Field

[0001] The present invention relates to the field of manufacturing scheduling, and specifically to an intelligent scheduling multi-objective optimization method based on a pulse propagation algorithm. The method is applied to scenarios requiring continuous production, such as steel cold rolling / hot rolling workshops and non-ferrous metal (aluminum / copper) rolling workshops. The workpieces targeted are plate and strip workpieces that meet the conditions for continuous rolling (such as cold-rolled steel plates and aluminum foil billets). The method is suitable for scenarios where multiple workpieces are continuously scheduled on a single production line, and is particularly suitable for production modes with urgent feeding demands and high thickness accuracy requirements in downstream processes (such as automotive plate cold rolling scheduling and power battery aluminum foil scheduling). Background Art

[0002] Workpiece scheduling is a critical link in the workpiece production process and is highly important and complex. This process covers a series of sophisticated process steps, from raw material preparation to finished product delivery, and each step requires strict time planning and resource allocation. In particular, when formulating production sequence plans, it is necessary to comprehensively consider multiple factors such as workpiece resource distribution, production concentration, and equipment utilization to ensure the efficiency and smoothness of the production process. In the past, a common approach to multi-objective scheduling problems was to convert them into single-objective problems through weighting methods. Although this method simplifies the problem in terms of operation, due to the significant dimensional differences and numerical ranges among the objectives, reasonably determining the weights has become a challenging task. If the weights are not selected scientifically, it is very easy to cause the scheduling results to deviate from the optimal state, fail to meet expectations and needs, and may even cause a series of negative effects such as uneven resource allocation and low production efficiency. Given the limitations of the weighting method, it is particularly important to deeply explore multi-objective optimization strategies for scheduling problems. Multi-objective optimization aims to simultaneously consider and balance multiple conflicting or mutually constrained objectives in order to seek solutions that can effectively explore and find a solution set close to the Pareto optimal frontier in a complex search space, providing decision makers with a variety of options. At the same time, combining domain knowledge and actual needs, appropriate improvement and customization of the algorithm can further enhance the optimization effect and ensure that the scheduling plan is both efficient and practical.

[0003] There are three problems with using the weighted method to deal with multi-objective problems: the difficulty in determining weights. When using the weighted method to deal with multi-objective scheduling problems, the primary difficulty faced is determining the weights, 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. Unreasonable weight allocation may cause the scheduling results to deviate from actual needs. For example, a steel plant once had an average daily waiting time of 2 hours for materials in the subsequent process due to weight deviation. The output plan is single. When dealing with multi-objective problems, traditional weighted methods can often only output a plan with the best comprehensive weighted objectives, which leads to the singleness of the output plan. This single-plan output mode greatly limits the flexibility and diversity of scheduling. Once this plan performs poorly in actual applications, planners need to spend time and energy on manual adjustments, or have to rebuild and solve the model, which will undoubtedly greatly reduce the efficiency of scheduling. For example, if the plan does not conform to the real-time status of the equipment (such as sudden wear of the roll), the planner needs to remodel, which takes more than 2 hours. Reliance on general-purpose solvers (such as Gurobi, CPLEX, etc.) leads to low efficiency and high cost. Existing scheduling technology also relies heavily 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 needs of the cold rolling workshop to generate adjustment plans within half an hour. Summary of the Invention

[0004] The purpose of the present invention is to provide an intelligent scheduling multi-objective optimization method based on a 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 a pulse propagation algorithm, the method comprising the following steps: S01: Scheduling data preparation stage, used to make pre-decision on schedulable resources in the pool and generate data for input models. The pool refers to a collection of workpieces that meet the production scheduling conditions. The pre-decision includes assigning feed matching parameters to workpieces, determining production batches, and pre-processing workpieces of the same specifications. S02: The multi-objective model establishment phase uses mathematical modeling to characterize the scheduling rules and optimization objectives. The optimization objectives include maximizing feed matching, minimizing inlet thickness fluctuation, and minimizing order thickness fluctuation. The scheduling rules include specification transition constraints, specific workpiece sequence constraints, and roll period upper limit constraints. S03: Pulse propagation algorithm stage, solving the multi-objective model by designing an ε-constraint and a pulse propagation algorithm; the ε-constraint is specifically introduced as a parameter and , the minimization of inlet thickness fluctuation and minimization of order thickness fluctuation are transformed into constraint conditions, and the maximization of feed matching is transformed into a single-objective model of minimizing the negative value of feed matching, and then the pulse propagation algorithm is used to solve the single-objective model; where: parameters is the upper limit of the inlet thickness fluctuation; parameter It is the upper limit of order thickness fluctuation.

[0006] Furthermore, in step S01: a pre-decision is made for the schedulable resources in the receiving pool and data for inputting the model is generated, thereby preparing the scheduling data. The scheduling data preparation process includes the following steps: S101. Assigning a material matching degree parameter to a workpiece. By constructing a scoring system for material matching, each workpiece is assigned a material matching degree parameter. The scoring system is divided into two parts: basic score and modified score. The basic score is assigned different scores based on the priority of the downstream process supply corresponding to the workpiece. The higher the score, the higher the material supply demand of the downstream process corresponding to the workpiece. The modified score modifies the basic score based on special workpieces and special circumstances. For example, urgent workpieces and must-be-scheduled workpieces are given a greater modification weight. The basic score is assigned based on the priority of the downstream process corresponding to the workpiece. For example, a workpiece with a downstream process of 'automotive sheet stamping' (delivery time ≤ 3 days) is assigned 80-100 points, while a workpiece with a downstream process of 'ordinary civilian sheet metal' (delivery time ≥ 7 days) is assigned 40-60 points. The modified score is adjusted based on the 'urgency and must-have attributes': 20-30 points are added for urgent orders (need to be delivered within 48 hours), 30-50 points are added for must-have workpieces (the downstream process has run out of material), and 0 points are added if there are no special circumstances.

[0007] S102. Decide on a production batch and the workpieces corresponding to the production batch; determine the next production batch based on the status of the production line, and screen the workpieces that can be arranged in each batch; calculate the sum of the feed matching degrees of the workpieces in each batch based on the feed matching degree of each workpiece determined in step S101; select the batch with the largest sum of feed matching degrees as the next batch to be arranged, and the workpieces in this batch are the workpieces screened out to be arranged; S103. Preprocess the workpieces of the same specifications. Since the goal includes minimizing the total specification fluctuation value, it is usually hoped that the workpieces of the same specifications can form a local "small batch" production to reduce the specification fluctuation. In order to reduce the scale of the problem, it is necessary to identify the workpieces of the same specifications. The specifications of the workpieces are detected and identified. For workpieces of the same specifications, only a maximum of N pieces are retained, where N is a configurable parameter, and the remaining workpieces are deleted from the workpieces to be arranged. After a plan is formed by completing the subsequent algorithm steps, the deleted workpieces of the same specifications are inserted into feasible positions while ensuring that all constraints are met.

[0008] The scheduling object is the workpiece. Each workpiece has several known attributes, such as inlet thickness, order thickness, feed matching, weight, etc. Multiple workpieces that meet the production requirements form a pool to be scheduled. The collection pool refers to a collection of workpieces that meet the conditions for production and manufacturing scheduling. The workpieces in the collection pool must meet the following conditions: 1. They have completed the previous process (such as hot rolling and flattening) and passed the quality inspection; 2. They have the process parameters required for rolling (such as material, width, initial hardness); 3. They have been entered into the production system, and the subsequent process has confirmed the feeding requirements to avoid the situation where there is no receiving process after scheduling.

[0009] The entry thickness is the material thickness of the workpiece before production rolling (the production rolling process may change the workpiece thickness) The order thickness is the material thickness of the workpiece when it is produced and processed into the finished product; The workpieces of the same specifications are those with the same entry width, entry thickness, order thickness, and steel grade. The core purpose of identifying workpieces of the same specifications is to reduce fluctuations in specification transitions: when joining workpieces of the same specifications, the rolling mill does not need to adjust parameters such as the roll gap and pressure, which can reduce equipment adjustment time (a single adjustment takes 5-8 minutes) and avoid thickness deviation during the adjustment process (the fluctuation value can be reduced by more than 60%). Even if the workpiece meets the core specification requirements of "entry thickness, order thickness, and material grade are all the same", there are still differences. These differences are an important basis for scheduling decisions (such as feed priority and insertion timing); these differences include feed matching parameters, urgency and delivery requirements, completion time and status of the previous process, and the acceptance capacity of the subsequent process.

[0010] Regarding "for workpieces of the same specification, only retain at most N pieces", N pieces are dynamically configurable and adjustable, mainly considering that some workpieces can be connected with other workpieces no matter where they are placed. For such "universal" workpieces, N pieces can be reserved during production scheduling, so that they can be put into production in the later production scheduling. Not all workpieces must be scheduled at the moment, and they can be scheduled according to a certain quantity or a certain time. Therefore, there is no need to insert the deleted and retained workpieces of the same specification into a certain position in this production scheduling; the reason for retaining at most N workpieces is to control the scale of the initial problem: if there are more than 10 workpieces of the same specification in the collection pool, the number of scheduling path combinations will increase exponentially (for example, the number of combinations of 15 workpieces exceeds 10 8 ), which doubles the algorithm time. Retaining N pieces (usually 2-5 pieces, which can be adjusted dynamically according to the total number of workpieces) can reduce the number of initial combinations by more than 50%. At the same time, when the temporarily stored workpieces are subsequently inserted, they can be directly connected because their specifications are consistent with those of the already arranged workpieces, without affecting the overall fluctuation constraint and feeding matching degree.

[0011] Furthermore, in step S02, mathematical modeling is used to describe production scheduling rules and optimization objectives for establishing a multi-objective model. The process of establishing the multi-objective model includes the following steps: S201: Establish a mathematical model for maximizing the feed matching degree, minimizing the inlet thickness fluctuation, and minimizing the order thickness fluctuation; and characterize the constraint conditions and objective function; the mathematical model is as follows: ; ; ; in, represents the maximum feed matching degree, represents the minimization of inlet thickness fluctuations, represents minimizing the fluctuation of order thickness; I represents the set of all workpieces to be selected, I={0,1,…,n}, 0 is the starting point, n is the end point; c i Indicates the feeding matching degree of workpiece i; y i Indicates whether artifact i is used; represents the workpiece that follows workpiece i and meets all transition specifications; r i,j represents the thickness fluctuation of the entrance where workpiece i and workpiece j meet; t i,j Indicates the order thickness fluctuation of workpiece i and workpiece j; Select 'maximize feed matching, minimize inlet thickness fluctuation, and minimize order thickness fluctuation' as the optimization objectives based on the following: The material matching degree is directly related to the connection between the downstream process and the material availability of the current process. If the material matching degree is low (for example, the workpiece urgently needed in the downstream automotive sheet stamping process is not scheduled for production), the downstream process will be left waiting for materials. Fluctuations in the inlet thickness affect the stability of the rolling mill: when the fluctuation exceeds 0.5 mm, the rolling mill is prone to "bouncing", resulting in partial thickness deviations in the workpiece and a 3%-5% increase in the scrap rate. Fluctuations in order thickness affect the qualified rate of finished products: the order thickness is the final thickness required by the customer. Fluctuations exceeding 0.1mm will cause the product to not meet the order requirements and the rework rate will exceed 10%.

[0012] The constraints are as follows: Constraint groups A1, A2, and A3 are specification transition constraints, which are used to ensure that the sorted workpieces can be welded to adjacent workpieces; Constraint A4 is a front-to-back order constraint for specific workpieces; Constraint A5 is a roll period upper limit constraint; A1: Each selected workpiece has exactly one predecessor and 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 scheduled before workpiece i and meet the specification transition constraint. That is, the sum of whether workpiece j and workpiece i are scheduled adjacently is 0; ; in, It means that the workpieces that can be arranged in front of workpiece i meet all the specification transition constraints between them. Indicates that the workpieces that can be ranked before workpiece i and meet all transition constraints are eliminated from the set of all selected workpieces I, that is, the set of workpieces that are ranked before workpiece i but cannot meet the transition constraints between workpiece i and workpiece i; x j,i Indicates whether workpiece i is scheduled to be produced immediately after workpiece j, and the value is 1 or 0, x j,i =1 means that workpiece i is placed immediately after workpiece j, and x j,i =0 means that workpiece i is not immediately after workpiece j; (2) For any workpiece i in the candidate set I, it cannot be adjacent to workpiece j in the set of workpieces that cannot be scheduled after workpiece i and meet the specification transition constraint. That is, the sum of whether workpiece i and workpiece j are scheduled adjacently is 0; ; in, It means that the workpieces that can be arranged behind workpiece i meet all the specification transition constraints between them. Indicates that the workpieces that can be ranked after workpiece i and meet all the transition specifications are eliminated from the set of all workpieces to be selected I; that is, the set of workpieces that are ranked after workpiece i and cannot meet the transition specification constraints with workpiece i; x i,j Indicates whether workpiece j is scheduled to be produced immediately after workpiece i, with a value of 1 or 0. i,j =1 means that workpiece j is placed immediately after workpiece i, and x i,j =0 means that workpiece j is not immediately after workpiece i; (3) For any workpiece i starting from the first position, if workpiece i is scheduled, then workpiece i can only be scheduled adjacent to a workpiece j among all the workpieces that can be scheduled before workpiece i, that is, both the left and right sides of the equal sign are 1; if workpiece i is not scheduled, then workpiece i cannot be scheduled adjacent to any workpiece j among all the workpieces that can be scheduled before workpiece i, that is, both the left and right sides of the equal sign are 0; ; in, It means that the workpieces that can be arranged in front of workpiece i satisfy all the transition constraints between them. i Indicates whether artifact i is used, y i =1 means workpiece i is placed in, y i=0 means that workpiece i is not included, and I\{0} means that the set of workpieces after the starting position 0 is eliminated from all optional sets; (4) For any workpiece i, if workpiece i is scheduled, then workpiece i can only be scheduled adjacent to a workpiece j among all the workpieces that can be scheduled after workpiece i, that is, both the left and right sides of the equal sign are 1; if workpiece i is not scheduled, then workpiece i cannot be scheduled adjacent to any workpiece j among all the workpieces that can be scheduled after workpiece i, that is, both the left and right sides of the equal sign are 0; ; in, It means that the workpieces that can be arranged behind workpiece i satisfy all the transition constraints between them. i Indicates whether artifact i is used, y i =1 means workpiece i is placed in, y i =0 means that workpiece i is not discharged; A2: The conditions to be used for the first and last items are: ; Workpiece 0 at the start position and workpiece n at the end position must be queued. Indicates that the last workpiece that has been queued during production must be queued. Indicates that this production schedule ends at a certain virtual workpiece n.

[0013] Starting point 0 is not a "virtual empty node" but the final workpiece of the previous batch. Forcibly selecting 0 ensures a seamless connection between the current production schedule and the preceding batch, avoiding interruptions in the rolling process. For example, the mill does not need to readjust the roll gap or pressure due to a "no starting workpiece," thus reducing equipment idle time.

[0014] The end point n is the "virtual end point workpiece" of the current batch production. Its core function is to "define the production boundary of the current batch" to form a closed production loop: after the current batch ends with n, the next batch can use n as the new "starting point 0" to realize a continuous production cycle.

[0015] A3: Eliminating sub-loop constraints is: ; Among them, u i and u j is an auxiliary variable; it represents the sequence number of workpiece i and workpiece j after they are arranged, ensuring that when workpiece i and workpiece j are arranged adjacently, the sequence numbers of workpiece j and workpiece i do not decrease; A4: Set a specific workpiece order constraint. If placing j before i will affect production quality, then place j after i: ; in represents the set of workpieces that precede or follow workpiece i and have an impact on the quality of workpiece i. This formula indicates that for any workpiece i, any workpiece j that precedes workpiece i and has an impact on its quality requires that the sequence number of workpiece j is greater than that of workpiece i. A5: Rolling period upper limit constraint: ; Among them, w i represents the tonnage of workpiece i; W represents the upper limit constraint of the roll period; for all workpieces i that are queued this time, the sum of their weight tonnage does not exceed the upper limit W of the roll period; The roll life limit constraint W is set based on the wear cycle of core equipment such as rolls. For example, in a cold rolling mill, 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, causing the thickness deviation of subsequent workpieces to exceed ±0.01mm (exceeding the requirements of the national standard GB / T 708-2019). Furthermore, exceeding the upper limit shortens the roll replacement cycle (from 3 days to 1 day), increasing equipment maintenance costs. Therefore, setting the roll life limit W is a key constraint for balancing production efficiency with equipment life and product precision. A6: Set the variable value range constraint: . Indicates that for any workpiece i, its corresponding sequence number is a natural number from 0 to n.

[0016] Furthermore, step S03 includes the following steps: S301: Perform multi-objective model conversion based on ε-constraint; S302: Establishing a solution model M(ε) based on the pulse propagation algorithm; S303: Implement the algorithm process of the delimitation phase; S304: Implementing the pulse phase algorithm process; S305: Setting the pulse propagation algorithm acceleration strategy.

[0017] Furthermore, in step S301: the above multi-objective model belongs to a multi-objective optimization model, and the parameters are introduced into the multi-objective optimization model. and , convert the second and third objectives into ε-constraints: ; ; Setting parameters and parameters The value sets are V1 and V2 respectively, let At the same time, the first goal is transformed into a minimization problem, for any , establish the following single-objective model with ε-constraint, denoted as model M(ε): : ; in Negative value that minimizes feed matching.

[0018] The first objective is to "maximize the feed matching degree"; the second objective is to "minimize the inlet thickness fluctuation"; and the third objective is to "minimize the order thickness fluctuation". The above three objectives correspond to the core optimization direction of the multi-objective model specified in claim 3. Through the ε-constraint transformation, the multi-objective problem is converted into a single-objective problem so that it can be solved by the pulse propagation algorithm.

[0019] Furthermore, in step S302: first, M(ε) is converted into a network flow problem, and a pulse propagation algorithm is designed to solve the network flow problem, and finally the overall algorithm flow is obtained; Reconstruct the model M(ε) into a network flow problem; consider the workpieces as nodes in the network graph and describe the connection relationship of the workpieces as arcs; establish a network graph G(N, E), where N is the set of nodes, satisfying N=I, and E is the set of arcs; any arc (i, j)∈E has three key properties: first, the thickness fluctuation r of the corresponding entrance of the connection i,j , the second is the corresponding order thickness fluctuation t i,j , and the third is the distance d spanned by the connection i,j , the d i,j The value is -c j Consider both entry thickness fluctuations and order thickness fluctuations as resource consumption along the arc segment. Based on this, the problem is transformed into finding a shortest path from starting point 0 to end point n in the network that consumes no more than ε, requiring that each node in the path be passed through at most once. This transforms the problem into the Elementary Shortest Path Problem with Resource Constraints (ESPPRC). Furthermore, the specific workpiece order constraint is an additional constraint that must be considered in ESPPRC. 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 delimitation stage and the pulse stage. The delimitation phase is used to determine the shortest distance from each node to the destination under given different resource consumption conditions; the so-called different resource consumption conditions refer to two types of resource consumption: entrance thickness fluctuation and order thickness fluctuation. The parameter and parameters After the constraints; The pulse phase is based on an implicit enumeration strategy of the solution space. This strategy uses mathematical rules to preemptively exclude invalid paths, avoiding explicit traversal of all possible path sets and exploring potential subspaces. A pulse signal is emitted from the starting node 0∈I, propagating 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 consumed resources r(p). To optimize search efficiency, a pruning strategy is used to limit the further propagation of the pulse and reduce the search space. Whenever a pulse successfully reaches the final node, it carries information about a complete and feasible path from the starting point to the end point. Finally, get the overall algorithm process; parameters in the algorithm input By the largest Value and maximum Value composition, that is ; Delimiting step length ,in and are the delimiting steps of the entrance thickness and ordering thickness in the pulse algorithm, respectively, where , ; The overall algorithm process is described as follows: Line 1 is responsible for initialization, including setting the initial state of partial paths, cumulative distance, resource consumption, and the optimal path set; Line 2 performs the bounding process, calculating and determining the shortest distance lower bound for each node in the network; Lines 3 to 5 generate the result path; traverse ∈V, call the recursive function pulse for each ε, and store the optimal path generated each time into the set P; Line 6 returns the set P of optimal paths found during the recursive search.

[0020] Further, in step S303: in the algorithm flow of the delimitation phase, let represents the length of the shortest path that satisfies the resource constraints found during the delimitation process, and As the upper limit of the iterative process; the bounding process can find the shortest distance to the end point for each node i∈I under the condition of resource consumption r ; When a path p reaches node i, if , then prune and no longer propagate; the working principle of the delimitation phase is: for each node i∈I, under a given resource consumption Solve ESPPRC in the case of , since both resources have been consumed, there are 0 resource units left and few feasible solutions, so the pulse process can quickly find the optimal solution; each optimal solution found is a given resource consumption Under the condition of the lower bound of the minimum distance that any partial path to node n∈I can achieve; after finding the limit, for each node i∈I, under the given resource consumption Solve an ESPPRC under the condition of ; the current problem has fewer constraints, but the resource consumption is The lower bound of the path distance has been obtained; by using the information calculated previously, the same process is repeated in reverse order; this process will produce a lower bound matrix represented as , which contains the lower bounds computed for each node i∈I at each discrete bounding step between 0 and ε , Similarly, as the available resources increase, the problem solved in the bounded solution has fewer constraints and becomes more difficult to solve, but the number of known bounds will also increase, thereby increasing the chance of pruning some paths using the bounded pruning strategy; in the specific implementation of Algorithm 2: Line 1 is responsible for initializing the value of resource consumption; Lines 2 to 6 start the delimiting scheme, traversing each possible resource consumption of each node; Lines 7-8 use the impulse algorithm to solve an ESPPRC problem for each node given the current resource consumption; Lines 9 to 13 store the optimal solution for each node found, that is, the lower bound of the shortest path length, in the corresponding position of the lower bound matrix; if a particular problem is not feasible under the given resource consumption, the lower bound is set to positive infinity.

[0021] Furthermore, in step S304: the recursive process pulse in the pulse phase algorithm process is for the head node set of each outgoing arc starting from the given node i Perform the operation; in the process of implementing the pruning strategy, the infeasibility check and delimitation check are first performed. The infeasibility pruning ensures the uniqueness of the path, that is, each node is visited at most once, and the correctness, that is, avoids production quality problems caused by node order errors; it is used to decide whether to prune the incoming pulse; if the pulse is not pruned, the current node is added to the partial path being constructed; then the algorithm is used to traverse all the arc head nodes of the current node, and recursively call the pulse process for each node to propagate the pulse; when the pulse process is called at the final node, the pulse process updates the known optimal path information as needed and stops further pulse propagation; after that, the algorithm recursively continues to propagate other potential pulses through the backtracking mechanism.

[0022] Furthermore, in step S305: the pulse propagation algorithm acceleration strategy is used to combine the characteristics of the scheduling problem, and proposes two strategies: storing the optimal path in the delimiting stage and improving the optimal path with the insertion algorithm to accelerate the pulse algorithm; The optimal path is stored in A during the delimitation phase to improve the 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 delimitation phase, starting from node i, given a resource consumption of Under these conditions, when solving ESPPRC, nodes that simultaneously meet the following two conditions are excluded from the search path: a. They are adjacent to workpiece i; b. The entrance width is larger than workpiece i; the optimal path obtained by solving is recorded as , save it to A, that is ; During the pulse process, for path p to reach node i, and the given resource consumption is When p and Is there an intersection between the node sets of path p and path ? Perform splicing and return it as the optimal path; if it exists, terminate the path p and propagate it to node i; The insertion algorithm improves the optimal path and is used to improve the partial path that has been searched, and checks whether there are possible insertion points and whether there are nodes such as B' that can further reduce the target value; in the pulse search process, a depth-first traversal method is used to explore the path; whenever the end point is traversed, a partial path can be obtained; considering a specific scenario, if the red line is traversed, a partial path {A, B, C} will be obtained; however, the actual situation may allow a new node B' to be inserted into the existing path to optimize the path, and B' represents a new node inserted into the existing path; for example, node B' can be reasonably inserted between B and C, thereby forming a possibly better path {A, B, B', C}.

[0023] Compared with the prior art, the present invention has the following beneficial effects: The introduction of the present invention greatly reduces the workload of planners; batch decisions and specific scheduling details can be fully automated by embedded advanced models and intelligent algorithms; this intelligent decision-making mechanism not only improves work efficiency, but also ensures the accuracy and rationality of production scheduling; the core of the present invention lies in constructing a multi-objective optimization model and cleverly converting the constraints of specification fluctuation types into ε-constraints; by adjusting different ε values, the model can automatically generate a variety of feasible decision-making plans; the algorithm will automatically traverse multiple preset ε value ranges to provide decision makers with a rich and diverse selection of production scheduling strategies, thereby meeting the needs of different scenarios and enhancing the flexibility and adaptability of decision-making; at the algorithm implementation level, the present invention innovatively introduces a pulse propagation algorithm, which can be divided into two steps: the delimitation stage and the pulse stage, in which the algorithm time is concentrated in the delimitation stage; it is worth noting that the delimitation matrix generated in the delimitation stage is highly reusable, and the delimitation stage does not need to be repeatedly executed under different ε values; this feature greatly reduces the workload of repeated calculations, effectively shortens the overall running time of the algorithm, and achieves a significant improvement in computational efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 This is a schematic diagram of the overall process of an intelligent scheduling multi-objective optimization method based on a pulse propagation algorithm according to the present invention; Figure 2 This is a schematic diagram of the overall algorithm flow of an intelligent scheduling multi-objective optimization method based on a pulse propagation algorithm according to the present invention; Figure 3 Schematic diagram of the delimitation process of an intelligent scheduling multi-objective optimization method based on a pulse propagation algorithm according to the present invention; Figure 4 A pulse process diagram of an intelligent scheduling multi-objective optimization method based on a pulse propagation algorithm according to the present invention; Figure 5 A schematic diagram of a path improvement generated by a depth-first search of an intelligent scheduling multi-objective optimization method based on a pulse propagation algorithm according to the present invention; Figure 6 This is a schematic diagram of an insertion algorithm for an intelligent scheduling multi-objective optimization method based on a pulse propagation algorithm according to the present invention. DETAILED DESCRIPTION

[0025] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0026] Embodiment: The present invention provides a technical solution, a multi-objective optimization method for intelligent scheduling based on pulse propagation algorithm, such as Figure 1 As shown, the method includes the following steps: S01: Scheduling data preparation stage, used to make pre-decision on the schedulable resources in the collection pool and generate data for the input model; the collection pool refers to a collection of workpieces that meet the production scheduling conditions; the pre-decision includes: assigning feed matching parameters to workpieces, deciding on production batches, and pre-processing workpieces of the same specifications. S02: The multi-objective model establishment phase uses mathematical modeling to characterize the scheduling rules and optimization objectives. The optimization objectives include maximizing feed matching, minimizing inlet thickness fluctuation, and minimizing order thickness fluctuation. The scheduling rules include specification transition constraints, specific workpiece sequence constraints, and roll period upper limit constraints. S03: Pulse propagation algorithm stage, solving the multi-objective model by designing an ε-constraint and a pulse propagation algorithm; the ε-constraint is specifically introduced as a parameter and , the minimization of inlet thickness fluctuation and minimization of order thickness fluctuation are transformed into constraint conditions, and the maximization of feed matching is transformed into a single-objective model of minimizing the negative value of feed matching, and then the pulse propagation algorithm is used to solve the single-objective model; where: parameters is the upper limit of the inlet thickness fluctuation; parameter This is the upper limit of order thickness fluctuation.

[0027] In step S01: for the schedulable resources in the collection pool, a preliminary decision is made and data for the input model is generated, thereby preparing the scheduling data. The scheduling data preparation process includes the following steps: S101. Assign material matching parameters to the workpieces. By building a scoring system for material matching, each workpiece is assigned a material matching parameter. The scoring system is divided into two parts: basic score and correction score. The basic score is assigned different scores according to the priority of the downstream process supply corresponding to the workpiece. The higher the score, the higher the material supply demand of the downstream process corresponding to the workpiece. The correction score modifies the basic score according to special workpieces and special circumstances. For example, urgent workpieces and must-be-scheduled workpieces are given a greater correction weight. The basic score is assigned based on the priority of the downstream process corresponding to the workpiece. For example, a workpiece with a downstream process of 'automotive sheet stamping' (delivery time ≤ 3 days) is assigned 80-100 points, while a workpiece with a downstream process of 'general civilian sheet metal' (delivery time ≥ 7 days) is assigned 40-60 points. The modified score is adjusted based on the 'urgency and must-have attributes': 20-30 points are added for urgent orders (required for delivery within 48 hours), 30-50 points are added for must-have workpieces (due to a shortage of material in the downstream process), and 0 points are added for no special circumstances. S102. Decide on a production batch and the workpieces corresponding to the production batch; determine the next production batch based on the status of the production line, and screen the workpieces that can be arranged in each batch; calculate the sum of the feed matching degrees of the workpieces in each batch based on the feed matching degree of each workpiece determined in step S101; select the batch with the largest sum of feed matching degrees as the next batch to be arranged, and the workpieces in this batch are the workpieces screened out to be arranged; S103. Preprocess the workpieces of the same specifications. Since the goal includes minimizing the total specification fluctuation value, it is usually hoped that the workpieces of the same specifications can form a local "small batch" production to reduce the specification fluctuation. In order to reduce the scale of the problem, it is necessary to identify the workpieces of the same specifications. The specifications of the workpieces are detected and identified. For workpieces of the same specifications, only a maximum of N pieces are retained, where N is a configurable parameter, and the remaining workpieces are deleted from the workpieces to be arranged. After a plan is formed by completing the subsequent algorithm steps, the deleted workpieces of the same specifications are inserted into feasible positions while ensuring that all constraints are met.

[0028] The scheduling object is the workpiece. Each workpiece has several known attributes, such as inlet thickness, order thickness, feed matching, weight, etc. Multiple workpieces that meet the production requirements form a pool to be scheduled. The collection pool refers to a collection of workpieces that meet the conditions for production and manufacturing scheduling. The workpieces in the collection pool must meet the following conditions: 1. They have completed the previous process (such as hot rolling and flattening) and passed the quality inspection; 2. They have the process parameters required for rolling (such as material, width, initial hardness); 3. They have been entered into the production system, and the subsequent process has confirmed the feeding requirements to avoid the situation where there is no receiving process after scheduling.

[0029] The entry thickness is the material thickness of the workpiece before production rolling (the production rolling process may change the workpiece thickness) The order thickness is the material thickness of the workpiece when it is produced and processed into the finished product; The workpieces of the same specifications are those with the same entry width, entry thickness, order thickness, and steel grade. The core purpose of identifying workpieces of the same specifications is to reduce fluctuations in specification transitions: when joining workpieces of the same specifications, the rolling mill does not need to adjust parameters such as the roll gap and pressure, which can reduce equipment adjustment time (a single adjustment takes 5-8 minutes) and avoid thickness deviation during the adjustment process (the fluctuation value can be reduced by more than 60%). Even if the workpiece meets the core specification requirements of "entry thickness, order thickness, and material grade are all the same", there are still differences. These differences are an important basis for scheduling decisions (such as feed priority and insertion timing); these differences include feed matching parameters, urgency and delivery requirements, completion time and status of the previous process, and the acceptance capacity of the subsequent process.

[0030] Regarding "for workpieces of the same specification, only retain at most N pieces", N pieces are dynamically configurable and adjustable, mainly considering that some workpieces can be connected with other workpieces no matter where they are placed. For such "universal" workpieces, N pieces can be reserved during production scheduling, so that they can be put into production in the later production scheduling. Not all workpieces must be scheduled at the moment, and they can be scheduled according to a certain quantity or a certain time. Therefore, there is no need to insert the deleted and retained workpieces of the same specification into a certain position in this production scheduling; the reason for retaining at most N workpieces is to control the scale of the initial problem: if there are more than 10 workpieces of the same specification in the collection pool, the number of scheduling path combinations will increase exponentially (for example, the number of combinations of 15 workpieces exceeds 10 8 ), which doubles the algorithm time. Retaining N pieces (usually 2-5 pieces, which can be adjusted dynamically according to the total number of workpieces) can reduce the number of initial combinations by more than 50%. At the same time, when the temporarily stored workpieces are subsequently inserted, they can be directly connected because their specifications are consistent with those of the already arranged workpieces, without affecting the overall fluctuation constraint and feeding matching degree.

[0031] In step S02: mathematical modeling is used to describe 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: S201: A mathematical model is established to represent maximizing the feed matching degree, minimizing the inlet thickness fluctuation, and minimizing the order thickness fluctuation; and the constraint conditions and objective function are characterized; the mathematical model is as follows: ; ; ; in, represents the maximum feed matching degree, represents the minimization of inlet thickness fluctuations, represents minimizing the fluctuation of order thickness; I represents the set of all workpieces to be selected, I={0,1,…,n}, 0 is the starting point, n is the end point; c i Indicates the feeding matching degree of workpiece i; y i Indicates whether artifact i is used; represents the workpiece that follows workpiece i and meets all transition specifications; r i,j represents the thickness fluctuation of the entrance where workpiece i and workpiece j meet; t i,j Indicates the order thickness fluctuation of workpiece i and workpiece j; Select 'maximize feed matching, minimize inlet thickness fluctuation, and minimize order thickness fluctuation' as the optimization objectives based on the following: The material matching degree is directly related to the connection between the downstream process and the material availability of the current process. If the material matching degree is low (for example, the workpiece urgently needed in the downstream automotive sheet stamping process is not scheduled for production), the downstream process will be left waiting for materials. Fluctuations in the inlet thickness affect the stability of the rolling mill: when the fluctuation exceeds 0.5 mm, the rolling mill is prone to "bouncing", resulting in partial thickness deviations in the workpiece and a 3%-5% increase in the scrap rate. Fluctuations in order thickness affect the qualified rate of finished products: the order thickness is the final thickness required by the customer. Fluctuations exceeding 0.1mm will cause the product to not meet the order requirements and the rework rate will exceed 10%.

[0032] The constraints are as follows: Constraint groups A1, A2, and A3 are specification transition constraints, which are used to ensure that the sorted workpieces can be welded to adjacent workpieces; Constraint A4 is a constraint on the front and back order of specific workpieces; Constraint A5 is a roll period upper limit constraint; A1: Each selected workpiece has exactly one predecessor and 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 scheduled before workpiece i and meet the specification transition constraint. That is, the sum of whether workpiece j and workpiece i are scheduled adjacently is 0; ; in, It means that the workpieces that can be arranged in front of workpiece i meet all the specification transition constraints between them. Indicates that the workpieces that can be ranked before workpiece i and meet all transition constraints are eliminated from the set of all selected workpieces I, that is, the set of workpieces that are ranked before workpiece i but cannot meet the transition constraints between workpiece i and workpiece i; x j,i Indicates whether workpiece i is scheduled to be produced immediately after workpiece j, and the value is 1 or 0, x j,i =1 means that workpiece i is placed immediately after workpiece j, and x j,i =0 means that workpiece i is not immediately after workpiece j; (2) For any workpiece i in the candidate set I, it cannot be adjacent to workpiece j in the set of workpieces that cannot be scheduled after workpiece i and meet the specification transition constraint. That is, the sum of whether workpiece i and workpiece j are scheduled adjacently is 0; ; in, It means that the workpieces that can be arranged behind workpiece i meet all the specification transition constraints between them. Indicates that the workpieces that can be ranked after workpiece i and meet all the transition specifications are eliminated from the set of all workpieces to be selected I; that is, the set of workpieces that are ranked after workpiece i and cannot meet the transition specification constraints with workpiece i; x i,j Indicates whether workpiece j is scheduled to be produced immediately after workpiece i, with a value of 1 or 0. i,j =1 means that workpiece j is placed immediately after workpiece i, and x i,j=0 means that workpiece j is not immediately after workpiece i; (3) For any workpiece i starting from the first position, if workpiece i is scheduled, then workpiece i can only be scheduled adjacent to a workpiece j among all the workpieces that can be scheduled before workpiece i, that is, both the left and right sides of the equal sign are 1; if workpiece i is not scheduled, then workpiece i cannot be scheduled adjacent to any workpiece j among all the workpieces that can be scheduled before workpiece i, that is, both the left and right sides of the equal sign are 0; ; in, It means that the workpieces that can be arranged in front of workpiece i satisfy all the transition constraints between them. i Indicates whether artifact i is used, y i =1 means workpiece i is placed in, y i =0 means that workpiece i is not included, and I\{0} means that the set of workpieces after the starting position 0 is eliminated from all optional sets; (4) For any workpiece i, if workpiece i is scheduled, then workpiece i can only be scheduled adjacent to a workpiece j among all the workpieces that can be scheduled after workpiece i, that is, both the left and right sides of the equal sign are 1; if workpiece i is not scheduled, then workpiece i cannot be scheduled adjacent to any workpiece j among all the workpieces that can be scheduled after workpiece i, that is, both the left and right sides of the equal sign are 0; ; in, It means that the workpieces that can be arranged behind workpiece i satisfy all the transition constraints between them. i Indicates whether artifact i is used, y i =1 means workpiece i is placed in, y i =0 means that workpiece i is not discharged; A2: The conditions to be used for the first and last items are: ; Workpiece 0 at the start position and workpiece n at the end position must be queued. Indicates that the last workpiece that has been queued during production must be queued. Indicates that this production schedule ends at a certain virtual workpiece n.

[0033] Starting point 0 is not a "virtual empty node" but the final workpiece of the previous batch. Forcibly selecting 0 ensures a seamless connection between the current production schedule and the preceding batch, avoiding interruptions in the rolling process. For example, the mill does not need to readjust the roll gap or pressure due to a "no starting workpiece," thus reducing equipment idle time.

[0034] The end point n is the "virtual end point workpiece" of the current batch production. Its core function is to "define the production boundary of the current batch" to form a closed production loop: after the current batch ends with n, the next batch can use n as the new "starting point 0" to realize a continuous production cycle.

[0035] A3: Eliminating sub-loop constraints is: ; Among them, u i and u j is an auxiliary variable; it represents the sequence number of workpiece i and workpiece j after they are arranged, ensuring that when workpiece i and workpiece j are arranged adjacently, the sequence numbers of workpiece j and workpiece i do not decrease; A4: Set a specific workpiece order constraint. If placing j before i will affect production quality, then place j after i: ; in represents the set of workpieces that precede or follow workpiece i and have an impact on the quality of workpiece i. This formula indicates that for any workpiece i, any workpiece j that precedes workpiece i and has an impact on its quality requires that the sequence number of workpiece j is greater than that of workpiece i. A5: Rolling period upper limit constraint: ; Among them, w i represents the tonnage of workpiece i; W represents the upper limit constraint of the roll period; for all workpieces i that are queued this time, the sum of their weight tonnage does not exceed the upper limit W of the roll period; The roll life limit constraint W is set based on the wear cycle of core equipment such as rolls. For example, in a cold rolling mill, 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, causing the thickness deviation of subsequent workpieces to exceed ±0.01mm (exceeding the requirements of the national standard GB / T 708-2019). Furthermore, exceeding the upper limit shortens the roll replacement cycle (from 3 days to 1 day), increasing equipment maintenance costs. Therefore, setting the roll life limit W is a key constraint for balancing production efficiency with equipment life and product precision. A6: Set the variable value range constraint: . Indicates that for any workpiece i, its corresponding sequence number is a natural number from 0 to n.

[0036] Step S03 includes the following steps: S301: Perform multi-objective model conversion based on ε-constraint; S302: Establishing a solution model M(ε) based on the pulse propagation algorithm; S303: Implement the algorithm process of the delimitation phase; S304: Implementing the pulse phase algorithm process; S305: Setting the pulse propagation algorithm acceleration strategy.

[0037] In step S301: the above multi-objective model belongs to a multi-objective optimization model, and the parameters are introduced into the multi-objective optimization model. and , convert the second and third objectives into ε-constraints: ; ; Setting parameters and parameters The value sets are V1 and V2 respectively, let At the same time, the first goal is transformed into a minimization problem, for any , establish the following single-objective model with ε-constraint, denoted as model M(ε): : ; in Negative value that minimizes feed matching.

[0038] In step S302: first, M(ε) is converted into a network flow problem, and a pulse propagation algorithm is designed to solve the network flow problem, and finally the overall algorithm flow is obtained; Reconstruct the model M(ε) into a network flow problem; consider the workpieces as nodes in the network graph and describe the connection relationship of the workpieces as arcs; establish a network graph G(N, E), where N is the set of nodes, satisfying N=I, and E is the set of arcs; any arc (i, j)∈E has three key properties: first, the thickness fluctuation r of the corresponding entrance of the connection i,j , the second is the corresponding order thickness fluctuation t i,j , and the third is the distance d spanned by the connection i,j , the d i,j The value is -c j Consider both entry thickness fluctuations and order thickness fluctuations as resource consumption along the arc segment. Based on this, the problem is transformed into finding a shortest path from starting point 0 to end point n in the network that consumes no more than ε, requiring that each node in the path be passed through at most once. This transforms the problem into the Elementary Shortest Path Problem with Resource Constraints (ESPPRC). Furthermore, the specific workpiece order constraint is an additional constraint that must be considered in ESPPRC. 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 delimitation stage and the pulse stage. The delimitation phase is used to determine the shortest distance from each node to the destination under given different resource consumption conditions; the so-called different resource consumption conditions refer to two types of resource consumption: entrance thickness fluctuation and order thickness fluctuation. The parameter and parameters After the constraints; The pulse phase is based on an implicit enumeration strategy of the solution space. This strategy uses mathematical rules to preemptively exclude invalid paths, avoiding explicit traversal of all possible path sets and exploring potential subspaces. A pulse signal is emitted from the starting node 0∈I, propagating 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 consumed resources r(p). To optimize search efficiency, a pruning strategy is used to limit the further propagation of the pulse and reduce the search space. Whenever a pulse successfully reaches the final node, it carries information about a complete and feasible path from the starting point to the end point. Finally, the overall algorithm process is obtained, such as Figure 2 As shown; parameters in the algorithm input By the largest Value and maximum Value composition, that is ; Delimiting step length ,in and are the delimiting steps of the entrance thickness and ordering thickness in the pulse algorithm, respectively, where , ; The overall algorithm process is described as follows: Line 1 is responsible for initialization, including setting the initial state of partial paths, cumulative distance, resource consumption, and the optimal path set; Line 2 performs the delimitation process to calculate and determine the lower bound of the shortest distance for each node in the network (see Algorithm 3 for the specific process); Lines 3 to 5 generate the result path; traverse ∈V, call the recursive function pulse for each ε, and store the optimal path generated each time into the set P; Line 6 returns the set P of optimal paths found during the recursive search.

[0039] In step S303: Figure 3 As shown, in the algorithm flow of the delimitation phase, let represents the length of the shortest path that satisfies the resource constraints found during the delimitation process, and As the upper limit of the iterative process; the bounding process can find the shortest distance to the end point for each node i∈I under the condition of resource consumption r ; When a path p reaches node i, if , then prune and no longer propagate; the working principle of the delimitation phase is: for each node i∈I, under a given resource consumption Solve ESPPRC in the case of , since both resources have been consumed, there are 0 resource units left and few feasible solutions, so the pulse process can quickly find the optimal solution; each optimal solution found is a given resource consumption Under the condition of the lower bound of the minimum distance that any partial path to node n∈I can achieve; after finding the limit, for each node i∈I, under the given resource consumption Solve an ESPPRC under the condition of ; the current problem has fewer constraints, but the resource consumption is The lower bound of the path distance has been obtained; by using the information calculated previously, the same process is repeated in reverse order; this process will produce a lower bound matrix represented as , which contains the lower bounds computed for each node i∈I at each discrete bounding step between 0 and ε , Similarly, as the available resources increase, the problem solved in the bounded solution has fewer constraints and becomes more difficult to solve, but the number of known bounds will also increase, thereby increasing the chance of pruning some paths using the bounded pruning strategy; in the specific implementation of Algorithm 2: Line 1 is responsible for initializing the value of resource consumption; Lines 2 to 6 start the delimiting scheme, traversing each possible resource consumption of each node; Lines 7-8 use the impulse algorithm to solve an ESPPRC problem for each node given the current resource consumption; Lines 9 to 13 store the optimal solution for each node found, that is, the lower bound of the shortest path length, in the corresponding position of the lower bound matrix; if a particular problem is not feasible under the given resource consumption, the lower bound is set to positive infinity.

[0040] In step S304: Figure 4 As shown, the recursive process pulse in the pulse phase algorithm process is for the head node set of each outgoing arc starting from a given node i. Perform the operation; in the process of implementing the pruning strategy, the infeasibility check and delimitation check are first performed. The infeasibility pruning ensures the uniqueness of the path, that is, each node is visited at most once, and the correctness, that is, avoids production quality problems caused by node order errors; it is used to decide whether to prune the incoming pulse; if the pulse is not pruned, the current node is added to the partial path being constructed; then the algorithm is used to traverse all the arc head nodes of the current node, and recursively call the pulse process for each node to propagate the pulse; when the pulse process is called at the final node, the pulse process updates the known optimal path information as needed and stops further pulse propagation; after that, the algorithm recursively continues to propagate other potential pulses through the backtracking mechanism.

[0041] In step S305: the pulse propagation algorithm acceleration strategy is used to combine the characteristics of the scheduling problem and propose two strategies: storing the optimal path in the delimiting stage and improving the optimal path with the insertion algorithm to accelerate the pulse algorithm; The optimal path is stored in A during the delimitation phase to improve the 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 delimitation phase, starting from node i, given the resource consumption of Under these conditions, when solving ESPPRC, nodes that simultaneously meet the following two conditions are excluded from the search path: a. They are adjacent to workpiece i; b. The entrance width is larger than workpiece i; the optimal path obtained by solving is recorded as , save it to A, that is ; During the pulse process, for path p to reach node i, and the given resource consumption is When p and Is there an intersection between the node sets of path p and path ? Perform splicing and return it as the optimal path; if it exists, terminate the path p and propagate it to node i; The insertion algorithm improves the optimal path and is used to improve the partial path that has been searched, and to check whether there are possible insertion points and whether there are nodes such as B' that can further reduce the target value; in the pulse search process, the depth-first traversal method is used to explore the path; whenever the end point is traversed, a partial path can be obtained; considering a specific scenario, if you traverse along the red line, you will get a partial path of {A, B, C}; however, the actual situation may allow the insertion of a new node B' in the existing path to optimize the path, and B' represents the new node inserted in the existing path; for example, node B' can be reasonably inserted between B and C to form a possibly better path {A, B, B', C}, such as Figure 5 As shown, reference Figure 6In Algorithm 4, an insertion algorithm is introduced to improve the searched partial path. 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.

[0042] The specific process of the present invention is described below by taking an example of a steel company: During the scheduling data preparation phase, a steel company's cold rolling mill had five production-qualified workpieces (numbered 1-5) in its collection pool. Together with the starting point 0 and the ending point 6, there were seven nodes requiring scheduling. Each workpiece was assigned a feed matching parameter: workpiece 1's feed matching was 80 (60 basic points + 20 emergency correction points), workpiece 2's was 70 (50 basic points + 20 standard correction points), workpiece 3's was 60 (60 basic points + no correction points), workpiece 4's was 50 (50 basic points + no correction points), and workpiece 5's was 40 (40 basic points + no correction points). The feed matching for starting point 0 and ending point 6 was fixed at 100. When deciding on a production batch, since there was only one batch in the collection pool, the sum of its feed matching degrees was calculated to be 80 + 70 + 60 + 50 + 40 = 300, making this batch the batch to be scheduled. When preprocessing workpieces of the same specification, specification A includes workpieces 1, 2, and 4, 2 pieces are retained (workpieces 1 and 2), and workpiece 4 is temporarily stored; specification B includes workpieces 3 and 5, and 2 pieces are retained and included in the schedule.

[0043] According to step S103, the purpose of pre-processing workpieces of the same specification is to reduce the scale of the initial scheduling problem, rather than to permanently exclude temporarily stored workpieces. The specific rules are: for workpieces of the same specification, initially only a maximum of N pieces (configurable parameters) are retained for scheduling calculations, and the remaining workpieces are temporarily removed from the "pool of workpieces to be scheduled" (i.e., "temporarily stored"); after the initial scheduling plan is formed, the temporarily stored workpieces are inserted into feasible positions under the premise of meeting all constraints (such as specification transition, sequence, roll period upper limit, etc.). In this example, specification A includes workpieces 1, 2, and 4, and N=2 is set (2 pieces are retained). Therefore, initially only workpieces 1 and 2 are retained for scheduling calculations, 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.

[0044] During the multi-objective model establishment phase, the constructed multi-objective model includes three optimization objectives: maximizing the feed matching degree, minimizing the inlet thickness fluctuation, and minimizing the order thickness fluctuation. In terms of constraints, the upper limit of the roll period is that the total weight does not exceed 10 tons; in the order constraint, if workpiece 5 is placed before workpiece 3, it will cause quality problems, so it is necessary to satisfy u5≥u3 (u iis the sequence number); starting point 0 and end point 6 must be used, that is, y0=1, y6=1. The entry thickness fluctuation and order thickness fluctuation are calculated based on the attribute differences between adjacent workpieces. For example, the entry thickness fluctuation from workpiece 0 to 1 is 2.0mm, and the order thickness fluctuation is 1.0mm. The entry thickness fluctuation from workpiece 1 to 3 is 1.0mm, and the order thickness fluctuation is 0.5mm.

[0045] In the pulse propagation algorithm stage, a multi-objective model conversion based on ε-constraint is first performed to set the upper limit of the inlet thickness fluctuation =2.0, upper limit of order thickness fluctuation =1.5, converting the original multi-objective model into a single-objective model min-Σc i y i In the delimitation phase, the shortest distance from each node to the end point is calculated. For example, the shortest distance from node 3 to the end point 6 is 3.0 under the resource conditions (entrance thickness fluctuation 0.5, order thickness fluctuation 0.3). In the pulse phase, a pulse is sent from the starting point 0 to explore the path. The path 0→1→3→6 is larger than the total entrance thickness fluctuation of 3.0. Pruned, path 0→2→4→6 due to the total entrance thickness fluctuation of 3.0 exceeds The paths 0→1→4→6 are pruned, while the total entry thickness fluctuation of 2.0 and the total order thickness fluctuation of 1.0 meet the constraints, and the total feed matching degree is 130. At the same time, the acceleration strategy is applied to concatenate the optimal path 0→2→6 stored in the delimitation stage with the exploration path, and a feasible path 0→1→4→2→6 with a total feed matching degree of 200 is obtained.

[0046] After the initial scheduling algorithm generates a basic path (e.g., 0→1→2→6), a secondary insertion check is performed on a temporarily stored workpiece (e.g., workpiece 4). The algorithm checks the transition constraints between workpiece 4 and adjacent workpieces in the path (e.g., whether the entry thickness and order thickness fluctuations meet requirements); checks whether the total weight after insertion still meets the roll period limit (10 tons); and confirms that the insertion does not violate specific workpiece sequence constraints (e.g., a front-to-back order that does not affect quality). 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.

[0047] The optimization results show that the optimal path 0→1→4→2→6 has a total feed 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 (which meets the 10-ton roll schedule limit constraint). Compared to the traditional weighted method, this method improves feed matching by 20% while meeting the thickness fluctuation constraint, shortens scheduling time from 2 hours to 15 minutes, and improves efficiency by 87.5%. Furthermore, by inserting pre-processed workpieces of the same specification, the number of specification changes is reduced by three, reducing production costs by approximately 12%.

[0048] Nodes 3 and 5, which were not included in the process, are processed differently based on the "phased scheduling + temporary storage insertion" mechanism and constraints. Their specific destinations are as follows: (1) The feasible position to be inserted into the current batch after temporary storage is based on the 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 arranged; after the subsequent algorithm steps form a plan, the deleted workpieces of the same specification are inserted into the feasible position under the condition that all constraints are met." In the example, if nodes 3 and 5 belong to the category of "temporary storage of workpieces of the same specification" (such as specification B includes 3 and 5, set N=1, initially only 3 or 5 is retained for scheduling, and the other workpiece is temporarily stored), then after the optimal path 0→1→4→2→6 is generated, the feasibility of connecting 3 and 5 with the adjacent nodes in the path will be checked: if the thickness fluctuation between the entrance of node 3 and workpiece 2 (2→6 section in the path) is 0.3mm≤ =2.0, order thickness fluctuation 0.2mm≤ =1.5, and the total weight after insertion (7 tons + weight of 3) ≤ 10 tons, then insert 3 between "2→6" to form a new path 0→1→4→2→3→6; if the constraints are not met during temporary storage (for example, the upper limit of the rolling period is exceeded after insertion), continue to temporarily store it to the next batch.

[0049] (2) Inclusion in the next batch production schedule (due to the current batch constraint) If nodes 3 and 5 are not temporarily stored but are not included in the optimal path because the "current batch constraint is not satisfied", they will automatically enter the "next batch collection pool" and participate in subsequent production scheduling: 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 entrance thickness fluctuation of 0→3 is 3.0mm> =2.0), does not meet the ε constraint of the current batch, and needs to adjust the ε value of the next batch (e.g., relax =3.5); Constraint 2: Rolling period limit overrun - if the sum of the weights of nodes 3 and 5 is 4 tons, and the total weight of the optimal path of the current batch is 7 tons, after adding 7+4=11 tons, which is greater than 10 tons (rolling period limit), it must 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 must meet the "not before 3" requirement (constraint A4), if node 3 is not included in the current batch, 5 must also be postponed to the next batch to avoid order conflicts that affect quality.

[0050] 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 embodied in other specific forms without departing from the spirit or essential characteristics of the invention. Therefore, the embodiments should be considered in all respects as illustrative and non-restrictive, and the scope of the invention is defined by the appended claims, not the foregoing description, and all variations within the meaning and range of equivalents of the claims are intended to be included therein. Any reference sign in a claim should not be construed as limiting the claim to which it relates.

Claims

1. An intelligent scheduling multi-objective optimization method based on pulse propagation algorithm, characterized in that: The following steps are involved: S01: Scheduling data preparation stage: Pre-decision is made for schedulable resources in the pool and data for the input model is generated. The pool is a collection of workpieces that meet the production scheduling conditions. Pre-decision includes assigning feed matching parameters to workpieces, determining production batches, and pre-processing workpieces of the same specifications. S02: Multi-objective model establishment phase, using mathematical modeling to characterize scheduling rules and optimization objectives. The optimization objectives include maximizing feed matching, minimizing inlet thickness fluctuation, and minimizing order thickness fluctuation. The scheduling rules include specification transition constraints, specific workpiece sequence constraints, and roll period upper limit constraints. S03: Pulse propagation algorithm stage, solving the multi-objective model by designing an ε-constraint and a pulse propagation algorithm; the ε-constraint is specifically introduced as a parameter and , the minimization of inlet thickness fluctuation and minimization of order thickness fluctuation are transformed into constraint conditions, and the maximization of feed matching is transformed into a single-objective model of minimizing the negative value of feed matching, and then the pulse propagation algorithm is used to solve the single-objective model; where: parameters is the upper limit of the inlet thickness fluctuation; parameter It is the upper limit of order thickness fluctuation.

2. The method according to claim 1, characterized in that Step S01 includes the following sub-steps: S101. Assigning a feed matching parameter to a workpiece; by constructing a workpiece feed matching scoring system, each workpiece is assigned a feed matching parameter; the scoring system is divided into two parts: basic score and modified score; the basic score is assigned different scores based on the priority of the downstream process supply corresponding to the workpiece; the modified score is used to modify the basic score based on special workpieces and special circumstances; S102, determining a production batch and the workpieces corresponding to the production batch; Determine the next batch to be produced based on the status of the production line, and screen the workpieces that can be arranged in each batch; calculate the sum of the feed matching degrees of the workpieces in each batch based on the feed matching degree of each workpiece determined in step S101; The batch with the largest sum of feed matching degrees is selected as the next batch to be sorted, and the workpieces in this batch are the workpieces to be sorted; S103, pre-processing workpieces of the same specifications; the workpieces of the same specifications refer to workpieces with the same specifications and attributes; Identify workpieces of the same specification and retain up to N of them, where N is a configurable parameter. Delete the remaining workpieces from the queue. After a plan is formed in subsequent algorithm steps, insert the deleted workpieces of the same specification into feasible locations while ensuring that all constraints are met.

3. 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 feed 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, represents the maximum feed matching degree, represents the minimization of inlet thickness fluctuations, represents minimizing the fluctuation of order thickness; I represents the set of all workpieces to be selected, I={0,1,…,n}, 0 is the starting point, n is the end point; c i Indicates the feeding matching degree of workpiece i; y i Indicates whether artifact i is used, yi =1 means workpiece i is loaded, yi =0 means that workpiece i is not discharged; represents the workpiece that follows workpiece i and meets all transition specifications; r i,j represents the thickness fluctuation of the entrance where workpiece i and workpiece j meet; t i,j represents the order thickness fluctuation of the connection between workpiece i and workpiece j; x i,j Indicates whether workpiece j is immediately after workpiece i, and the value is 1 or 0. x i,j =1 means that workpiece j is immediately after workpiece i, x i,j =0 means that workpiece j is not immediately after workpiece i; The constraints include specification transition constraints, specific workpiece front and back order constraints, roll period upper limit constraints and variable value range constraints.

4. The method according to claim 3, characterized in that The constraints are as follows: A1: Each selected workpiece has exactly one predecessor and 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 ranked before workpiece i and meet the specification transition constraint, that is, ； in, It means that the workpieces that can be arranged in front of workpiece i meet all the specification transition constraints between them. Indicates that the workpieces that can be ranked before workpiece i and meet all transition specifications are eliminated from all the workpiece sets I to be selected; x j,i Indicates whether workpiece i is scheduled to be produced immediately after workpiece j, and the value is 1 or 0, x j,i =1 means that workpiece i is placed immediately after workpiece j, and x j,i =0 means that workpiece i is not immediately after 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 ranked after workpiece i and meet the specification transition constraint, that is, ； in, It means that the workpieces that can be arranged behind workpiece i meet all the specification transition constraints between them. It means that the workpieces that can be ranked after workpiece i and meet all the transition specifications are eliminated from the set of all workpieces to be selected I; (3) For any workpiece i starting from the first position, if workpiece i is scheduled, then workpiece i can only be scheduled adjacent to a workpiece j among all the workpieces that can be scheduled before workpiece i, that is, ； (4) For any workpiece i, if workpiece i is scheduled, then workpiece i can only be scheduled adjacent to one workpiece j among all the workpieces that can be scheduled behind workpiece i, that is, ； A2: Workpiece 0 at the start position and workpiece n at the end position must be queued, i.e. ； A3: Eliminating sub-loop constraints is: ； Among them, u i and u j is an auxiliary variable, indicating the sequence number of workpiece i and workpiece j after they are queued; A4: For a specific workpiece, if j is placed before i, it will affect the production quality. ； in It represents the set of workpieces that are placed before workpiece i and will affect the quality of workpiece i; A5: Rolling period upper limit constraint: ； Among them, w i represents the tonnage of workpiece i; W represents the upper limit constraint of the roll period; A6: Variable value range constraints: 。 5. The method according to claim 1, wherein Step S03 includes the following sub-steps: S301: Perform multi-objective model conversion based on ε-constraint; S302: Establishing a solution model M(ε) based on the pulse propagation algorithm; S303: Implementing the delimitation phase algorithm process, which determines the shortest distance from each node to the end point under given resource consumption conditions; S304: implementing a pulse phase algorithm process, which adopts an implicit enumeration strategy of the solution space and executes a strategy of recursively exploring all possible paths but retaining only feasible paths to reduce the search space; S305: Setting the pulse propagation algorithm acceleration strategy.

6. The method according to claim 5, characterized in that In step S301, the multi-objective model conversion based on ε-constraint is specifically as follows: Introducing parameters into multi-objective optimization models and , convert the second and third objectives into ε-constraints: ； ； Setting parameters and parameters The value sets of are V1 and V2 respectively, let At the same time, the first objective is transformed into a minimization problem, and for any ε∈V, a single-objective model M(ε) with ε-constraint is established: ： ； in Negative value that minimizes feed matching.

7. The method according to claim 5, characterized in that In step S302, a solution model M(ε) based on the pulse propagation algorithm is established as follows: Reconstruct the model M(ε) as a network flow problem; consider artifacts as nodes in a network graph, and describe the connection relationships between artifacts as arcs. Build a network graph G(N, E), where N is the set of nodes, satisfying N=I, and E is the set of arcs. Any arc (i, j)∈E has three key properties: The corresponding entrance thickness fluctuation r i,j ; The order thickness fluctuation corresponding to the connection t i,j ; The distance spanned by the connection d i,j ; The d i,j The value is -c j , where c j is the feeding matching degree of workpiece j; The entry thickness fluctuation and order thickness fluctuation are both regarded as resource consumption passing through the arc segment; The problem is transformed into finding a shortest path from the starting point 0 to the end point n in the network that consumes no more than ε of resources, requiring that each node in the path be passed at most once; The pulse propagation algorithm consists of two core stages: the delimitation stage and the pulse stage. The delimitation stage is used to determine the shortest distance from each node to the end point under given different resource consumption conditions. The so-called different resource consumption conditions refer to two types of resource consumption: entry thickness fluctuation and order thickness fluctuation. The parameter and parameters The pulse phase is based on an implicit enumeration strategy of the solution space, that is, invalid paths are excluded in advance through mathematical rules, avoiding explicit traversal of all possible path sets and exploring potential subspaces; a pulse signal is sent from the starting node 0∈I, and the pulse signal propagates along the arc segments 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 consumed resources 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.

8. The method according to claim 5, characterized in that In step S303, the algorithm flow of the delimitation phase is specifically as follows: make represents the length of the shortest path that satisfies the resource constraints found during the delimitation process, and As an upper limit in the iterative process; The delimitation process is to find the shortest distance to the end point for each node i∈I under the condition that the resource consumption is r ; When a path p reaches node i, if , then prune and no longer propagate; Initial Settings ,in =max(V1), =max(V2); For each node i∈I, given resource consumption Solve ESPPRC under the given resource consumption. Solve an ESPPRC in the case where is the delimiting step size of the order thickness in the pulse algorithm; By using the information calculated previously, we continue to repeat the same process in reverse order to produce the lower bound matrix , which contains for each node i∈I between 0 and The lower bound calculated for each discrete bounding step between , is the delimiting step size of the inlet thickness in the pulse algorithm, Same thing.

9. The method according to claim 5, characterized in that In step S304, the pulse phase algorithm flow is specifically as follows: The recursive process pulse is the set of head nodes of each outgoing arc starting from a given node i. When implementing the pruning strategy, first perform an infeasibility check and a delimitation check. Infeasibility pruning ensures the uniqueness and correctness of the path. If the pulse has not been pruned, add the current node to the partial path being constructed; Traverse all arc-head nodes of the current node and recursively call the pulse process for each node to propagate the pulse; When the pulse process is called 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 the backtracking mechanism.

10. The method according to claim 5, characterized in that In step S305, the pulse propagation algorithm acceleration strategy includes two strategies: storing the optimal path in the delimitation phase and improving the optimal path through the insertion algorithm; The optimal path is stored in A during the delimitation phase to improve the 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 delimitation phase, starting from node i, given a resource consumption of When solving ESPPRC, exclude nodes that meet both of the following conditions from the search path: a. Neighboring parts belonging to workpiece i; b. The entrance width attribute value is greater than the entrance width attribute value of workpiece i; The optimal path obtained is recorded as , save it to A, that is ; During the pulse process, for path p to reach node i, and the given resource consumption is When p and Is there an intersection between the node sets of path p and path ? Perform splicing and return it as the optimal path; if it exists, terminate the path p and propagate it to node i; The insertion algorithm improves the optimal path for improving the searched partial path, checking whether there are possible insertion points and whether there are nodes that can further reduce the target value; During the pulse search process, the depth-first traversal method is used to explore the path; each time the traversal reaches the end point, a partial path is obtained; new nodes are inserted into the existing path to optimize the path.

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