Tundish production scheduling optimization method

Abstract

The invention provides a tundish production scheduling optimization method, which is characterized in that an optimization model is established by taking the minimum use amount of tundishes as a target, and constraint conditions comprise delivery time constraint, taboo constraint, mixed casting constraint, bedding constraint and maximum continuous casting heat constraint; and the established optimization model is solved by adopting a genetic algorithm, so that an optimized production scheduling scheme is obtained, and the optimized production scheduling scheme comprises steel types produced by each heat and tundish distribution conditions of each heat. According to the tundish production scheduling optimization method, a potential optimal tundish usage amount candidate scheme is rapidly screened out in a global range through a genetic algorithm, and constraint verification and correction are carried out in cooperation with traditional CSPs, so that the constraint verification range of a traditional CSPs model is reduced, and the overall solving efficiency is improved.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of steelmaking, and particularly relates to a tundish production scheduling optimization method. BACKGROUND

[0002] The tundish is a kind of refractory container used in the steelmaking process, which is responsible for receiving molten steel poured from a ladle and then distributing the molten steel to various crystallizers for casting. In order to reduce production costs and improve the utilization efficiency of the tundish, it is necessary to optimize the production scheduling of the tundish based on the requirements of the steelmaking process and the delivery time limit after receiving a production order, so as to complete the production of all orders with the least number of tundishes.

[0003] There are three types of restrictions on the use of tundishes, which are "padding", "mixed pouring" and "taboo". Among them: for some steel grades with similar compositions, they can be arranged to be poured by the same tundish and follow the specified order, which is "mixed pouring"; for example, steel grade B is similar to steel grade A in composition, steel grade C is similar to steel grade B in composition, but steel grade C is not similar to steel grade A in composition, so they can be poured in the same tundish in the order of steel grade A, B and C. On the contrary, some steel grades have clear requirements that they cannot be arranged to be poured in the same tundish, which is "taboo". After the production of steel grade D in the previous heat, the subsequent plan is to produce steel grade F, but due to the large difference in composition between steel grade D and steel grade F (usually there is also a taboo relationship between D and F), a certain number of heats of steel grade E must be arranged to "wash the ladle" (i.e. by producing steel grade E to approach the composition of the trace amount of molten steel in the ladle to that of steel grade F); this is "padding" between steel grade D and steel grade F by inserting steel grade E.

[0004] For the above-mentioned optimization of the tundish, the traditional constraint satisfaction problem (CSPs) solving method is prone to slow solving speed and difficulty in quickly locating the global optimum due to constraint combination explosion when facing a large number of heats (tens to hundreds of heats). SUMMARY

[0005] In view of the deficiencies in the prior art, the present application provides a tundish production scheduling optimization method to optimize the use of tundishes.

[0006] The present application achieves the above technical purpose by the following technical means.

[0007] A tundish production scheduling optimization method:

[0008] An optimization model is established with the least number of tundishes as the target;

[0009] A genetic algorithm is used to solve the optimization model to obtain an optimized production scheduling scheme, including the steel grade produced by each heat and the distribution of the tundish for each heat.

[0010] Further, the objective function of the optimization model is:

[0011] ming N

[0012] wherein g N is the total number of tundishes required for all N heats, and N is the total number of heats;

[0013] For n = 1 ~ N, there are:

[0014]

[0015] wherein g n represents the tundish to which the heat n belongs.

[0016] Further, the optimization model includes the following constraints: delivery time constraint, taboo constraint, mixed pouring constraint, bedding constraint, maximum continuous pouring heat constraint.

[0017] Further, the delivery time constraint is:

[0018]

[0019] wherein N ′ is the maximum value of n satisfying t n ≤ T s , D s is the order quantity of steel grade s, d n is the yield of heat n, p n is a judgment coefficient for determining whether heat n produces steel grade s, s n is the steel grade produced by heat n, t n is the completion time of heat n, and T s is the delivery time of steel grade s.

[0020] Further, the taboo constraint is that the heats belonging to the same tundish must satisfy the taboo relationship between their respective steel grades.

[0021] The mixed pouring constraint is that the heats belonging to the same tundish must satisfy the mixed pouring relationship between their respective steel grades.

[0022] The bedding constraint is that the different steel grades of adjacent heats must satisfy the bedding relationship.

[0023] The maximum continuous pouring heat constraint is that the number of heats belonging to the same tundish is ≤ the maximum continuous pouring heat of the tundish.

[0024] Further, in the genetic algorithm, the chromosome coding design includes: chromosome length = N, the nth gene site is (s n , g n ).

[0025] Further, the genetic algorithm comprises:

[0026] Selection operation: roulette selection method is adopted, and solutions with greater fitness value F are reserved, wherein the fitness function is:

[0027]

[0028] In the formula, p is a constraint satisfaction coefficient, which is calculated as the number of satisfied constraint terms / the total number of constraint terms;

[0029] Cross operation: single-point cross is adopted, and constraint checking is performed after cross, including maximum continuous casting furnace constraint and mixed casting constraint, if the constraint is violated, the cross is abandoned, and the parent is reselected;

[0030] Mutation operation: 1-2 gene sites are randomly selected, and the g n value of the gene sites is modified, and constraint checking is performed after mutation, including taboo constraint and padding constraint, if the constraint is violated, the mutation is abandoned.

[0031] Further, the genetic algorithm is checked and corrected after each iteration, wherein the production scheduling scheme that satisfies all constraint conditions is reserved to the next generation population; for the constraint violation, the constraint propagation method is used for correction, and the scheme that satisfies all constraints after correction is reserved to the next generation population, otherwise it is eliminated.

[0032] Further, the genetic algorithm is initialized according to the following rules:

[0033] The furnace sequence of the steel grade with padding relationship is sorted according to the padding relationship, and the intermediate package serial number of the steel grade with padding relationship at the rear is greater than that of the steel grade with padding relationship at the front;

[0034] The steel grade with mixed casting relationship is preferentially allocated to the same intermediate package;

[0035] The number of furnace sequences of the intermediate package is less than the maximum continuous casting furnace sequence of the intermediate package.

[0036] Further, in the genetic algorithm, when N≤30, the population size is 50-80; when N>30, the population size is 80-120.

[0037] The beneficial effects of the present application are:

[0038] (1) The present application provides an intermediate package production optimization method, wherein the genetic algorithm is used to quickly screen out a potential optimal intermediate package consumption candidate scheme in a global range, and then the traditional CSPs are used for constraint checking and correction, so as to reduce the constraint checking range of the traditional CSPs model, and improve the overall solving efficiency.

[0039] (2) The combination of the genetic algorithm and the traditional CSP algorithm in this invention improves the applicability of the traditional CSP algorithm without changing the constraints and objectives, and better meets the actual application needs of enterprises to "respond quickly to orders and arrange production in a timely manner". Detailed Implementation

[0040] The embodiments of the present invention are described in detail below. The embodiments described below with reference to the present invention are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0041] I. Optimization Problem Modeling

[0042] 1. Furnace number

[0043] A furnace batch, which is a production batch from the start of smelting to the completion of casting, is the smallest production unit in the metallurgical industry. In a production plan, there are N furnace batches in total, and any furnace batch is denoted as furnace batch n (the nth furnace batch), where n = 1 to N.

[0044] 2. Steel type

[0045] Based on the production order, the total required steel grades and quantities are known. Therefore, it is necessary to plan the steel grades to be produced in each heat batch; let s be the steel grade produced in heat batch n. n .

[0046] 3. Intermediate package

[0047] Intermediate packages are assigned to each furnace batch, and the intermediate package to which furnace batch n belongs is denoted as g. n Only adjacent heats can be assigned to the same intermediate package; for example, heats 1-3 are assigned to the first intermediate package, and heats 4-8 are assigned to the second intermediate package. In this embodiment, this can be represented mathematically as follows:

[0048]

[0049] The total number of intermediate packages required for all N furnace cycles is g. N .

[0050] Therefore, the objective function of the optimization problem is:

[0051] ming N

[0052] That is, to minimize the number of intermediate packages.

[0053] 4. Constraints

[0054] 4.1) Delivery time constraints

[0055] The order has a delivery deadline, and the delivery deadline of different steel grades is different, so some steel grades need to be produced in advance (put in the front of the furnace) to meet the delivery deadline. The delivery deadline of steel grade s is T s The completion time of each furnace is determined, and the completion time of furnace n is t n s According to T n and t n , the furnace whose completion time t s is before the delivery deadline T s can be determined. Further, the above delivery deadline constraint can be converted to: the quantity of steel grade s produced by the furnace whose completion time t

[0056]

[0057] In the formula, N ′ is the maximum value of n that satisfies t n ≤T s , D s is the order quantity of steel grade s, d n is the yield of furnace n, and usually the yield of each furnace is equal and a constant value, and p n is a judgment coefficient for judging whether furnace n produces steel grade s or not, which is 1 when furnace n produces steel grade s, and 0 when furnace n does not produce steel grade s.

[0058] 4.2) Taboo constraint

[0059] The furnaces belonging to the same tundish must satisfy the taboo relationship between their respective steel grades; that is, if the steel grades of two adjacent furnaces are not allowed to be put into the same tundish, they need to be allocated to different tundishes.

[0060] 4.3) Mix pouring constraint

[0061] The furnaces belonging to the same tundish must satisfy the mix pouring relationship. For example, as described in the background art, if steel grade A and steel grade C want to be mixed poured in the same tundish, steel grade B must be inserted between them as a transition, and the furnaces are arranged in the order of A, B, and C for casting.

[0062] 4.4) Pad constraint

[0063] The different steel grades of adjacent furnaces must satisfy the pad relationship, and if they do not satisfy the pad relationship, a specific steel grade of a specified number of furnaces must be inserted between them according to the pad relationship. For example, as described in the background art, steel grade D and steel grade F have a pad relationship, and steel grade E must be inserted between them according to the pad relationship. For the steel grade inserted according to the pad relationship, even if there is no demand for this steel grade in the order, it must be produced for a specified number of furnaces to satisfy the pad relationship.

[0064] ​4.5) Maximum continuous casting heats constraint

[0065] The number of heats belonging to the same tundish must be ≤ maximum continuous casting heats of the tundish.

[0066] II. Solution

[0067] For the above established tundish scheduling optimization model, the present embodiment first uses genetic algorithm to solve, to obtain a solution meeting the requirements, i.e. a scheduling scheme, including the steel grade produced by each heat and the tundish allocation of each heat. The specific settings are as follows:

[0068] 1. Chromosome coding design

[0069] Variable-length integer coding is adopted, wherein: chromosome length = total number of heats N; the variable s n and g n constitute a point (s n ,g n ) in the problem space as a gene locus, then the chromosome can be coded as: {(s1,g1),(s2,g2),…,(s N ,g N )}.

[0070] 2. Initialization

[0071] Initialization is performed according to the following rules:

[0072] 2.1) For steel grades with matting relationship, the heats are sorted according to the matting relationship, and the tundish serial number of the steel grade after the matting relationship is greater than that of the steel grade before the matting relationship;

[0073] 2.2) Steel grades with mixed casting relationship are preferentially allocated to the same tundish;

[0074] 2.3) The number of heats of the tundish ≤ maximum continuous casting heats of the tundish;

[0075] 3. Population size

[0076] The population size is set based on the number of heats, wherein: when the total number of heats N ≤ 30, the population size is 50-80; when the total number of heats N > 30, the population size is 80-120. Thus, it is ensured that the initial population covers the candidate range of "tundish number from small to large", i.e. from the theoretical minimum number (i.e. = N / maximum continuous casting heats of the tundish) to the maximum number (i.e. = N, each heat is allocated a tundish separately).

[0077] 4. Search for optimal solution within the constraint boundary

[0078] 4.1) Selection operation

[0079] The roulette wheel selection method is adopted, and "the fewer the tundish numbers" and "the higher the constraint satisfaction degree" are used as the fitness function core, that is, F = (1 - ρ) * (1 - (1 - ρ) * (1 - ρ) *... * (1 - ρ)) + ρ, where F is the fitness value, and ρ is the constraint satisfaction coefficient, which is calculated as the number of satisfied constraint terms / total constraint terms. According to the fitness value F, the solution with a larger fitness value is reserved.

[0080]

[0081] In the formula, F is the fitness value, and ρ is the constraint satisfaction coefficient, which is calculated as the number of satisfied constraint terms / total constraint terms. According to the fitness value F, the solution with a larger fitness value is reserved.

[0082] Note: Each existing contraindication, mixed pouring relationship, and padding relationship is recorded as one constraint; the number of tundishes is counted as the corresponding number of constraint terms; and the number of delivery time requirements is counted as the corresponding number of constraints. For example, a certain production arrangement has 2 contraindications, 3 mixed pouring relationships, 4 padding relationships, is allocated 10 tundishes, and has 5 delivery time requirements, so the total number of constraints = 24.

[0083] 4.2) Cross operation

[0084] Single-point crossover is adopted, and the crossover point is selected at any position in the furnace sequence, so as to exchange the second half of the genes of the two parent individuals. After crossover, the constraints are checked, including the maximum continuous pouring furnace constraint and the mixed pouring constraint, and if the constraints are violated, the crossover is abandoned, and the parents are reselected.

[0085] 4.3) Mutation operation

[0086] 1-2 gene sites are randomly selected, and the tundish number to which the gene sites belong is modified. After mutation, the constraints are checked, including the contraindication constraint and the padding constraint, and if the constraints are violated, the mutation is abandoned, and the mutation operation is re-executed.

[0087] 5. Scheme correction

[0088] After each iteration of the above genetic algorithm, the traditional CSP algorithm is used for checking and correction, wherein the production arrangement that satisfies all the constraint conditions is marked as an "effective scheme" and is reserved to the next generation population. For the schemes that violate the constraints, the constraints are corrected based on the constraint propagation method, for example, the excess furnace is adjusted to the adjacent tundish with compatible steel grades; the schemes that satisfy all the constraints after correction are reserved to the next generation population, and otherwise, the schemes are marked as "invalid schemes" and are eliminated.

[0089] After the above genetic algorithm is iterated to a set number of times, the production arrangement with the least number of tundish uses is obtained through optimization.

[0090] The present application is not limited to the above embodiments, and any obvious improvements, replacements or modifications made by those skilled in the art without departing from the essential content of the present application shall fall within the protection scope of the present application.

Claims

1. A method for optimizing intermediate package scheduling, characterized in that: An optimization model is established with the goal of minimizing the use of intermediate packages. The optimization model is solved using a genetic algorithm to obtain the optimized production scheduling scheme, which includes the steel grades produced in each heat and the allocation of tundishes for each heat.

2. The intermediate package scheduling optimization method according to claim 1, characterized in that: The objective function of the optimization model is: ming N In the formula, g N This represents the total number of intermediate packages required for all N furnace runs, where N is the total number of furnace runs. For n = 1 to N, we have: In the formula, g n This indicates the intermediate package to which furnace number n belongs.

3. The intermediate package scheduling optimization method according to claim 2, characterized in that: The optimization model includes the following constraints: delivery date constraint, taboo constraint, mixed casting constraint, preparatory constraint, and maximum consecutive casting cycles constraint.

4. The intermediate package scheduling optimization method according to claim 3, characterized in that: The delivery date constraint is: In the formula, N ′ To satisfy t n ≤T s The maximum value of n, D s For the order quantity of steel grade s, d n p represents the output of furnace n. n It is a determination coefficient used to determine whether heat n produces steel grade s, s n For the steel grade produced in furnace n, t n T is the completion time of furnace n. s This refers to the delivery date for steel grade S.

5. The intermediate package scheduling optimization method according to claim 3, characterized in that: The taboo constraint is that for heats belonging to the same tundish, the steel grades must satisfy a taboo relationship. The mixing constraint is that for heats belonging to the same tundish, the steel grades must meet the mixing relationship. The aforementioned padding constraint is that different steel grades in adjacent heats must satisfy a padding relationship. The maximum number of consecutive casting cycles is constrained as follows: the number of cycles belonging to the same tundish is less than or equal to the maximum number of consecutive casting cycles for the tundish.

6. The intermediate package scheduling optimization method according to claim 4, characterized in that: In the genetic algorithm, the chromosome coding design includes: chromosome length = N, and the nth gene locus is (s n ,g n ).

7. The intermediate package scheduling optimization method according to claim 6, characterized in that: The genetic algorithm includes: Selection operation: A roulette wheel selection method is used to retain solutions with larger fitness values ​​F, where the fitness function is: In the formula, ρ is the constraint satisfaction coefficient, which is calculated as the number of satisfied constraints / the total number of constraints; Cross operation: Single-point cross is adopted. After the cross is performed, the constraints are checked, including the maximum number of consecutive pouring cycles and the mixed pouring constraints. If the constraints are violated, the cross is abandoned and a new parent is selected. Mutation operation: Randomly select 1-2 gene loci and modify their g... n Value selection, and validation of constraints after mutation, including taboo constraints and paving constraints. If a constraint is violated, the mutation is abandoned.

8. The intermediate package scheduling optimization method according to claim 7, characterized in that: The genetic algorithm is verified and corrected after each iteration. Production scheduling schemes that satisfy all constraints are retained in the next generation population. For those that violate constraints, corrections are made based on the constraint propagation method. After correction, schemes that satisfy all constraints are retained in the next generation population, while those that do not are eliminated.

9. The intermediate package scheduling optimization method according to claim 6, characterized in that: The genetic algorithm is initialized according to the following rules: For steel grades with a pre-laying relationship, the heat order is sorted according to the pre-laying relationship, and the tundish number of the steel grade with the pre-laying relationship is greater than the tundish number of the steel grade with the pre-laying relationship. Steel grades that are to be mixed in casting should be preferentially allocated to the same tundish; The number of tundish furnace runs is less than or equal to the maximum number of consecutive tundish furnace runs.

10. The intermediate package scheduling optimization method according to claim 6, characterized in that: In the genetic algorithm, when N≤30, the population size is 50-80; when N>30, the population size is 80-120.

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