CN106055836A - Multi-target optimization method for casting sequence selection, ranking and casting time policy of continuous casting machine - Google Patents

Abstract

The present invention provides a multi-target optimization method for casting sequence selection, ranking and a casting time policy of a continuous casting machine. The method includes the following steps of establishing a multi-target optimization model, wherein the multi-target optimization model takes minimum total punishment, accumulated metal on the production line and non-effective use amount of high-quality molten iron of production batch plan execution conditions of a steel plant as a target function, and the multi-target optimization model is formed by constraint equations of related processing requirements; acquiring a production batch plan of the steel plant, coding based on casting sequence selection and performing population initialization; decoding based on a main constraint satisfaction method, calculating an adaptability value, and acquiring an initial solution set; performing non-dominated ranking and crowding distance ranking; selecting some individuals in the population as parents; performing crossing and variation on the parents; decoding a calculation result and calculating adaptability; determining an elitist solution set, and calculating a crowding distance and ranking; and outputting the elitist solution set, selecting the most satisfied scheme and transmitting the most satisfied scheme to a steelmaking-continuous casting production operating control system. Through adoption of the multi-target optimization method, a furnace casting period of continuous casting production is controlled stably, the algorithm efficiency is better than that of a traditional non-dominated ranking genetic algorithm and a strength pareto evolutionary algorithm.

Description

Multi-objective optimization method for casting time selection, sequencing and casting starting time decision of continuous casting unit

Technical Field

The invention relates to the technical field of steel production control, in particular to a multi-objective optimization method for casting heat selection, sequencing and casting start time decision of a continuous casting machine set.

Background

The core task of the decision-making problem of the furnace number composition and the casting time of the to-be-cast times in the continuous casting production is to determine a specific casting operation plan of a continuous casting machine and also to make a reasonable steelmaking continuous casting production plan, and is to select a proper furnace number from a batch plan preselection pool as a selected furnace number (comprising furnace number selection and sequencing) in the to-be-cast times of the continuous casting machine in a planning period and determine whether continuous casting is performed among the furnace numbers and the casting time. At present, for the problem, a steel mill basically depends on manual experience to make a decision, and the scientificity and the effectiveness of a decision result are difficult to guarantee. The decision problem of the heat and time of continuous casting is a typical multi-target multi-constraint optimization decision problem, so that the multi-target optimization modeling and solving method for researching the problem has important practical significance and theoretical value.

In recent years, the related research on multi-objective problems in the field of steelmaking-continuous casting production planning and scheduling mainly focuses on the steelmaking-continuous casting production batch planning and production scheduling.

The prior research is carried out respectively and independently aiming at the formulation problems of a production batch plan and a steelmaking-continuous casting multi-target scheduling plan, the former mainly relates to the formulation of a casting time plan or a combined optimization method of a group casting plan and a furnace time plan, does not relate to the problems of furnace time selection, sequencing and casting start time determination on a continuous casting machine, and only determines the number of furnaces in the casting time in the batch plan; the research of the latter is focused on a specific scheduling method of a steelmaking continuous casting scheduling plan under multiple targets, and the sequence of each casting time to be started and the casting time of a continuous casting machine are generally assumed as known conditions, so that the determination of the casting time to be started and the casting time in the casting time plan executable on the continuous casting machine is avoided being influenced by factors such as metal resource balance on a production line, and the like, and the practical problem is greatly simplified. The method for respectively researching the continuous casting and the continuous casting of the steel plant has obvious difference with actual production requirements, the production management of the steel plant needs to comprehensively consider a production batch plan and simultaneously carry out optimization decision on the multi-target problem of the group casting and the casting starting of the continuous casting machine on the basis of considering the actual production constraint, namely the problem of making a casting operation plan of the continuous casting machine is substantially solved, and the decision result is used as a precondition for making a steelmaking continuous casting operation plan schedule. However, due to the lack of understanding on the importance of the problems and the high difficulty of modeling and solving, the production practice is determined by a dispatcher according to the manual experience, so that a great deal of uncertainty is brought to the production, and the realization of the ordered, stable and efficient production target is influenced.

Disclosure of Invention

In order to overcome the defects in the prior art, the invention aims to provide a multi-objective optimization method for selecting and sequencing casting heat times and deciding casting starting time of a continuous casting machine set.

In order to achieve the above purpose, the invention provides a multi-objective optimization method for casting heat selection, sequencing and casting start time decision of a continuous casting machine set, which comprises the following steps:

s1, connecting the controller with an MES database of a steel mill to obtain a production batch plan in an MES plan pre-selection pool of the steel mill, wherein the batch plan comprises the number of casting times distributed to each casting machine, the type of steel types to which each furnace belongs in the casting times, the section specification and a pre-set casting starting time;

s2, establishing an objective function with the minimum total punishment of the planned execution condition of the production batch of the steel plant, the minimum production line backlog metal quantity and the minimum non-effective utilization quantity of the high-quality molten iron, wherein the objective function is as follows:

min F＝{f₁,f₂,f₃} (1)

wherein,

$f_1=\underset{i=1}{\overset{I}{\mathrm{\Σ}}}\underset{k=1}{\overset{K_i}{\mathrm{\Σ}}}({\mathrm{\ξ}}_{ik(k+1)}^1+{\mathrm{\ξ}}_{ik(k+1)}^2)\·z_{ik}\·z_{i(k+1)}+\underset{i=1}{\overset{I}{\mathrm{\Σ}}}{d}_i\·(K_i-\underset{k=1}{\overset{K_i}{\mathrm{\Σ}}}{z}_{ik})+\underset{i=1}{\overset{I}{\mathrm{\Σ}}}\underset{k^d=1}{\overset{K_i^d}{\mathrm{\Σ}}}\left(\right|x_{{\mathrm{ik}}^d}-{\mathrm{\τ}}_{{\mathrm{ik}}^d}^{date}|\·{\mathrm{\ψ}}_i+y_{{\mathrm{ik}}^d}\·e_i)---\left(2\right)$

f₂＝Q_O(3)

$f_3=Q_E\·{\mathrm{\π}}^p+Q_I\·{\mathrm{\δ}}^p-\underset{i=1}{\overset{I}{\mathrm{\Σ}}}\underset{k=1}{\overset{K_i}{\mathrm{\Σ}}}{z}_{ik}\·v_{ik}\·q_i\·\frac{1}{1-\mathrm{\η}}---\left(4\right)$

Q_O＝Q_E+Q_IV-Q_C-Q_L-Q_S(5)

$Q_C=\underset{i=1}{\overset{I}{\mathrm{\Σ}}}{\mathrm{rq}}_i+\underset{i=1}{\overset{I}{\mathrm{\Σ}}}\underset{k^d=1}{\overset{K_i^d}{\mathrm{\Σ}}}\left(min\right({\mathrm{\τ}}_e,x_{{\mathrm{ik}}^d}+{\mathrm{\τ}}_{{\mathrm{ik}}^d})-x_{{\mathrm{ik}}^d})\·\mathrm{\ρ}\·{\mathrm{wa}}_{{\mathrm{ik}}^d}\·{\mathrm{ws}}_{{\mathrm{ik}}^d}---\left(6\right)$

$Q_L=Q_C\·\frac{\mathrm{\η}}{1-\mathrm{\η}}---\left(7\right)$

$Q_S=\frac{Q_C\·{\mathrm{\τ}}_A}{({\mathrm{\τ}}_e-{\mathrm{\τ}}_s)\·(1-\mathrm{\η})}+Q_{rcon}---\left(8\right)$

(2) the formula represents the sum of the punishment cost of steel type difference and delivery date difference between the selected furnace numbers, the punishment cost of the residual furnace numbers which are not cast, and the punishment cost of casting on time when each furnace number is not cast;

(3) formula represents the overstocked metal quantity Q of the production line_o；

(4) The formula represents the ineffective utilization amount of high-quality molten iron;

(5) the formula represents the metal amount of the backlog and is set based on the balance of metal resources of the production lineRespectively by the planned period of iron input Q_EAmount of metal Q stocked in production line at the beginning of the production period_IVContinuous casting of steel Q_CAmount of metal loss Q_LIs favorable for producing stable metal quantity Q in the end-of-term production line safety stock_SForming;

(6) the steel casting amount of each continuous casting machine is respectively composed of the steel casting amount of the remained task in the previous planning period and the steel casting amount of each heat in the casting time to be started;

(7) the formula represents the metal loss amount corresponding to the steel casting amount;

(8) the formula represents the metal quantity in the safety stock of the production line, which needs to add a random fluctuation demand metal quantity Q on the basis of the average metal quantity in the stock of the production line_rcon；

Wherein, the specific meanings of the symbols are as follows:

symbol and set of definition:

i, casting machine serial number, I belongs to I, and I is a continuous casting machine set;

k is the furnace number of each casting machine in the preselection pool, K ∈ K_i，K_ijFor a pre-selection pool casting machine i casting times j heat times set, K_iGenerating k for all the heat sets of the continuous casting machine i of the pre-selection pool in sequence according to the preset casting starting time of each casting machine;

k^dthe serial number of the furnace to be poured is counted,is the set of the furnaces to be cast of the continuous casting machine i,the number of the casting furnaces is preset to be the lowest number of the casting furnaces of the casting machine i;

secondly, known parameters:

q_ikin the casting machine i heat kWeight of molten steel;

v_ikpreselecting whether the furnace k of the pool casting machine i is high-quality steel;

wa_ikpreselecting the section specification of a furnace k of a pool casting machine i;

i-waiting casting heat k of casting machine^dThe section specification of (1);

ws_ikpre-selecting the pulling speed of a furnace k of a pool casting machine i;

i-waiting casting heat k of casting machine^dThe pull rate of (2);

rq_ithe weight of molten steel left on a casting machine i;

rho is the density of the molten steel;

eta is the metal loss coefficient;

τ_s、τ_ethe starting time and the ending time of the planning period;

τ_Aaverage logistics time of the whole process;

i-waiting casting heat k of casting machine^dThe casting period of (2);

the preset casting time of the heat k of the casting machine i;

e_ithe loss cost coefficient of the i-furnace intermittent casting of the casting machine;

Q_rconrandomly fluctuating the required metal amount;

^p、π^p、^p'the proportion of high-quality variety steel of the left-over task and the proportion of high-quality molten iron of the iron feeding and the initial metal amount;

ψ_ithe different cost coefficient of casting on time;

the additional cost caused by the difference of steel types between adjacent furnaces is only the same steel type class a if the steel type code is the same as 0₁Belong to the different steel types a₂；

The difference of the scheduled casting time adds the expense,β₁a cost factor for the difference in delivery dates of adjacent heats;

d_ithe furnace number of the casting machine i is not selected as the delay loss cost coefficient of the furnace number to be cast;

the penalty factor is used for removing illegal solutions by setting the penalty factor, and the M is a positive number which is large enough to ensure that the solutions are punished by a large enough fitness value when the solutions do not meet the constraint;

the dimensional unity coefficient;

and thirdly, decision variables to be solved:

the casting machine i is selected as the to-be-cast heat k^dThe casting starting time;

binary variable, 1 represents the number of casting times k of the casting machine i^dThe casting is stopped with the furnace just before, 0 represents continuous casting with the furnace just before;

z_ikbinary variable, 1 represents that a certain heat k in a casting machine i in a preselection pool is selected as a heat to be cast, and 0 represents that the certain heat k is not selected;

s3, establishing a constraint relation between the pre-selection pool heat and the heat to be cast in the production batch plan, a metal resource balance related constraint relation, a continuous casting equipment available time constraint relation and a sequence and time constraint relation between the heat to be cast;

s4, selecting to code based on the furnace serial number and performing population initialization;

s5, decoding and calculating the fitness value to obtain an initial solution set, wherein the fitness function is as follows:

$\begin{array}{cc}\min & F=\{f_{{\mathrm{eval}}_1},f_{{\mathrm{eval}}_2},f_{{\mathrm{eval}}_3}\}\end{array}---\left(9\right)$

wherein,

$f_{{\mathrm{eval}}_1}=f_1---\left(10\right)$

$f_{{\mathrm{eval}}_3}=f_3+M\·max\{Q_D,Q_E\·{\mathrm{\π}}^p+Q_{IV}\·{\mathrm{\δ}}^p\}---\left(12\right)$

(9) the formula represents the whole calculation process to obtain the fitness functionIs the target;

(10) formula represents fitness function valueIs equal to the value of the objective function f₁；

(11) Formula represents fitness function valueIs equal to the value of the objective function f₂Adding the sum of the punishment of violating the backlog metal quantity relation constraint and the punishment of exceeding the planned period of the casting starting time;

(12) formula represents fitness function valueIs equal to the value of the objective function f₃The sum of punishments of the high-quality molten iron which is beyond the supply of the high-quality molten iron for planning;

s6, performing non-dominated sorting and crowded distance sorting on the solutions in the initial solution set;

s7, selecting a part of individuals in the population in the step S6 as parents;

s8, performing multipoint intersection on parents and parents of the father and the son of the father selected in the step S7 according to the casting machine segmentation, and performing random variation according to the casting machine segmentation point taking to ensure the consistency of the chromosome characteristics and the real production furnace serial number characteristics;

s9, decoding the result calculated in the step S8 and calculating the fitness, wherein the fitness function is the fitness function in the step S5;

s10, determining an elite solution set, limiting the number of individuals with the calculated crowding distance, and calculating the crowding distance and sequencing;

s11, judging whether the maximum iteration number is reached, if so, executing the step S12, otherwise, executing the step S7;

s12, outputting an elite solution set, and selecting a maximum satisfaction scheme as a continuous casting start-up heat time decision method by using a fuzzy optimization method;

and S13, transmitting the maximum satisfaction degree scheme to a steelmaking-continuous casting production operation control system, and realizing effective production operation control on selection, sequencing and casting starting time decision of the to-be-cast furnaces on each continuous casting machine by the system according to the maximum satisfaction degree scheme.

The multi-objective optimization method for continuous casting machine casting heat and time decision establishes a multi-objective optimization model for continuous casting heat and time decision by analyzing the problem of casting heat and time decision of a continuous casting machine of a steel mill on the basis of comprehensively considering the practical influence factors of the mutual relation between the heat and the heat to be cast, metal resource balance, continuous casting equipment resource condition, heat time sequence and the like in a production batch plan, and designs an Improved Algorithm (Improved NSGAII, INSGAII) for model solution on the basis of a Non-dominant sequencing Genetic Algorithm (Non-dominant sequencing Genetic Algorithm, NSGAII), thereby improving the calculation speed and accuracy.

Additional aspects and advantages of the invention will be set forth in part in the description which follows and, in part, will be obvious from the description, or may be learned by practice of the invention.

Drawings

The above and/or additional aspects and advantages of the present invention will become apparent and readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings of which:

FIG. 1 is an algorithmic flow chart of the method of the present invention;

FIG. 2 is a schematic diagram of a preferred embodiment of the present invention of a code selected based on a furnace number;

FIG. 3 is a diagram of an elite solution set truncation principle in a preferred embodiment of the present invention;

FIG. 4 is a model decision fitness minimum evolution process in a preferred embodiment of the present invention

FIG. 5 is a Gantt decision diagram in a preferred embodiment of the present invention;

fig. 6 is a gantt chart of the manual decision in the example shown in fig. 5.

Detailed Description

Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the accompanying drawings are illustrative only for the purpose of explaining the present invention, and are not to be construed as limiting the present invention.

Steel plants typically have multiple types, multiple models, of continuous casting machines that perform different types of tasks (variety specifications, etc.). The production lot planning is to periodically reach a planned pre-selection pool (referred to as a pre-selection pool for short) of a Manufacturing Execution System (MES) of a steel mill by a production command center ERP of an upper management department according to casting machines in a form of scheduled casting times, wherein information of the planned pre-selection pool generally comprises the number of casting times distributed to each casting machine, the type of steel types, section specifications, scheduled casting starting time and the like of each furnace in the casting times, and belongs to a rough plan. Before a steel plant makes a scheduling plan of steelmaking-continuous casting production, the decision of continuous casting start-up furnace number and time is needed to be made. Specifically, according to actual factors such as batch planning information, a predicted iron feeding amount in a period (referred to as a planning period for short), a stock metal amount of a primary production line, a task state of continuous casting equipment and the like, it is determined which furnace number is selected from batch planning of each casting machine in a pre-selection pool as a to-be-cast furnace number of the planning period, and whether each to-be-cast furnace number is continuously cast with a previous furnace number and the casting time of each furnace number is determined. The scheduling execution mode directly aims at the heat to carry out the casting task arrangement of the continuous casting machine is more beneficial to exerting the continuous casting capacity of the continuous casting machine and realizing the multi-target management requirement of a steel mill.

The method of the invention can set the following preconditions: firstly, according to the batch plan information entering a preselection pool, furnace numbering is carried out according to the sequence of preset casting starting time of all furnaces of the same target casting machine, so as to distinguish the basic information of the furnace to be determined on each continuous casting machine; in the planning period, the to-be-cast heat of each casting machine is only selected from the heat with the same target casting machine in the preselection pool; and thirdly, when the furnace number which is not selected to be cast in the planning period exists in the pre-selection pool, the furnace number can be reserved as a decision to be continued in the planning period immediately after the casting machine.

Optimizing the target: the design is mainly carried out from the perspective of being beneficial to orderly production plan and effectively utilizing metal resources such as molten iron and the like. And the punishment violating the production batch plan, the backlog metal quantity on the production line and the minimization of the ineffective utilization quantity of the high-quality molten iron are optimized. The violation punishment on the production batch plan mainly relates to the problem of reselecting and sequencing the heat in a preselected pool under the requirement of just-in-time system, and the execution effect of the plan can be quantitatively described by using the punishment mode of group casting and just-in-time system (Tang Lixin, Wang Meng, Yang Buxi, Yangxi. steelmaking-continuous casting, an optimal casting plan model and algorithm [ J ] steel, 1997,32(7):19-21) with unknown casting times; the backlog metal amount on the production line represents the balance relation of metal resources in a planning period, and a quantitative expression of the backlog metal amount can be described as [ backlog metal amount ] + [ accumulated iron amount ] - [ accumulated steel pouring amount ] - [ accumulated metal loss amount ] - [ end online safety stock metal amount ], wherein the online safety stock metal amount is favorable for the stability of production; the ineffective utilization amount of the high-quality molten iron reflects the management requirement that a steel mill needs to use limited high-quality molten iron resources for producing high-quality steel.

Constraint conditions are as follows: the method mainly comprises the mutual relation between the heat in the pre-selection pool and the heat to be cast, the balance relation of metal resources, the available time of continuous casting equipment, the time sequence relation of the heat and the like.

For ease of description, the main symbols involved in defining the model solution are as follows:

(1) symbols and collections

I, casting machine serial number, I belongs to I, and I is a continuous casting machine set;

j is the pre-selection pool pouring sequence number j_i∈J_i,J_iThe casting times of a continuous casting machine i of the pre-selection pool are integrated;

k is the furnace number of each casting machine in the preselection pool, K ∈ K_i，K_ijFor a pre-selection pool casting machine i casting times j heat times set, K_iGenerating k for all the heat sets of the continuous casting machine i of the pre-selection pool in sequence according to the preset casting starting time of each casting machine;

k^dthe serial number of the furnace to be poured is counted,is the set of the furnaces to be cast of the continuous casting machine i,the number of the casting furnaces is preset to be the lowest number of the casting furnaces of the casting machine i;

(2) parameters are known, where the unit or value in parentheses,

q_ikthe weight (t) of molten steel of a heat k of a casting machine i;

mark_ikpre-selecting steel grade codes of a furnace k of a pool casting machine i;

stye_ikpre-selecting the steel grade of the furnace k of the pool casting machine i;

v_ikpreselecting whether the furnace k of the pool casting machine i is high-quality steel (1 is yes, 0 is no);

wa_ikpreselecting section specification (m) of furnace k of pool casting machine i²)；

I-waiting casting heat k of casting machine^dSection size (m)²)；

ws_ikPreselecting the drawing speed (m.min) of the i heat k of the pool casting machine^-1)；

The casting machine i is pulled at the casting speed kd (m.min)^-1)；

rq_iThe weight (t) of the molten steel left on the casting machine i;

Rgrade_isteel grade codes of tasks left on a casting machine i;

rs_icasting speed (m.min.) of a leaving task on casting machine i^-1)；

ra_iSection specification (m) of the leaving-behind task on casting machine i²)；

Rho. molten steel density (t m)^-3)；

η metal loss coefficient (t.t)^-1)；

τ_s、τ_eThe beginning and ending time (min) of the planning period;

τ_Aaverage logistics time (min) of the whole process;

τ_ikthe casting period (min), tau, of the pre-selected bath casting machine i heat k_ik＝q_i/ρ·wa_ik·ws_ik；

I-waiting casting heat k of casting machine^dCasting period (min);

minimum interval time (min) between heats of a casting machine i;

the preset casting time (min) of the heat k of the casting machine i;

maximum available time (min) of casting machine i;

the earliest available operation time (min) between the casting times of the casting machine i;

e_icasting machine i heat intermittent casting loss cost coefficient (CNY Time)^-1)；

Q_E、Q_IVPlanning the iron feeding amount and the metal inventory amount (t) on the initial production line;

Q_rconrandomly fluctuating demand metal amounts (t);

^p、π^p、^p'the proportion of high-quality variety steel of the left-over task and the proportion of high-quality molten iron of the iron feeding and the initial metal amount;

ψ_idifferential Charge coefficient (CNY-Charge) for on-time casting^-1)；

The additional cost caused by the difference of steel type between adjacent furnaces is 0 (CNY. Charge) if the steel type code is the same^-1) Only belong to the same steel type class a₁(CNY·Charge^-1) Belong to the different steel types a₂(CNY·Charge^-1)；

The difference of the scheduled casting time adds the expense,β₁charge factor (CNY-Charge) for difference between adjacent heat delivery periods^-1)；

d_iThe furnace number of the casting machine i is not selected as the delay loss cost coefficient (CNY. Charge) of the furnace number to be cast^-1)；

(3) Decision variables

The casting machine i is selected as the to-be-cast heat k^dThe casting start time (min);

binary variable, 1 represents the number of casting times k of the casting machine i^dThe casting is stopped with the furnace just before, 0 represents continuous casting with the furnace just before;

z_ikthe binary variable 1 indicates that a certain heat k in the casting machine i in the preselection pool is selected as a heat to be cast, and 0 indicates that the certain heat k is not selected.

The invention provides a multi-objective optimization method for continuous casting machine casting heat and time decision, as shown in figure 1, comprising the following steps:

s1, connecting the controller with an MES database of the steel mill, obtaining a production batch plan in an MES plan pre-selection pool of the steel mill, wherein the batch plan comprises the number of casting times distributed to each casting machine, the type of steel types to which each heat belongs in the casting times, section specifications and a pre-determined casting starting time, selecting coding based on the heat serial number, and performing population initialization;

s2, establishing a multi-objective optimization function of continuous casting starting heat and time decision according to the decision objective of minimizing the total punishment of the violation production batch plan, the backlog metal amount on the production line and the ineffective utilization amount of the high-quality molten iron, wherein the objective function equation is as follows:

min F＝{f₁,f₂,f₃} (1)

wherein,

$f_1=\underset{i=1}{\overset{I}{\mathrm{\Σ}}}\underset{k=1}{\overset{K_i}{\mathrm{\Σ}}}({\mathrm{\ξ}}_{ik(k+1)}^1+{\mathrm{\ξ}}_{ik(k+1)}^2)\·z_{ik}\·z_{i(k+1)}+\underset{i=1}{\overset{I}{\mathrm{\Σ}}}{d}_i\·(K_i-\underset{k=1}{\overset{K_i}{\mathrm{\Σ}}}{z}_{ik})+\underset{i=1}{\overset{I}{\mathrm{\Σ}}}\underset{k^d=1}{\overset{K_i^d}{\mathrm{\Σ}}}\left(\right|x_{{\mathrm{ik}}^d}-{\mathrm{\τ}}_{{\mathrm{ik}}^d}^{date}|\·{\mathrm{\ψ}}_i+y_{{\mathrm{ik}}^d}\·e_i)---\left(2\right)$

f₂＝Q_O(3)

$f_3=Q_E\·{\mathrm{\π}}^p+Q_I\·{\mathrm{\δ}}^p-\underset{i=1}{\overset{I}{\mathrm{\Σ}}}\underset{k=1}{\overset{K_i}{\mathrm{\Σ}}}{z}_{ik}\·v_{ik}\·q_i\·\frac{1}{1-\mathrm{\η}}---\left(4\right)$

Q_O＝Q_E+Q_IV-Q_C-Q_L-Q_S(5)

$Q_C=\underset{i=1}{\overset{I}{\mathrm{\Σ}}}{\mathrm{rq}}_i+\underset{i=1}{\overset{I}{\mathrm{\Σ}}}\underset{k^d=1}{\overset{K_i^d}{\mathrm{\Σ}}}\left(min\right({\mathrm{\τ}}_e,x_{{\mathrm{ik}}^d}+{\mathrm{\τ}}_{{\mathrm{ik}}^d})-x_{{\mathrm{ik}}^d})\·\mathrm{\ρ}\·{\mathrm{wa}}_{{\mathrm{ik}}^d}\·{\mathrm{ws}}_{{\mathrm{ik}}^d}---\left(6\right)$

$Q_L=Q_C\·\frac{\mathrm{\η}}{1-\mathrm{\η}}---\left(7\right)$

$Q_S=\frac{Q_C\·{\mathrm{\τ}}_A}{({\mathrm{\τ}}_e-{\mathrm{\τ}}_s)\·(1-\mathrm{\η})}+Q_{rcon}---\left(8\right)$

(2) the formula shows that the sum of the punishment cost of steel type difference and delivery date difference between the selected furnace numbers, the punishment cost of the residual furnace numbers which are not cast and the punishment cost of casting on time of each furnace number is minimum;

(3) formula represents the overstocked metal quantity Q of the production line_oMinimum;

(4) the formula shows that the ineffective utilization amount of the high-quality molten iron is minimum;

(5) the formula represents the backlog metal amount, is set based on the metal resource balance of the production line, and is respectively based on the planned iron feeding amount Q_EAmount of metal Q stocked in production line at the beginning of the production period_IVContinuous casting of steel Q_CAmount of metal loss Q_LIs favorable for producing stable metal quantity Q in the end-of-term production line safety stock_SForming;

(6) the steel casting amount of each continuous casting machine is respectively composed of the steel casting amount of the remained task in the previous planning period and the steel casting amount of each heat in the casting time to be started;

(7) the formula represents the metal loss amount corresponding to the steel casting amount;

(8) the formula represents the metal quantity stored in the production line safety, which needs to add a random fluctuation demand metal quantity Q on the basis of the average metal quantity stored in the production line_rconThe average in-line metal inventory may be calculated according to "average inventory-average throughput per unit time × average flow time".

Aiming at the sorting problem of the selected heat, the corresponding relation between the serial number of the selected heat and the casting starting time is indirectly embodied in the process of coding and decoding.

S3, establishing a constraint relation between the pre-selection pool heat and the heat to be cast in the production batch plan, a metal resource balance related constraint relation, a continuous casting equipment available time constraint relation and a sequence and time constraint relation between the heat to be cast;

the constraint conditions when solving are as follows:

firstly, constraint of the relationship between the pre-selection pool heat and the to-be-cast pool heat in the production batch plan:

$\underset{k=1}{\overset{K_i}{\mathrm{\Σ}}}{z}_{ik}=K_i^d,\∀i\∈\[1,I\]---\left(9\right)$

$K_i^d\≥K_i^n,\∀i\∈\[1,I\]---\left(11\right)$

(9) the formula represents the relation between the selected heat number of each continuous casting machine in the preselection pool and the number of the to-be-cast heat number of each casting machine in the planning period.

(10) The formula is set for adapting to resource limiting conditions, and indicates that the number of furnaces to be cast of each casting machine does not exceed the minimum value of the total number of batch plan furnaces of the preselected pool and the capacity requirement of the casting machine, wherein,representing rounding up and mean () representing calculating the average.

(11) The formula is set for improving the utilization rate of the tundish and the continuous casting equipment, and means that if the casting machine is started, the casting machine is required to be more than the preset minimum number of casting furnaces of the casting machine.

② metal resource balance related constraint:

Q_O≥0 (12)

Q_D≤Q_E·π^p+Q_IV·^p’(13)

$Q_D=({\mathrm{\δ}}^p\·\underset{i=1}{\overset{I}{\mathrm{\Σ}}}{\mathrm{rq}}_i+\underset{i=1}{\overset{I}{\mathrm{\Σ}}}\underset{k^d=1}{\overset{K_i^d}{\mathrm{\Σ}}}{v}_{{\mathrm{ik}}^d}\·(min\left({\mathrm{\τ}}_e,x_{{\mathrm{ik}}^d}+{\mathrm{\τ}}_{{\mathrm{ik}}^d}\right)-x_{{\mathrm{ik}}^d})\·\mathrm{\ρ}\·{\mathrm{wa}}_{{\mathrm{ik}}^d}\·{\mathrm{ws}}_{{\mathrm{ik}}^d})\·1/(1-\mathrm{\η})---\left(14\right)$

(12) the non-negative production line backlog metal amount of formula (I) is set to ensure stable production between schedule periods.

(13) The formula shows that the amount of high-quality molten iron required by the cast high-quality steel should not exceed the sum of the initial inventory and the amount of high-quality molten iron entering iron in the planned period.

(14) The formula represents the amount of high-quality molten iron Q required for casting high-quality steel_DThe device consists of two parts of high-quality molten iron required by a leaving task and a time to be fired respectively.

And thirdly, restricting the available time of the continuous casting equipment, wherein the casting starting time of the selected furnace is not earlier than the earliest available time of the casting machine.

${\mathrm{\τ}}_i^{earliest}\≤x_{{\mathrm{ik}}^d},\∀i\∈\[1,I\],\∀k^d\∈\[1,K_i^d\]---\left(15\right)$

Fourthly, restraining the sequence and time between furnaces to be cast:

$y_{{\mathrm{ik}}^d}\left\{\begin{array}{c}=1,{\mathrm{wa}}_{{\mathrm{ik}}^d}\≠{\mathrm{wa}}_{i(k^d-1)},\∀i\∈\[1,I\],\∀k^d\∈\[1,K_i^d\]\\ =0,{\mathrm{wa}}_{{\mathrm{ik}}^d}={\mathrm{wa}}_{i(k^d-1)},\∀i\∈\[1,I\],\∀k^d\∈\[1,K_i^d\]\end{array}\right.---\left(16\right)$

${\mathrm{\τ}}_s\≤x_{{\mathrm{ik}}^d}\≤{\mathrm{\τ}}_e,\∀i\∈\[1,I\],\∀k^d\∈\[2,K_i^d\]---\left(17\right)$

${\mathrm{\τ}}^{\′}+{\mathrm{\τ}}_i^{gap}\·y_{{\mathrm{ik}}^d}\≤x_{{\mathrm{ik}}^d}\≤{\mathrm{\τ}}^{\′}+({\mathrm{\τ}}_e-{\mathrm{\τ}}^{\′})\·y_{{\mathrm{ik}}^d},\∀i\∈\[1,I\],\∀k^d\∈\[1,K_i^d\]---\left(18\right)$

(16) the formula shows that the furnace discontinuity specification is not forced to be broken at the same time.

(17) The formula shows that the casting time of each furnace to be cast is selected to be within the planning period.

(18) When the furnace to be cast and the remained task are cast continuously, the casting time point takes the remained task ending time, and tau' ═ rq_i/ρ·ra_i·rs_iWhen the continuous casting is not carried out, the time from the end time of the left task to the end of the planned period is taken,when the times to be started are mutually and continuously cast, the casting starting time point takes the end time of the previous furnace,when the continuous casting is not carried out, the time from the end time of the previous furnace to the end of the planned period is taken,

and S4, selecting and coding according to the furnace serial number and performing population initialization.

And S5, decoding and calculating the fitness value to obtain an initial solution set. Because the metal resource constraint (12) and (13) formulas are simultaneously influenced by the whole decision variables, the quantitative relation between the metal resource constraint (12) and each decision variable value range is difficult to accurately express, and the reason is preventedValue, etc. leading toThe upper value limit may exceed the upper limit τ of the planning period_eWill beAnd τ_eThe relationship (c) is also incorporated into a penalty function structure, the fitness function structure is as follows, and the fitness function is used for solving:

$\begin{array}{cc}\min & F=\{f_{{\mathrm{eval}}_1},f_{{\mathrm{eval}}_2},f_{{\mathrm{eval}}_3}\}\end{array}---\left(19\right)$

$f_{{\mathrm{eval}}_1}=f_1---\left(20\right)$

$f_{{\mathrm{eval}}_3}=f_3+M\·max\{Q_D,Q_E\·{\mathrm{\π}}^p+Q_{IV}\·{\mathrm{\δ}}^p\}---\left(22\right)$

(19) the formula represents the whole calculation process to obtain the fitness functionIs the target;

(20) formula represents fitness function valueIs equal to the value of the objective function f₁；

(21) Formula represents fitness function valueIs equal to the value of the objective function f₂Adding the sum of the punishment of violating the backlog metal quantity relation constraint and the punishment of exceeding the planned period of the casting starting time;

(22) formula represents fitness function valueIs equal to the value of the objective function f₃The sum of punishments of the high-quality molten iron which is beyond the supply of the high-quality molten iron for planning;

m is a penalty factor, the illegal solution is removed by setting a penalty factor, M is a positive number (which is specifically determined according to a specific problem, here, 100000 is selected) which is large enough to ensure that the solution is punished by a large enough fitness value when the solution does not meet the constraint (there is no specific regulation, as long as the illegal solution can be removed by setting a penalty, the generally punished fitness value should be at least one order of magnitude higher than the non-punished fitness value, otherwise, the illegal solution is difficult to be removed by the punishment);

the dimensional unity coefficient;

obtaining an effective z_ik、And after the fitness function, according to z_ikObtaining the batch plan information of each to-be-fired number by comparing with the furnace number table, and further calculatingAnd calculating the fitness value of the individual after the coefficients are equal.

S6, the solutions in the initial solution set are sorted by non-dominated sorting and congestion distance sorting.

S7, selecting a part of the individuals in the population in step S6 as parents, in a preferred embodiment of the present invention, 2/3, 1/2, 1/3 or 1/4 individuals in the population can be selected as parents, and 1/2 individuals can be selected as parents, which ensures accurate and fast calculation.

And S8, performing multipoint intersection on parents and parents of the parent selected in the step S7 according to the casting machine segmentation, and performing point taking random variation according to the casting machine segmentation to ensure the consistency of the chromosome characteristics and the serial number characteristics of the real production furnace.

And S9, decoding the result calculated in the step S8 and calculating the fitness, wherein the fitness function is the fitness function in the step S5.

S10, determining an elite solution set, limiting the number of individuals with the calculated crowding distance, and calculating the crowding distance and sequencing.

S11, judging whether the maximum iteration number is reached, if so, executing step S12, otherwise, executing step S7.

And S12, outputting an elite solution set, and selecting a maximum satisfaction degree scheme by using a fuzzy optimization method as a continuous casting starting furnace time decision method.

And S13, transmitting the maximum satisfaction degree scheme to a steelmaking-continuous casting production operation control system, and realizing effective production operation control on selection, sequencing and decision of casting starting times on each continuous casting machine by the system according to the maximum satisfaction degree scheme.

The method solves the problem that the furnace number selected in a preselection pool is used as a gene for coding, adopts the improvement measures of adjusting the traditional calculation sequence and limiting the number of crowding distance individuals in the elite solution set strategy, and finally determines the final optimized solution by using the method of fuzzy optimization of pareto solution.

As shown in FIG. 1, in the initialization stage, the algorithm designs a batch plan and the selection with the furnace number (z) under the constraint of the relation between the furnace number to be cast_ik) Solving for genes by decoding whether or not the furnaces are continuously cast (i.e. for continuous casting)) And casting time (i.e. start time)) To reduce the invalid search space of the solution; in the genetic operation stage of the main cycle, the consistency of the chromosome characteristics and the serial number characteristics of the real production furnace is ensured by adopting the method of multi-point crossing of parents and parents segmented according to a casting machine and random variation of point taking segmented according to the casting machine; in the non-domination sorting stage of the main cycle, on the premise of not influencing the performance of the solution, a new method which takes the limitation of calculating the number of crowding distance individuals as a core is designed, and the method reduces the calculation load of NSGAII in the step of retaining the elite solution by only calculating the restrictive measure of sorting the individuals directly related to the inclusion of the elite solution set, and still adopts the rules in NSGAII in the steps of non-domination sorting and filling the elite solution set; at the end ofIn the solution forming stage, a final decision scheme is selected from the pareto solution set by adopting a fuzzy optimization technology so as to be directly used by a dispatcher.

In this embodiment, the search efficiency is improved, and the encoding method includes:

s31, counting the total furnace times K of each casting machine i in the preselection pool_iThe predetermined time of starting pouring is planned according to the batch for each heatIn the embodiment, the sequence of the furnace sequence numbers is ensured to be consistent with the preset casting time sequence of the batch plan so as to ensure the smooth operation of the subsequent operation.

S32, randomly generating length K according to the selected number range of the heat in the constraint (9-11) formula_iAnd each casting machine binary sequence corresponds to the furnace number reference table one by one. For example, chromosome (0,1,1,0,1) represents K_i＝5，Corresponding to the reference table, the serial numbers of 2 nd, 3 rd and 5 th furnaces are selected as furnaces to be started, the 1 st and 4 th furnaces are not selected, and the proportion of 0-1 in the gene segment of the same casting machine can be changed within the range of meeting the constraint requirement.

S33, connecting the chromosome gene segments of the casting machines to form a complete chromosome, and randomly generating an initial population with a set scale, wherein codes selected based on the furnace number are shown in figure 2.

In the present embodiment, z is selected by the furnace number_ikFor the possibility of illegal solution of gene chromosome in the course of cross variation, for the convenience of optimization, the selection with furnace number (i.e. z) is obtained_ik) After being a coding string of a gene, except for the need to repair an illegal chromosome z_ikAnd solving other two types of decision variables by decoding according to constraint conditions: whether or not continuous casting is carried out between furnaces (i.e. continuous casting between furnaces)) And casting time (i.e. start time)) And constructing a proper fitness function by combining the constraint conditions. The decoding process is as follows:

s41, processing of illegal chromosomes: the illegal chromosomes after cross mutation can be divided into two types: the total number of the selected to-be-started heat is larger than the constraint (10) so that the upper limit of the calculated heat range and the lower limit of the heat range calculated by the constraint (11) formula are smaller, 1 which is larger than the upper limit of the constraint is changed into 0 randomly for the former, 0 which is lower than the lower limit of the constraint is changed into 1 randomly for the latter, and chromosomes which do not violate the constraint are unchanged;

s42, generating a to-be-started heat sequence according to the heat sequence with 1 appearing from left to right in the chromosome of each casting machine, contrasting the heat characteristics in the reference table and the batch plan, and generating by combining the constraint (16) formula

Step3, if a certain furnace in the sequence of the furnace to be started and the previous furnace are disconnected from casting and have the earliest available time, determining according to the constraint formulas (15) and (17)Otherwise, determining according to constraint (17-18)

In the present embodiment, the fitness function is obtainedAnd z_ik、After, according to z_ikComparison table with furnace numberObtaining the batch plan information of each time of firing, and calculatingAfter the coefficients are equal, the fitness value of each chromosome can be calculated.

In this embodiment, the method for determining the elite solution set includes:

and S51, merging the parent chromosomes and the child chromosomes, defining the domination relationship among individuals, giving sequence number grades to each individual according to the domination relationship, sequencing to generate non-dominated individual sets with different sequence number grades, and recording the number of the non-dominated individuals in each sequence number grade. In the present embodiment, the inter-individual dominance relationship is determined by:

assuming that for all targets, S1 is smaller than S2 for any two solutions S1 and S2, we call S1 dominates S2, and if the solution of S1 is not dominated by other solutions, S1 is called non-dominated solution; if S1 and S2 have mutual dominance relationship among the values of the objective function, namely, S1 and S2 are referred to as non-dominant solutions, for all the objectives f1, f2 and f3, f1(S1) < f1(S2), f2(S2) < f2(S2) and f3(S1) > f3 (S2); the set of all non-dominant solutions is the pareto solution set.

S52, determining the maximum sequence number that the elite solution set can accommodate according to the capacity of the elite solution set, the number of non-dominated individuals in each sequence number grade and the sequence number grade from small to large, determining the maximum sequence number that the elite solution set can accommodate according to the artificially set capacity of the elite solution set, wherein the individuals smaller than the sequence number value need to calculate the crowding distance, and the individuals beyond the sequence number range do not calculate the crowding distance and sort, and are directly discarded;

s53, calculating the sum of the number of solutions in the elite solution set and the number of solutions under the current non-dominant grade, judging whether the sum of the number of solutions is larger than the size of the elite solution set, if so, executing a step S54, and if not, executing a step S55;

s54, calculating the crowding distance of the current non-dominated level individuals, arranging the crowding distance in a descending order, and sequentially adding elite solutions into an elite solution set from large to small according to the crowding distance;

s55, calculating the crowding distance under the current non-dominant grade and adding the elite solution into an elite solution set;

s56, judging whether reaching the elite solution set size, if reaching, executing step S11 in the specification, if not, adding 1 to the non-dominant grade, and executing step S53.

In this embodiment, the rule for adding the elite solution to the elite solution set is: setting the size of the elite solution set, adding individuals in the elite solution set from small to large according to the rank ordering number until the elite solution set is filled, preferentially adding individuals with large crowding distance when two individuals with the same ranking number meet in the same rank order, and discarding the individuals exceeding the size of the elite solution set.

The purpose of the elite solution strategy is to ensure that good parent furnaces can smoothly enter children. As shown in fig. 3, the steps of the elite solution set strategy of the conventional NSGAII are as follows:

firstly, defining a domination relationship among individuals, assigning a sequence number grade to each individual according to the domination relationship, and sequencing to generate a non-domination individual set with different sequence number grades;

calculating the crowding distance between individuals of all sequence numbers in the set according to the fitness value of adjacent individuals;

setting the size of the elite solution set, adding individuals in the size from small to large according to the rank ordering number until the elite solution set is filled, preferentially adding individuals with large crowding distance when two individuals with the same rank ordering number meet in the same rank order, abandoning the individuals exceeding the size of the elite solution set, wherein the process is also called as elite solution set truncation, and the principle of the elite solution set truncation is shown in figure 3.

In the process of calculating the crowding distance, NSGAII calculates and orders a large number of crowding distances of non-dominated individuals which exceed the capacity of an elite solution set, have higher sequence numbers and can be abandoned, and when the problem size is larger and the number of iterations is larger, the time waste is more prominent. For this reason, the modifications or adjustments of INSGAII are as follows:

step1, except the content of the NSGAII Step I, recording the number of non-dominant individuals in each sequence number level;

step2, determining the maximum sequence number that the elite solution set can contain according to the capacity of the elite solution set, the number of non-dominated individuals in each sequence number grade and the sequence number grade from small to large;

and Step3, calculating and sorting the crowding distances in each grade according to the sequence number determined in Step2, and filling the elite solution set according to the rules of Step three of NSGAII.

INSGAII changes the congestion distance and the filling sequence of the elite solution set in NSGAII, only calculates the congestion distance of part of non-dominant individuals (such as individuals in brackets in FIG. 3) related to the inclusion of the elite solution set, does not calculate the congestion distance of the non-dominant individuals (individuals with # in the set B in FIG. 3) whose sequence numbers are greater than the maximum sequence number contained when the elite solution set is to be filled and whose sequence numbers are discarded, and creates conditions for saving the calculation time.

In this embodiment, the genetic manipulation includes crossover and mutation, wherein crossover is the phenomenon that the selection characteristics of the furnace number may be inconsistent with the real parameters of the casting machine if the whole chromosome is randomly selected and crossed because each casting machine coding section directly corresponds to the characteristics of the production lot plan, therefore, a method of parent-child multi-point crossover segmented according to the casting machine is adopted, wherein ① first takes two different complete chromosomes, ② uses the chromosomes according to the lengths of the chromosomes of each casting machineDivided into i sections, ③ crossed at randomly chosen cross points within each of the caster dye sections.

Variation of length of chromosome of each casting machineDividing the casting machine into i sections, and randomly selecting variation points in each casting machine dye body section: if the value of the variation point is 0, it becomes 1,otherwise it is changed from 1 to 0.

In the embodiment, the solution result is an elite solution set represented by a fitness value, and in order to be directly applied by a dispatcher, the elite solution set is converted into a target function value set by using a formula (19-21) and then an optimal compromise solution is determined by a fuzzy optimization method. The fuzzy optimization method comprises the following steps:

s71, calculating the specific gravity omega of each individual in the target function value set_(r,m)，ω_(r,m)Representing the proportion of the mth objective function value in the individual r,respectively representing the minimum and maximum values of the mth objective function value in the set of objective function values:

${\mathrm{\&omega;}}_{(r,m)}=\left\{\begin{array}{cc}1,& f_{(r,m)}\&le;f_{\left(m\right)}^{\min }\\ \frac{f_{\left(m\right)}^{\max }-f_{(r,m)}}{f_{\left(m\right)}^{\max }-f_{\left(m\right)}^{\min }},& f_{\left(m\right)}^{\min }<f_{{\mathrm{eval}}_{(r,m)}}<f_{\left(m\right)}^{\max }\\ 0,& f_{(r,m)}\&GreaterEqual;f_{\left(m\right)}^{\max }\end{array}\right.---\left(23\right)$

s72, normalizing satisfaction omega of all individuals_rWherein N is the population size of the elite solution set;

${\mathrm{\&omega;}}_r=\frac{\underset{m=1}{\overset{4}{\mathrm{\&Sigma;}}}{\mathrm{\&omega;}}_{(r,m)}}{\underset{r=1}{\overset{N}{\mathrm{\&Sigma;}}}\underset{m=1}{\overset{4}{\mathrm{\&Sigma;}}}{\mathrm{\&omega;}}_{(r,m)}}---\left(24\right)$

s73, selecting the individual with the maximum standard satisfactionFor the final casting heat and time decision scheme z_ik、

Based on actual production data of the decision of casting heat and time of a continuous casting machine in a certain domestic steel mill, model instance verification and model adaptability and algorithm performance test are carried out to check the effectiveness of the model and the algorithm.

Example of model validation: the plant has 5 continuous casting machines, and the decision of the casting heat and time in the production is completed by a manual experience mode, which is called manual decision for short. Taking daily operation time as a planning period, taking production actual performance data as a manual decision result, and taking the result as the basis of verification and comparison of a model decision example. The production input data are shown in tables 1-3, respectively, limited to space, and Table 1 only gives the planned batch casting time of the scheduled start time of the first furnaceSequentially adding tau to the scheduled starting time of other furnaces in the same casting time_ik。

To test model adaptability and algorithm performance, first, based on the data in tables 1-3, parameters I, ∑ K were varied_i、Q_E、τ_AThe value of (a) forms a problem of 4 different scales, wherein the parameter I ═ 2 represents casting by only casting machines No. 1 and No. 2, and I ═ 3 represents casting by only casting machines No. 1, No. 2 and No. 3, and so on; secondly, three comparative examples are additionally constructed, and the adaptability of the model and the performance of the algorithm are tested by comparing results of solving 4 problems of different scales respectively by using different examples. The structural purposes and characteristics of the comparative examples are described below:

(1) to verify the effectiveness of the selected multi-objective Algorithm, a Strength-based Pareto Evolutionary Algorithm (SPEAII) is designed, and encoding and decoding are performed in the same text.

(2) For testing the effectiveness of the selected coding method and the improved elite solution strategy at the same time, coding is carried out by taking NSGAII as a base and taking the furnace number as a gene, and the genetic manipulation and the elite solution strategy are the same as in the literature (DEB K, PRATAP A, AGARWAL S, equivalent.A fast and elitist multi-objective genetic algorithm: NSGA-II [ J ]. IEEEtransformations on evolution computing, 2002,6(2): 182-) -197) and are marked as NSGAII (r);

(3) in order to test the effect of the elite solution set improvement strategy, the coding mode is adopted, and the genetic operation and the elite solution strategy are similar to the literature in the point (2) and are marked as NSGAII;

the final Pareto solution set preference for each comparative example is the same as that herein, with performance testing taking the average of 10 runs.

The matlab7.0a is used as a platform for programming, each example independently operates in an environment of Intel (R) core (TM) i3-4010U/1.70GHz/4.00GB/WIN7, wherein the parameters of the example are set to be the population size of 40, the iteration number of 100, the cross probability of 0.8 and the variation probability of 0.2, and in addition, the external population size of SPEAII is 40.

TABLE 1 batch plan principal parameters

TABLE 2 casting machine Main parameters

TABLE 3 auxiliary parameters

FIG. 4 is a minimum fitness value evolution process of the present invention; table 4 shows the comparison of objective function values in two decision-making manners, where the decision-making result of the present invention is a pareto solution set, the objective function value corresponding to the serial number 14 is a fuzzy optimization result of the pareto solution set, and the artificial and model decision-making objective function values have the same calculation manner; FIG. 5 is a Gantt chart of the decision scheme of the present invention corresponding to scheme number 14 in Table 4; fig. 6 is a human decision gantt chart.

TABLE 4 comparison of objective function values for two decision-making modes

As can be seen from fig. 4 to 6 and table 4, the method of the present invention facilitates stable control of the heat casting cycle. Under the condition of the same metal resource amount, the casting machine pulling speed can be set in advance within the process requirement range, and the casting starting time and the number of casting furnaces of each casting machine are arranged, so that the phenomenon of casting period fluctuation is effectively avoided. Because of the lack of means for the optimization decision of the casting time and the casting time of the multiple casting machines, once the casting machine is artificially decided to be cast, the casting machine can only be maintained to continuously cast by frequently adjusting the casting machine pulling speed, so that the casting period of at least 15 times fluctuates severely. Frequent fluctuation of the heat casting period can seriously restrict the improvement of the casting blank quality.

The method of the invention is beneficial to the planning management of the steelmaking continuous casting. The 1 st objective function value and the 2 nd objective function value of the method are better than the artificial decision, while the third objective function value is slightly worse, because the model decision can be optimized in the global range; the manual decision can optimize the third target by changing the casting sequence of the furnaces to be cast on the casting machine 1# and 2# and even arbitrarily adding the variety steel (the furnace number NaN in figure 6) which is not in the planned period, but the type, the number, the sequence and the casting time of each furnace to be cast cannot be accurately determined, so that the 1 st and 2 nd target function values are deteriorated. As can be seen from the Gantt chart feature, model decisions help its users to link the top level lot plan with the steel mill operating plan to pursue plan management in steelmaking continuous casting.

Aiming at the phenomena of multiple influencing factors and large manual decision randomness of the decision problem of the casting machine casting heat and time in the practical production environment, the invention establishes a continuous casting machine casting heat and time decision optimization model which takes the total violation punishment of batch planning, the production line backlog metal quantity, the minimum non-effective utilization quantity of high-quality molten iron as a target function and the production process and production organization requirements as constraints on the basis of comprehensively considering the constraints of the relation between the batch planning preselected pool heat and the furnace to be cast, the metal resource balance, the available time of continuous casting equipment, the time sequence between the furnace to be cast and the like.

An improved non-dominated sorting genetic algorithm INSGAII suitable for the characteristics of the model is designed. The algorithm takes the furnace number selection as a gene, reduces the invalid search space of the solution by a step-by-step processing method for generating other two decision variables through decoding, adopts a new measure for adjusting the calculation sequence of the traditional elite solution set and limiting the unconventional crowded distance of the calculation sequence to reduce the calculation load of the elite solution link, and carries out fuzzy optimization on the final elite solution set to generate a model optimized solution which is convenient for visual understanding so as to be convenient for reference of model users.

The experimental test result shows that the model is beneficial to the stable control of each heat casting period of the continuous casting production and the practical plan management of the steel-making-continuous casting production; meanwhile, an algorithm performance test shows that: compared with the traditional non-dominated sorting genetic algorithm NSGAII and the strength pareto evolutionary algorithm SPEAII, the improved non-dominated sorting genetic algorithm INSGAII has higher efficiency in solving the multi-target problem of continuous casting melting time decision.

In the description herein, references to the description of the term "one embodiment," "some embodiments," "an example," "a specific example," or "some examples," etc., mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above do not necessarily refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.

While embodiments of the invention have been shown and described, it will be understood by those of ordinary skill in the art that: various changes, modifications, substitutions and alterations can be made to the embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.

Claims (7)

1. A multi-objective optimization method for selection, sequencing and casting time decision of a casting heat of a continuous casting machine set is characterized by comprising the following steps:

s1, connecting the controller with an MES database of a steel mill to obtain a production batch plan in an MES plan pre-selection pool of the steel mill, wherein the batch plan comprises the number of casting times distributed to each casting machine, the type of steel types to which each furnace belongs in the casting times, the section specification and a pre-set casting starting time;

s2, establishing an objective function with the minimum total punishment of the planned execution condition of the production batch of the steel plant, the minimum production line backlog metal quantity and the minimum non-effective utilization quantity of the high-quality molten iron, wherein the objective function is as follows:

min F＝{f₁,f₂,f₃} (1)

wherein,

$f_1=\underset{i=1}{\overset{I}{\&Sigma;}}\underset{k=1}{\overset{K_i}{\&Sigma;}}({\mathrm{\&xi;}}_{ik(k+1)}^1+{\mathrm{\&xi;}}_{ik(k+1)}^2)\&CenterDot;z_{ik}\&CenterDot;z_{i(k+1)}+\underset{i=1}{\overset{I}{\&Sigma;}}{d}_i\&CenterDot;(K_i-\underset{k=1}{\overset{K_i}{\&Sigma;}}{z}_{ik})+\underset{i=1}{\overset{I}{\&Sigma;}}\underset{k^d=1}{\overset{K_i^d}{\&Sigma;}}\left(\right|x_{{\mathrm{ik}}^d}-{\mathrm{\&tau;}}_{{\mathrm{ik}}^d}^{date}|\&CenterDot;{\mathrm{\&psi;}}_i+y_{{\mathrm{ik}}^d}\&CenterDot;e_i)---\left(2\right)$

f₂＝Q_O(3)

$f_3=Q_E\&CenterDot;{\mathrm{\&pi;}}^p+Q_I\&CenterDot;{\mathrm{\&delta;}}^p-\underset{i=1}{\overset{I}{\&Sigma;}}\underset{k=1}{\overset{K_i}{\&Sigma;}}{z}_{ik}\&CenterDot;v_{ik}\&CenterDot;q_i\&CenterDot;\frac{1}{1-\mathrm{\&eta;}}---\left(4\right)$

Q_O＝Q_E+Q_IV-Q_C-Q_L-Q_S(5)

$Q_C=\underset{i=1}{\overset{I}{\&Sigma;}}{\mathrm{rq}}_i+\underset{i=1}{\overset{I}{\&Sigma;}}\underset{k^d=1}{\overset{K_i^d}{\&Sigma;}}\left(\min \right({\mathrm{\&tau;}}_e,x_{{\mathrm{ik}}^d}+{\mathrm{\&tau;}}_{{\mathrm{ik}}^d})-x_{{\mathrm{ik}}^d})\&CenterDot;\mathrm{\&rho;}\&CenterDot;{\mathrm{wa}}_{{\mathrm{ik}}^d}\&CenterDot;{\mathrm{ws}}_{{\mathrm{ik}}^d}---\left(6\right)$

$Q_L=Q_C\&CenterDot;\frac{\mathrm{\&eta;}}{1-\mathrm{\&eta;}}---\left(7\right)$

$Q_S=\frac{Q_C\&CenterDot;{\mathrm{\&tau;}}_A}{({\mathrm{\&tau;}}_e-{\mathrm{\&tau;}}_s)\&CenterDot;(1-\mathrm{\&eta;})}+Q_{rcon}---\left(8\right)$

(2) the formula represents the sum of the punishment cost of steel type difference and delivery date difference between the selected furnace numbers, the punishment cost of the residual furnace numbers which are not cast, and the punishment cost of casting on time when each furnace number is not cast;

(3) formula represents the overstocked metal quantity Q of the production line_o；

(4) The formula represents the ineffective utilization amount of high-quality molten iron;

(5) the formula represents the backlog metal amount, is set based on the metal resource balance of the production line, and is respectively based on the planned iron feeding amount Q_EAmount of metal Q stocked in production line at the beginning of the production period_IVContinuous casting of steel Q_CAmount of metal loss Q_LPeriod favorable to production stabilityLast production line safety stock metal quantity Q_SForming;

(6) the steel casting amount of each continuous casting machine is respectively composed of the steel casting amount of the remained task in the previous planning period and the steel casting amount of each heat in the casting time to be started;

(7) the formula represents the metal loss amount corresponding to the steel casting amount;

(8) the formula represents the metal quantity in the safety stock of the production line, which needs to add a random fluctuation demand metal quantity Q on the basis of the average metal quantity in the stock of the production line_rcon；

Wherein, the specific meanings of the symbols are as follows:

symbol and set of definition:

i, casting machine serial number, I belongs to I, and I is a continuous casting machine set;

k is the furnace number of each casting machine in the preselection pool, K ∈ K_i，K_ijFor a pre-selection pool casting machine i casting times j heat times set, K_iGenerating k for all the heat sets of the continuous casting machine i of the pre-selection pool in sequence according to the preset casting starting time of each casting machine;

k^dthe serial number of the furnace to be poured is counted, is the set of the furnaces to be cast of the continuous casting machine i,the number of the casting furnaces is preset to be the lowest number of the casting furnaces of the casting machine i;

secondly, known parameters:

q_ikthe weight of molten steel of a casting machine i, heat k;

v_ikpreselecting whether the furnace k of the pool casting machine i is high-quality steel;

wa_ikpreselecting the section specification of a furnace k of a pool casting machine i;

casting machine i to-be-cast heat k^dThe section specification of (1);

ws_ikpre-selecting the pulling speed of a furnace k of a pool casting machine i;

casting machine i to-be-cast heat k^dThe pull rate of (2);

rq_ithe weight of molten steel left on a casting machine i;

rho is the density of the molten steel;

eta is the metal loss coefficient;

τ_s、τ_ethe starting time and the ending time of the planning period;

τ_Aaverage logistics time of the whole process;

casting machine i to-be-cast heat k^dThe casting period of (2);

the preset casting starting time of the i heat k of the casting machine;

e_ithe loss cost coefficient of the i-furnace intermittent casting of the casting machine;

Q_rconrandomly fluctuating the required metal amount;

^p、π^p、^p'the proportion of high-quality variety steel of the left-over task and the proportion of high-quality molten iron of the iron feeding and the initial metal amount;

ψ_ithe different cost coefficient of casting on time;

the additional cost caused by the steel grade difference between adjacent furnaces only belongs to the same steel grade class a if the steel grade code is the same as 0₁Belong to different steelsSpecies class a₂；

The difference in the start-up time is predetermined for an additional fee,β₁a cost factor for the difference in delivery dates of adjacent heats;

d_ithe furnace number of the casting machine i is not selected as the delay loss cost coefficient of the furnace number to be cast;

the penalty factor is used for removing illegal solutions by setting the penalty factor, and the M is a positive number which is large enough to ensure that the solutions are punished by a large enough fitness value when the solutions do not meet the constraint;

the coefficients are unified for dimension;

and thirdly, decision variables to be solved:

the casting machine i is selected as a to-be-cast heat k^dThe casting starting time;

binary variable, 1 denotes the number of times k the casting machine i is to be started^dThe casting is stopped with the furnace just before, 0 represents continuous casting with the furnace just before;

z_ikbinary variable, 1 represents that a certain heat k in a casting machine i in a preselection pool is selected as a heat to be cast, and 0 represents that the certain heat k is not selected;

s3, establishing a constraint relation between the pre-selection pool heat and the heat to be cast in the production batch plan, a metal resource balance related constraint relation, a continuous casting equipment available time constraint relation and a sequence and time constraint relation between the heat to be cast;

s4, selecting to code based on the furnace serial number and performing population initialization;

s5, decoding and calculating the fitness value to obtain an initial solution set, wherein the fitness function is as follows:

$\begin{array}{cc}\min & F=\{f_{{\mathrm{eval}}_1},f_{{\mathrm{eval}}_2},f_{{\mathrm{eval}}_3}\}\end{array}---\left(9\right)$

wherein,

$f_{{\mathrm{eval}}_1}=f_1---\left(10\right)$

$f_{{\mathrm{eval}}_3}=f_3+M\&CenterDot;max\{Q_D,Q_E\&CenterDot;{\mathrm{\&pi;}}^p+Q_{IV}\&CenterDot;{\mathrm{\&delta;}}^p\}---\left(12\right)$

(9) the formula represents the whole calculation process to obtain the fitness functionIs the target;

(10) formula represents fitness function valueIs equal to the value of the objective function f₁；

(11) Formula represents fitness function valueIs equal to the value of the objective function f₂Adding the sum of the punishment of violating the backlog metal quantity relation constraint and the punishment of exceeding the planned period of the casting starting time;

(12) formula represents fitness function valueIs equal to the target letterValue f₃The sum of punishments of the high-quality molten iron which is beyond the supply of the high-quality molten iron for planning;

s6, performing non-dominated sorting and crowded distance sorting on the solutions in the initial solution set;

s7, selecting a part of individuals in the population in the step S6 as parents;

s8, performing multipoint intersection on parents and parents of the father and the son of the father selected in the step S7 according to the casting machine segmentation, and performing random variation according to the casting machine segmentation point taking to ensure the consistency of the chromosome characteristics and the real production furnace serial number characteristics;

s9, decoding the result calculated in the step S8 and calculating the fitness, wherein the fitness function is the fitness function in the step S5;

s10, determining an elite solution set, limiting the number of individuals with the calculated crowding distance, and calculating the crowding distance and sequencing;

s11, judging whether the maximum iteration number is reached, if so, executing the step S12, otherwise, executing the step S7;

s12, outputting an elite solution set, and selecting a maximum satisfaction scheme as a continuous casting start-up heat time decision method by using a fuzzy optimization method;

and S13, transmitting the maximum satisfaction degree scheme to a steelmaking-continuous casting production operation control system, and realizing effective production operation control on selection, sequencing and casting starting time decision of the to-be-cast furnaces on each continuous casting machine by the system according to the maximum satisfaction degree scheme.

2. The multi-objective optimization method for the selection and sequencing of the casting heat and the decision of the casting starting time of the continuous casting machine set according to claim 1, wherein the constraint relationship of the relation between the pre-selected pool heat and the to-be-cast heat in the production lot plan in the step S3 is as follows:

$\underset{k=1}{\overset{K_i}{\&Sigma;}}{z}_{ik}=K_i^d,\&ForAll;i\&Element;\&lsqb;1,I\&rsqb;---\left(13\right)$

$K_i^d\&GreaterEqual;K_i^n,\&ForAll;i\&Element;\&lsqb;1,I\&rsqb;---\left(15\right)$

(13) the formula represents the relationship between the selected heat number of each continuous casting machine in the preselection pool and the number of the to-be-cast heat number of each casting machine in the planning period,

(14) the formula is set for adapting to resource limiting conditions, and indicates that the number of furnaces to be cast of each casting machine does not exceed the minimum value of the total number of batch plan furnaces of the preselected pool and the capacity requirement of the casting machine, wherein,meaning rounding up, mean () meaning calculating the mean,

(15) the formula is set for improving the utilization rate of the tundish and the continuous casting equipment, and indicates that the number of the casting machines must be more than the preset minimum number of casting furnaces of the casting machines if the casting machines are started;

the related constraint relation of metal resource balance is as follows:

Q_O≥0 (16)

Q_D≤Q_E·π^p+Q_IV·^p’(17)

$Q_D=({\mathrm{\&delta;}}^p\&CenterDot;\underset{i=1}{\overset{I}{\&Sigma;}}{\mathrm{rq}}_i+\underset{i=1}{\overset{I}{\&Sigma;}}\underset{k^d=1}{\overset{K_i^d}{\&Sigma;}}{v}_{{\mathrm{ik}}^d}\&CenterDot;(\min \left({\mathrm{\&tau;}}_e,x_{{\mathrm{ik}}^d}+{\mathrm{\&tau;}}_{{\mathrm{ik}}^d}\right)-x_{{\mathrm{ik}}^d})\&CenterDot;\mathrm{\&rho;}\&CenterDot;{\mathrm{wa}}_{{\mathrm{ik}}^d}\&CenterDot;{\mathrm{ws}}_{{\mathrm{ik}}^d})\&CenterDot;1/(1-\mathrm{\&eta;})---\left(18\right)$

(16) the formula represents that the backlog metal quantity of the production line is not negative;

(17) the formula represents that the amount of high-quality molten iron required by the cast high-quality steel does not exceed the sum of the initial inventory and the amount of high-quality molten iron entering iron in the planned period;

(18) the formula represents the amount of high-quality molten iron Q required for casting high-quality steel_DRespectively consisting of two parts of high-quality molten iron quantities required by a leaving task and a time to be fired;

the available time constraint relation of the continuous casting equipment is as follows:

${\mathrm{\&tau;}}_i^{earliest}\&le;x_{{\mathrm{ik}}^d},\&ForAll;i\&Element;\&lsqb;1,I\&rsqb;,\&ForAll;k^d\&Element;\&lsqb;1,K_i^d\&rsqb;---\left(19\right)$

the casting time of the selected heat is not earlier than the earliest available time of the casting machine;

the sequence and time constraint relation among the furnaces to be cast is as follows:

$y_{{\mathrm{ik}}^d}\left\{\begin{array}{c}=1,{\mathrm{wa}}_{{\mathrm{ik}}^d}\&NotEqual;{\mathrm{wa}}_{i(k^d-1)},\&ForAll;i\&Element;\&lsqb;1,I\&rsqb;,\&ForAll;k^d\&Element;\&lsqb;1,K_i^d\&rsqb;\\ =0,{\mathrm{wa}}_{{\mathrm{ik}}^d}={\mathrm{wa}}_{i(k^d-1)},\&ForAll;i\&Element;\&lsqb;1,I\&rsqb;,\&ForAll;k^d\&Element;\&lsqb;1,K_i^d\&rsqb;\end{array}\right.---\left(20\right)$

${\mathrm{\&tau;}}_s\&le;x_{{\mathrm{ik}}^d}\&le;{\mathrm{\&tau;}}_e,\&ForAll;i\&Element;\&lsqb;1,I\&rsqb;,\&ForAll;k^d\&Element;\&lsqb;2,K_i^d\&rsqb;---\left(21\right)$

${\mathrm{\&tau;}}^{\&prime;}+{\mathrm{\&tau;}}_i^{gap}\&CenterDot;y_{{\mathrm{ik}}^d}\&le;x_{{\mathrm{ik}}^d}\&le;{\mathrm{\&tau;}}^{\&prime;}+({\mathrm{\&tau;}}_e-{\mathrm{\&tau;}}^{\&prime;})\&CenterDot;y_{{\mathrm{ik}}^d},\&ForAll;i\&Element;\&lsqb;1,I\&rsqb;,\&ForAll;k^d\&Element;\&lsqb;1,K_i^d\&rsqb;---\left(22\right)$

(20) the formula shows that the casting is forcibly stopped when the furnace discontinuity specifications are different,

(21) the formula shows that the casting time of each furnace to be cast is selected to be in the planning period,

(22) when the furnace to be cast and the remained task are cast continuously, the casting time point takes the remained task ending time, and tau' ═ rq_i/ρ·ra_i·rs_iWhen the continuous casting is not carried out, the time from the end time of the left task to the end of the planned period is taken,when the times to be started are mutually and continuously cast, the casting starting time point takes the end time of the previous furnace,when non-continuous casting is carried out, the interval between the end time of the previous furnace and the furnace is taken to reach the planning periodAt a certain time between the end of the day,

3. the multi-objective optimization method for the selection, the sequencing and the decision of the casting time of the continuous casting machine set according to claim 1, wherein the coding method in step S4 of claim 1 is as follows:

s31, counting the total furnace times K of each casting machine i in the preselection pool_iThe predetermined time of starting pouring is planned according to the batch for each heatSequencing in sequence, giving a furnace number to each sequenced furnace in sequence, establishing a reference table of the furnace number of each casting machine, and ensuring that the sequence of the furnace number is consistent with the sequence of the scheduled casting time of the batch plan;

s32, determining the selected heat number range and randomly generating the length K_iThe binary sequences of the casting machines correspond to the furnace number reference table one by one, and the range of the number of the selected furnaces is determined according to the constraint relation of the relationship between the furnace number of the pre-selection pool and the furnace number to be cast in the production batch plan;

and S33, connecting the chromosome gene segments of the casting machines to form a complete chromosome, and randomly generating an initial population with a set scale.

4. The multi-objective optimization method for the casting time selection, the sequencing and the casting start time decision of the continuous casting machine set according to claim 1, wherein the decoding method comprises the following steps:

s41, processing of illegal chromosomes: the illegal chromosomes after cross mutation can be divided into two types: the total number of the selected to-be-started heat is larger than the upper limit of the range of the heat quantity calculated in the claim 3 and smaller than the lower limit of the range of the heat quantity calculated in the claim 3, 1 which is larger than the number of the upper limit of the constraint is changed into 0 randomly for the former, 0 which is lower than the number of the lower limit of the constraint is changed into 1 randomly for the latter, and chromosomes which do not violate the constraint are not changed;

s42, generating a to-be-started heat sequence according to the heat sequence with 1 appearing from left to right in the chromosome of each casting machine, contrasting the heat sequence reference table and the heat characteristics in the batch plan, and generating by combining the constraint (20) formula

S43, if a certain furnace and a previous furnace in the sequence of the furnace to be opened are disconnected from each other and have the earliest available time, determining the furnace to be opened according to the constraint formulas (19) and (21)Otherwise, determining according to constraint (21-22)

5. The multi-objective optimization method for the selection and sequencing of the casting times and the decision of the casting starting time of the continuous casting machine set according to claim 1, wherein the method for determining the elite solution set comprises the following steps:

s51, merging the chromosomes of the parent generation and the chromosomes of the child generation, defining a dominance relation between individuals, giving sequence number grades to each individual according to the dominance relation and sequencing to generate a non-dominance individual set with different sequence number grades, and recording the number of the non-dominance individuals in each sequence number grade;

s52, determining the maximum sequence number that the elite solution set can contain according to the capacity of the elite solution set, the number of non-dominated individuals in each sequence number grade and the sequence number grade from small to large;

s53, calculating the sum of the number of solutions in the elite solution set and the number of solutions under the current non-dominant grade, judging whether the sum of the number of solutions is larger than the size of the elite solution set, if so, executing a step S54, and if not, executing a step S55;

s54, calculating the crowding distance of the current non-dominated level individuals, arranging the crowding distance in a descending order, and sequentially adding elite solutions into an elite solution set from large to small according to the crowding distance;

s55, calculating the crowding distance under the current non-dominant grade and adding the elite solution into an elite solution set;

s56, judging whether reaching the elite solution set size, if reaching, executing step S11 as claimed in claim 1, if not, adding 1 to the sequence number grade of the non-dominant solution, and executing step S53.

6. The multi-objective optimization method for the selection and sequencing of the casting times and the decision of the casting time of the continuous casting machine set according to claim 1, wherein the rules for adding the elite solution to the elite solution set are as follows: setting the size of the elite solution set, adding individuals in the elite solution set from small to large according to the rank ordering number until the elite solution set is filled, preferentially adding individuals with large crowding distance when two individuals with the same ranking number meet in the same rank order, and discarding the individuals exceeding the size of the elite solution set.

7. The multi-objective optimization method for selecting, sequencing and making a casting time decision of a continuous casting unit according to claim 1, wherein a maximum satisfaction scheme is selected as a continuous casting making time decision method, and the fuzzy optimization method comprises the following steps:

s71, calculating the specific gravity omega of each individual in the target function value set_(r,m)，ω_(r,m)Representing the proportion of the mth objective function value in the individual r,respectively representing the minimum and maximum values of the mth objective function value in the set of objective function values:

${\mathrm{\&omega;}}_{(r,m)}=\left\{\begin{array}{cc}1,& f_{(r,m)}\&le;f_m^{\min }\\ \frac{f_{\left(m\right)}^{\max }-f_{(r,m)}}{f_{\left(m\right)}^{\max }-f_{\left(m\right)}^{\min }},& f_{\left(m\right)}^{\min }<f_{{\mathrm{eval}}_{(r,m)}}<f_{\left(m\right)}^{\max }\\ 0,& f_{(r,m)}\&GreaterEqual;f_{\left(m\right)}^{\max }\end{array}\right.---\left(23\right)$

s72, normalizing satisfaction omega of all individuals_rWherein N is the population size of the elite solution set;

${\mathrm{\&omega;}}_r=\frac{\underset{m=1}{\overset{4}{\&Sigma;}}{\mathrm{\&omega;}}_{(r,m)}}{\underset{r=1}{\overset{N}{\&Sigma;}}\underset{m=1}{\overset{4}{\&Sigma;}}{\mathrm{\&omega;}}_{(r,m)}}---\left(24\right)$

s73, selecting the individual with the maximum standard satisfactionFor the final casting heat and time decision scheme z_ik、