CN116088457B

CN116088457B - Steelmaking continuous casting scheduling method and device of distributed robust joint opportunity constraint model

Info

Publication number: CN116088457B
Application number: CN202310371510.9A
Authority: CN
Inventors: 宋士吉; 牛晟盛; 杨琬露
Original assignee: Tsinghua University
Current assignee: Tsinghua University
Priority date: 2023-04-10
Filing date: 2023-04-10
Publication date: 2023-06-27
Anticipated expiration: 2043-04-10
Also published as: CN116088457A

Abstract

The invention provides a steelmaking continuous casting scheduling method and device of a distributed robust joint opportunity constraint model, belonging to the technical field of production scheduling and production internal and external resource optimization, wherein the method comprises the following steps: taking the shortest total flow time as an optimization target, taking the furnace processing time as a random variable, and constructing a distributed robust joint opportunity constraint model for the steelmaking continuous casting scheduling problem; considering the correlation between constraint conditions, and converting the distributed robust joint opportunity constraint model into a distributed robust joint opportunity constraint model based on CVaR approximation according to CVaR approximation and a dual theory; based on an iterative lifting solving algorithm, solving a distributed robust joint opportunity constraint model based on CVaR approximation to obtain a steelmaking continuous casting scheduling scheme. In the invention, the uncertainty of the processing time of the furnace is considered, so that the obtained steelmaking continuous casting scheduling scheme is more in line with the actual situation, the casting interruption phenomenon in the steelmaking continuous casting process can be greatly reduced, and the stability of the production process is improved.

Description

Steelmaking continuous casting scheduling method and device of distributed robust joint opportunity constraint model

Technical Field

The invention belongs to the technical field of production scheduling and production internal and external resource optimization, and particularly relates to a steelmaking continuous casting scheduling method and device of a distributed robust joint opportunity constraint model.

Background

Steelmaking continuous casting is one of the most important links in the steel production process, and because the actual processing flow involves more manual links and the uncertain factors such as machine faults, unqualified molten steel quality, planned temporary change and the like, the production cannot be executed according to the plan. As the key working procedures of the upstream and the downstream are connected, the production plan of the upstream and the downstream can be changed along with the change of the production plan, and the overall production efficiency of the iron and steel enterprises is further affected. Therefore, an effective steelmaking continuous casting scheduling method is important for improving production efficiency and reducing production cost.

Early research on the steelmaking continuous casting production scheduling problem is mainly focused on a deterministic model, and the steelmaking continuous casting production scheduling problem is solved by using an operation research-based method, an intelligent optimization algorithm, an expert system, a fuzzy method and the like. However, the uncertainty of the steelmaking continuous casting process is numerous, and the scheduling scheme obtained by the deterministic model cannot achieve good performance, and is not feasible even in many cases. Therefore, aiming at the uncertain factors of the steelmaking continuous casting process, a plurality of scholars research a dynamic scheduling method, so that when an emergency occurs, the steelmaking continuous casting process is rescheduled according to the current production condition. Dynamic scheduling has good effects when dealing with significant impact events, such as long-term machine failures, order additions or deletions, and the like. However, in the steelmaking continuous casting process, the occurrence frequency of non-significant influence events is far greater than that of significant influence events, such as short-term faults of machines, fluctuation of processing time and transportation time, and the like. Rescheduling of the production process is frequently performed against these fluctuations not only wastes a lot of resources, but also makes the production plan unstable. And the dynamic scheduling model considers that the processing environment is determined, so that the obtained rescheduling scheme still cannot solve the problem of future parameter fluctuation.

Aiming at uncertainty factors in the steelmaking continuous casting scheduling process, the current research is limited to a robust optimization method and a random programming method based on an uncertainty set. Robust optimization based on uncertainty sets only considers support set information and therefore has great conservation, while stochastic programming methods generally assume that uncertainty parameters follow a particular distribution, and in practical production environments, exact distributions of uncertainty parameters are often difficult to obtain, especially for new production lines or new machines or workpieces. Compared with the two methods, the robust optimization method based on the distribution function set is more focused by students in recent years, and has been applied to a plurality of brand new fields or problems.

However, the main research work of the robust optimization method based on the distribution function set is based on classical scheduling models of single machine and parallel machine, and only takes the total flow time in a linear form and the like as an optimization target. The prior art does not give a proper model and a model transformation solution scheme, so that the method is not suitable for the production scheduling problem containing uncertain constraints, such as steelmaking continuous casting scheduling problem.

Disclosure of Invention

In view of the above, embodiments of the present invention provide a steelmaking continuous casting scheduling method and apparatus for a distributed robust joint opportunity constraint model to overcome or at least partially solve the above problems.

In a first aspect of the embodiment of the invention, a steelmaking continuous casting scheduling method of a distributed robust joint opportunity constraint model is disclosed, and the method comprises the following steps:

taking the shortest total flow time as an optimization target, taking the furnace processing time as a random variable, and constructing a distributed robust joint opportunity constraint model for the steelmaking continuous casting scheduling problem;

considering the correlation between constraint conditions, and converting the distributed robust joint opportunity constraint model into a distributed robust joint opportunity constraint model based on CVaR approximation according to CVaR approximation and a dual theory;

based on an iterative lifting solving algorithm, solving the distributed robust joint opportunity constraint model based on CVaR approximation to obtain a steelmaking continuous casting scheduling scheme, wherein the steelmaking continuous casting scheduling scheme comprises: all heats and start-up times for the runs.

Optionally, the method further comprises:

aiming at the condition that the constraint conditions are mutually independent, converting the distributed robust joint opportunity constraint model into a distributed robust joint opportunity constraint model based on an independent hypothesis;

And solving the distributed robust joint opportunity constraint model based on the independence assumption based on the iterative lifting solving algorithm to obtain a steelmaking continuous casting scheduling scheme under the constraint independent condition.

Optionally, the constructing a distributed robust joint opportunity constraint model of steelmaking continuous casting scheduling problem with shortest total flow time as an optimization target and furnace processing time as a random variable includes:

determining parameters and decision variables of the distributed robust joint opportunity constraint model;

the uncertain furnace processing time is taken as an uncertain parameter of the distributed robust joint opportunity constraint model, the uncertain parameters are specifically unknown respectively, but the uncertain parameters belong to a distribution function set with a support set and known moment information;

determining an objective function of the distributed robust joint opportunity constraint model, wherein the objective function takes minimum total flow time as an optimization target;

and determining constraint conditions of the distributed robust joint opportunity constraint model, wherein the constraint conditions of the distributed robust joint opportunity constraint model are used for constraining the feasibility of a distribution set and a scheduling scheme obeyed by uncertain processing time.

Optionally, the objective function of the distributed robust joint opportunity constraint model is expressed as:

Wherein (1)>

The function of the upper limit is represented by,

representing a minimum function,/->

Indicating desire(s)>

Representing the aggregate of all runs, +.>

Indicate->

All heat sets in each casting, +.>

Representing distribution(s)>

Representing the distribution function set to which the uncertain process time belongs, < ->

Representing the processing casting time->

Is a continuous casting machine of->

Representing the processing watering time->

Is +.>

Order of (2)>

Representing the watering time->

Start-up time of the first heat of (a),/-)>

Representing the heat +.>

In the process of casting->

Processing time on continuous casting machine, +.>

Indicate->

The third of the number of times>

Total processing time of all heats before the individual heats, +.>

Representing the watering time->

Middle->

Finishing time of each heat, +.>

Representing the watering time->

The sum of the finishing times of all the heats, < >>

Representing the sum of the finishing times of all heats in all runs.

Optionally, the constraint condition of the distributed robust joint opportunity constraint model includes:

uncertain heat processing time constraints, including: the specific distribution of the uncertain heat processing time is unknown, but the uncertain heat processing time belongs to a distribution function set determined by a support set, a mean value vector and a covariance matrix;

A heat continuity constraint comprising: on the same continuous casting machine, when casting is completed in a certain heat, the subsequent heat reaches the continuous casting machine and can start to process;

a single casting initiation processing time constraint comprising: the starting processing time of each casting time is more than or equal to the preparation time, and the starting processing time of each casting time is more than or equal to the completion time of the first furnace time of the casting time in the last working procedure plus the transportation time;

adjacent runner start machining time constraints, comprising: two adjacent casting times on the same continuous casting machine, wherein the starting processing time of the next casting time is more than or equal to the finishing time plus the preparation time of the previous casting time;

a heat start processing time constraint comprising: in addition to the continuous casting machine, two adjacent heats on the same machine, and the starting processing time of the subsequent heat needs to be more than or equal to the finishing time of the previous heat;

the processing time constraint of the adjacent working procedures of the same furnace number comprises the following steps: in two adjacent processes in the same furnace, the starting processing time of the next process is more than or equal to the finishing time plus the transportation time of the last process.

Optionally, the converting the distributed robust joint opportunity constraint model into a distributed robust joint opportunity constraint model based on CVaR approximation according to CVaR approximation and dual theory includes:

Converting an objective function in the distributed robust joint opportunity constraint model into a general representation form;

and converting the distributed robust joint opportunity constraint approximation in the distributed robust joint opportunity constraint model into a semi-positive constraint through CVaR approximation and a dual theory.

Optionally, the solving the distributed robust joint opportunity constraint model based on CVaR approximation based on the iterative lifting solving algorithm includes:

generating a plurality of constraint factor vectors in advance;

solving an optimal solution and an optimal value of the distributed robust joint opportunity constraint model based on CVaR approximation according to the value of the constraint factor vector aiming at each constraint factor vector;

updating the value of the constraint factor vector according to the optimal solution and the optimal value, and solving the distributed robust joint opportunity constraint model based on CVaR approximation with the updated value of the constraint factor vector to obtain a new optimal solution and an optimal value;

and after the iteration ending condition is met, obtaining an optimal solution and an optimal value corresponding to the constraint factor vector, and selecting a final optimal solution and an optimal value from the optimal solutions and the optimal values corresponding to the constraint factor vectors.

Optionally, the converting the distributed robust joint opportunity constraint model into the distributed robust joint opportunity constraint model based on the independence assumption includes:

and (3) converting the distributed robust joint opportunity constraint in the distributed robust joint opportunity constraint model into a distributed robust independent opportunity constraint by giving the establishment probability of each constraint condition.

Optionally, the solving the distributed robust joint opportunity constraint model based on the independence assumption based on the iterative lifting solution algorithm includes:

generating a plurality of probability distribution vectors in advance;

aiming at each probability distribution vector, carrying out approximate transformation on the distributed robust joint opportunity constraint model based on the independence assumption according to the value of the probability distribution vector, and obtaining the optimal solution and the optimal value of the steelmaking continuous casting scheduling problem through solving;

calculating the maximum probability and corresponding parameters which can be established under the optimal solution, updating the value of the probability distribution vector according to the parameters, and continuously calculating a new optimal solution and an optimal value by using the updated probability distribution vector;

And after the iteration ending condition is met, obtaining an optimal solution and an optimal value corresponding to the probability distribution vector, and selecting a final optimal solution and an optimal value from the optimal solutions and the optimal values corresponding to the probability distribution vectors.

In a second aspect of the embodiment of the present invention, a steelmaking continuous casting scheduling apparatus of a distributed robust joint opportunity constraint model is disclosed, the apparatus comprising:

the model building module is used for building a distributed robust joint opportunity constraint model for steelmaking continuous casting scheduling problem by taking the shortest total flow time as an optimization target and the furnace processing time as a random variable;

the model conversion module is used for converting the distributed robust joint opportunity constraint model into a distributed robust joint opportunity constraint model based on CVaR approximation according to the correlation between constraint conditions and the CVaR approximation and the dual theory;

the problem solving module is used for solving the distributed robust joint opportunity constraint model based on CVaR approximation based on an iterative lifting solving algorithm to obtain a steelmaking continuous casting scheduling scheme, wherein the steelmaking continuous casting scheduling scheme comprises: all heats and start-up times for the runs.

The embodiment of the invention has the following advantages:

In the embodiment of the invention, the shortest total flow time is taken as an optimization target, the furnace processing time is taken as a random variable, a distributed robust joint opportunity constraint model of a steelmaking continuous casting scheduling problem is constructed, the correlation among constraint conditions is considered, the distributed robust joint opportunity constraint model is converted into a distributed robust joint opportunity constraint model based on CVaR approximation according to CVaR approximation and a dual theory, and the obtained deterministic optimization problem is not convex, so that an iterative lifting solving algorithm is designed, and the distributed robust joint opportunity constraint model based on CVaR approximation is solved, so that the steelmaking continuous casting scheduling scheme is obtained. Because the uncertainty of the processing time of the heat is considered in the embodiment, the obtained steelmaking continuous casting scheduling scheme is more in line with the actual situation, the casting interruption phenomenon in the steelmaking continuous casting process can be greatly reduced, and the stability of the production process is improved.

Drawings

In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings that are needed in the description of the embodiments of the present invention will be briefly described below, it being obvious that the drawings in the following description are only some embodiments of the present invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.

FIG. 1 is a flow chart of steps of a steelmaking continuous casting scheduling method of a distributed robust joint opportunity constraint model provided by an embodiment of the invention;

FIG. 2 is a schematic diagram of a steelmaking continuous casting process according to an embodiment of the present invention;

FIG. 3 is a flowchart illustrating steps for performing iterative solution based on a CVaR approximation-based distributed robust joint opportunity constraint model according to an embodiment of the present invention;

FIG. 4 is a flowchart illustrating steps for performing iterative solution on a distributed robust joint opportunity constraint model based on an independence assumption according to an embodiment of the present invention;

fig. 5 is a schematic structural diagram of a steelmaking continuous casting scheduling device of a distributed robust joint opportunity constraint model provided by an embodiment of the invention.

Detailed Description

In order that the above objects, features and advantages of the present invention will be readily apparent, a more particular description of embodiments of the invention will be rendered by reference to the appended drawings, which are illustrated in the appended drawings. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.

The embodiment of the invention provides a steelmaking continuous casting scheduling method of a distributed robust joint opportunity constraint model, as shown in fig. 1, fig. 1 is a step flow chart of the steelmaking continuous casting scheduling method of the distributed robust joint opportunity constraint model, which comprises steps S101 to S103:

step S101: and constructing a distributed robust joint opportunity constraint model of the steelmaking continuous casting scheduling problem by taking the shortest total flow time as an optimization target and the furnace processing time as a random variable.

As shown in fig. 2, the steelmaking continuous casting production process specifically includes: and three main processes of steelmaking, refining and continuous casting. In the steelmaking stage, the upstream molten iron is transported to a converter, the carbon content in the molten iron is reduced by oxygen blowing, and a furnace of molten steel from the converter is called a heat, which is a basic unit of a steelmaking continuous casting production process; in the refining stage, the furnace number after the steel making is completed is conveyed to a refining furnace, and chemical components in molten steel are further adjusted to remove impurities in the molten steel or alloy components are added to meet different steel grade requirements; in the continuous casting stage, molten steel after refining is transported to a continuous casting machine, molten steel flows from a ladle through a tundish, is solidified into a slab at the bottom of the continuous casting machine through a mold, and a batch of heats having the same chemical composition and continuously cast on the continuous casting machine is called a casting pass. In the whole process, continuous casting is ensured as much as possible for all the heats in one casting, because the same tundish is used for all the heats in one casting, and if casting is interrupted, the tundish needs to be replaced again, which causes a great deal of fixed cost and consumes a great deal of time. Meanwhile, the heat preservation and heating are needed to be carried out again when the furnace number which does not complete continuous casting is remained, so that more economic losses are brought, and the occurrence of the casting breaking times is reduced, namely the production cost is reduced.

In this embodiment, the steelmaking continuous casting scheduling problem with uncertain furnace processing time is focused on, and a distributed robust joint opportunity constraint model is established for the problem. The distributed robust joint opportunity constraint model takes the furnace processing time as a random variable, the distribution of the distributed robust joint opportunity constraint model is unknown but belongs to a distribution function set with a support set and known moment information, the total flow time in the steelmaking continuous casting process is taken as an optimization target, and the constraint related to the uncertain processing time is processed by adopting the robust joint opportunity constraint model.

Specifically, the method uses the shortest total flow time as an optimization target, uses the furnace processing time as a random variable, and constructs a distributed robust joint opportunity constraint model of steelmaking continuous casting scheduling problem, and comprises the steps of A1 to A4:

step A1: parameters and decision variables of the distributed robust joint opportunity constraint model are determined.

In this embodiment, parameters of the distributed robust joint opportunity constraint model mainly include:

representing the aggregate of all heats, +.>

Representing the aggregate of all runs, +.>

Representing the set of all machines->

Indicating all processing heats +.>

Is (including continuous casting machine) is +.>

Represents the set of all casters, +. >

Representing the processing casting time->

Is a continuous casting machine of->

Indicate->

All heat sets in each casting, +.>

Representing the heat +.>

In the machine->

Directly subsequent heat of upper processing, +.>

Representing slave machine->

To->

Is (are) transported in time>

Representing the processing heat +.>

Is->

Is directly subsequent to the machine, ">

Representing the processing heat +.>

Is->

Is used for the direct-to-direct preceding machine of (a),

representing the heat +.>

In the machine->

Processing time of the above->

Indicating the preparation time of adjacent runs, +.>

Representing the heat +.>

In the machine->

Sequence number of upper process,/->

Representing the casting time of the same continuous casting machine>

Is directly and subsequently poured for times.

Decision variables of the distributed robust joint opportunity constraint model mainly comprise:

representing the watering time->

A start-up time for a first heat of the furnace; />

Representing the heat +.>

In the machine->

Start-up time in which>

。

Step A2: and taking the uncertain furnace processing time as an uncertain parameter of the distributed robust joint opportunity constraint model, wherein the specific distribution of the uncertain parameter is unknown, but the uncertain parameter belongs to a distribution function set with a known support set and moment information.

In this embodiment, considering the case where the processing time of the heat is not determined (that is, the processing time is a random variable), the method is used

Representing the heat +.>

In the machine->

Processing time above, all uncertain processing time constitute vector +.>

Wherein the uncertainty parameter belongs to a set of distribution functions for which the support set and moment information are known, the support set and moment information being known to refer to the type of support set of the set of distribution functions, the support set parameters, the mean vector and the covariance matrix being known. Specifically, vector->

Distribution function set->

The definition is as follows:

wherein (1)>

Is->

Support set of->

And->

Are respectively->

Mean and covariance matrix of (c).

Step A3: and determining an objective function of the distributed robust joint opportunity constraint model, wherein the objective function takes the minimum total flow time as an optimization target.

In this embodiment, the objective function represents the minimum total flow time of all heats in completing all the casts under the condition of uncertainty of the distribution function set of the processing time, namely, the specific meaning of the objective function is as follows: minimizing the total flow-through time.

Specifically, the objective function of the distributed robust joint opportunity constraint model is expressed as:

(equation 1)

Wherein, the liquid crystal display device comprises a liquid crystal display device,

representing the upper limit function>

Representing a minimum function,/->

Indicating desire(s)>

Representing the aggregate of all runs, +.>

Indicate->

All heat sets in each casting, +. >

Representing distribution(s)>

Representing the processing casting time->

Is a continuous casting machine of->

Representing the processing watering time->

Is +.>

Order of (2)>

Representing the watering time->

Start-up time of the first heat of (a),/-)>

Representing the heat +.>

In the process of casting->

Processing time on continuous casting machine, +.>

Indicate->

The third of the number of times>

The total processing time of all the heats before the individual heats,

representing the watering time->

Middle->

The finishing time of each heat is equal to the finishing time of each heat,

representing the watering time->

The sum of the finishing times of all the heats,

representing the sum of the finishing times of all heats in all runs.

Further, since the objective function is the desire to minimize the total flow-through time, the objective function of the distributed robust joint opportunity constraint model may be rewritten as:

(equation 2)

and->

Is uncertain processing time->

And->

Is a mean value of (c). Equation 2 shows that the sum of the finishing times for all heats in all runs is the smallest, i.e., the total flow-through time is the smallest.

Step A4: and determining constraint conditions of the distributed robust joint opportunity constraint model, wherein the constraint conditions of the distributed robust joint opportunity constraint model are used for constraining the feasibility of a distribution set and a scheduling scheme obeyed by uncertain furnace processing time.

In this embodiment, the distributed robust joint opportunity constraint model for the steelmaking continuous casting scheduling problem includes 6 types of constraint conditions, wherein the 1 type constraint is a distribution set constraint to which the uncertain heat processing time is subjected, and the other 5 types of constraint are feasibility constraint of the scheduling scheme.

Specifically, the constraint condition of the distributed robust joint opportunity constraint model includes: the method comprises the steps of determining a heat processing time constraint, a heat continuity constraint, a single casting start processing time constraint, an adjacent casting start processing time constraint, a heat start processing time constraint and a heat adjacent process start processing time constraint. Wherein the uncertain heat processing time constraint belongs to a distribution set constraint obeyed by the uncertain heat processing time; the furnace continuity constraint, the single casting time constraint, the adjacent casting time constraint, the furnace start processing time constraint and the adjacent process start processing time constraint of the same furnace belong to the feasibility constraint of a scheduling scheme.

1) An uncertain heat processing time constraint belonging to a set of distribution functions defined by a support set, a mean vector and a covariance matrix.

Uncertain heat processing time

Is unknown, but the uncertain heat treatment time belongs to a supported set +.>

Mean vector->

And covariance matrix->

The determined distribution function is concentrated and expressed as follows:

(equation 3)

2) A heat continuity constraint comprising: on the same continuous casting machine, when a certain heat finishes casting, the subsequent heat has arrived at the continuous casting machine and can start processing, the expression is as follows:

(equation 4)

is a mathematical expression of the chance constraint, i.e. the probability that an event is true is not lower than +.>

，

，/>

Representing the heat +.>

Finishing time of previous heat, +.>

Representing the heat +.>

The time to reach the caster, therefore, equation 4 represents the set of distribution functions +.>

Lower heat->

The time to reach the continuous casting machine is less than or equal to the heat degree +.>

The probability of establishment of the finishing time of the previous heat is equal to or greater than +.>

。

3) A single casting initiation processing time constraint comprising: the start processing time of each casting time is required to be equal to or longer than the preparation time, and the expression is as follows:

(equation 5)

representing the watering time->

Start-up time of the first heat of (a),/-)>

Indicating the preparation time for adjacent runs.

The starting processing time of each casting time is equal to or more than the completion time of the last working procedure of the first furnace time of the casting time plus the transportation time, and the expression is as follows:

(equation 6)

representing the watering time->

The first heat of the furnace is added with the completion time of the last process and the transportation time. Equation 6 shows the distribution function set +.>

Lower, watery->

The first heat of (2) has a start processing time of equal to or longer than that of the first heat, and is watered>

The probability of the completion time of the previous process plus the establishment of the transport time is greater than or equal to +.>

。

4) Adjacent runner start machining time constraints, comprising: two adjacent casting times on the same continuous casting machine, the starting processing time of the next casting time is more than or equal to the finishing time plus the preparation time of the previous casting time, and the expression is as follows:

(equation 7)

representing the and the casting times on the same continuous casting machine>

The start processing time of the next casting run,

representing the watering time->

The sum of the completion time of the adjacent casting runs and the preparation time of the adjacent casting runs. Equation 7 shows the distribution function set +.>

Lower, casting times on the same continuous casting machine>

The processing time of the direct subsequent casting time is greater than or equal to +.>

The probability of establishment of the sum of the completion time of (2) and the preparation time of the adjacent casting times is equal to or greater than +.>

。

5) A heat start processing time constraint comprising: in addition to the continuous casting machine, two adjacent heats on the same machine, the start processing time of the subsequent heat needs to be greater than or equal to the completion time of the previous heat. That is, two heats that are processed on the same machine, the next heat must be processed after the last heat is completed, and the expression is as follows:

(equation 8)

representing the heat +.>

Is in machine +.>

Start processing time,/->

Representing the heat +.>

In the machine->

Start processing time,/->

Expressed in machine->

Top heat +.>

And the start-up time of the immediately subsequent heat. Equation 8 shows the distribution function set +.>

In the following, in addition to the continuous casting machine, in the machine +.>

Top heat +.>

The difference between the start processing time of the immediately subsequent heat is greater than or equal to heat +.>

In the machine->

The probability of establishment of the processing time is equal to or greater than +.>

。

6) The processing time constraint of the adjacent working procedures of the same furnace number comprises the following steps: in two adjacent processes in the same furnace, the starting processing time of the next process is more than or equal to the finishing time plus the transportation time of the last process. That is, for two processes of the same heat, the latter process can be started only when the former process is completed and the heat is transported to the next process, and the expression is as follows:

(equation 9)

representing the heat +.>

In the machine->

Starting processing time for starting on the machine immediately following, +.>

Representing slave machine->

To the transport time of the directly subsequent machine. Equation 9 shows the distribution function set +. >

Lower, except for the continuous casting machine, the heat is +.>

In the machine->

The difference between the start processing time and the start processing time of the directly subsequent machine is greater than or equal to the heat>

In the machine->

The probability of establishment of the processing time plus the transport time is equal to or greater than->

。

In this embodiment, in the distributed robust joint opportunity constraint model of the steelmaking continuous casting scheduling problem, the above-mentioned 5-class scheduling scheme feasibility joint opportunity constraint (namely, the heat continuity constraint, the single-casting start processing time constraint, the adjacent-casting start processing time constraint, the heat start processing time constraint, and the same heat adjacent-process start processing time constraint) may be expressed as a general form, as shown in formula 10. When (when)

When the model is called distributed robust associationThe joint opportunity constraint, unlike the distributed robust independent opportunity constraint model, requires that multiple constraints hold at the same time with a certain probability.

(equation 10)

and->

Indicating an indeterminate heat treatment time +.>

Uncertainty constraint parameters of influence, +.>

Indicating the steelmaking continuous casting schedule, i.e. the start-up times of all heats and runs,/->

. Equation 10 ensures that all constraints are +. >

Is true. In the distributed robust joint opportunity constraint model, the furnace processing time is indeterminate +.>

Is unknown, so in order to ensure the robustness of the distributed robust joint opportunity constraint model, for a certain steelmaking continuous casting scheduling scheme +.>

All constraints need to be met with a certain probability in the worst case. Hypothesis parameter->

And->

About indeterminate heat treatment time +.>

Can be expressed in the following linear form:

(equation 11)

is a random vector of length L, and the set of distribution functions is defined as follows:

wherein, support set->

In the form of polyhedron->

And->

The first and second moments are the uncertain heat treatment time, respectively. For the distributed robust joint opportunity constraint as shown in equation 10, it can be rewritten as follows:

(equation 12)

。

in this embodiment, the processing time of the heat is considered as a random variable within a certain distribution set. The common steelmaking continuous casting model is modified based on the method, so that the steelmaking continuous casting model is more reasonable, and a distributed robust joint opportunity constraint model is provided to determine the start processing time of each casting time and each furnace time in the steelmaking continuous casting process. And the support set in the polyhedral form is introduced into the distribution function set based on the accurate moment information, so that the modeling of the robust joint opportunity constraint model under the distribution function set is given for the first time. So that the obtained distributed robust joint opportunity constraint model is more in line with the actual situation of the steelmaking continuous casting scheduling problem.

Step S102: and taking correlation among constraint conditions into consideration, and converting the distributed robust joint opportunity constraint model into a distributed robust joint opportunity constraint model based on CVaR approximation according to CVaR approximation and a dual theory.

In this embodiment, in the steelmaking continuous casting scheduling problem, random variables between different constraints are not completely independent of each other, and omitting the correlation between the constraints in this case often results in performance loss of the final result. Therefore, for the case of independence, a transformation method of a distributed robust joint opportunity constraint model based on CVaR (Conditional Value at Risk, conditional risk value) approximation and dual theory is provided. Specifically, converting an objective function in the distributed robust joint opportunity constraint model into a general representation form; and converting the distributed robust joint opportunity constraint approximation in the distributed robust joint opportunity constraint model into a semi-positive constraint through CVaR approximation and a dual theory.

Specifically, the method for converting the distributed robust joint opportunity constraint approximation in the distributed robust joint opportunity constraint model into the semi-positive constraint by CVaR approximation and the dual theory comprises the following steps of:

1) The transformation method of CVaR approximation is adopted.

For any arbitrary, using CVaR approximation method

And a given constraint factor vector->

If->

Is a feasible solution of the constraint as shown in formulas 13-16, then +.>

And is also a viable solution to the constraint shown in equation 12.

(equation 13)

(equation 14)

(equation 15)

(equation 16)

、/>

、/>

intermediate variables, which are all approximate transformations of CVaR, < >>

，/>

And->

The first and second moments are the uncertain heat treatment time, respectively.

2) The transformation method of dual approximation is adopted.

The present embodiment considers the support set for indefinite processing times as polyhedral, i.e

Then a dual approximation method may be used to give an approximation constraint for the constraint shown in equations 13-16 after the CVaR approximation transformation.

Assume that

Is +.>

For any given +.>

If present->

,/>

,/>

,/>

,/>

,/>

,/>

,/>

,/>

,/>

,/>

,/>

The constraints shown in the following formulas 17 to 25 are satisfied:

(equation 17)

(equation 18)

(equation 19)

(equation 20)

(equation 21)

(equation 22)

(equation 23)

(equation 24)

(equation 25)

Then

Is a viable solution to the constraints shown in equations 13-16.

From this, it can be derived that: when the heat processing time is not determined

When the support set of (a) is a cube，

Expressing the objective function shown in equation 1 as a general expression shown in equation 26, the constraint shown in equation 12 can be approximated to be translated into the constraint shown in equations 27-35, and then the distributed robust joint opportunity constraint model based on CVaR approximation is expressed as:

(equation 26)

(equation 27)

(equation 28)

(equation 29)

(equation 30)

(equation 31)

(formula 32)

(equation 33)

(equation 34)

(equation 35)

representing the functional relation between the start processing time and the uncertain processing time of each casting and furnace time,/->

Representation->

In uncertain distribution->

Total flow-through time,/>

Representing distribution(s)>

Representing the upper limit function>

Representing a minimum function,/->

Representing an uncertain process time random vector, +.>

Belongs to a supported set->

Mean vector->

And covariance matrix->

The determined distribution function set:

the support set is a cube: />

，/>

And->

Respectively indicate->

Upper and lower bounds of>

For a given constraint factor vector, +.>

,/>

,/>

,/>

,/>

,/>

,/>

,/>

,/>

,/>

To approximately translate the intermediate variables.

In summary, we present the constraint factor vector

The approximation of the distributed robust joint opportunity constraint model is converted into a semi-positive constraint method under the condition of fixed value.

In the embodiment, considering that random variables among different constraints are not completely independent of each other in the steelmaking continuous casting scheduling problem, under the condition that the constraints have correlation, a more general transformation method of a distributed robust joint opportunity constraint model is provided based on CVaR approximation and a dual theory, and the distributed robust joint opportunity constraint model based on CVaR approximation is obtained, so that a solving result is more in line with the actual production scheduling problem.

Step S103: based on an iterative lifting solving algorithm, solving the distributed robust joint opportunity constraint model based on CVaR approximation to obtain a steelmaking continuous casting scheduling scheme, wherein the steelmaking continuous casting scheduling scheme comprises: all heats and start-up times for the runs.

In the embodiment, the constraints of the distributed robust joint opportunity constraint model of the steelmaking continuous casting scheduling problem are related to each other, so that the model constraint is converted into the semi-positive constraint by adopting CVaR approximation and a dual theory. Due to the differences

The value of (2) can also be obtained by different steelmaking continuous casting scheduling schemes>

Directly and simultaneously->

And->

Optimization then causes the constraints to become non-convex, making the problem difficult to solve.

Therefore, the embodiment designs an iterative lifting solution algorithm to continuously pair

Is improved to give a +.>

. The iterative lifting solution algorithm is fixed +.>

To approximate the distributed robust joint opportunity constraint into a semi-normal constraint to solve, and then to perform the optimization according to the obtained optimal solution>

And the value of (2) is updated so that the objective function can be continuously reduced along with the iterative process. Specifically, note- >

To give +.>

The constraint shown in the formulas 27-35 is satisfied under the value +.>

Is>

To give +.>

The constraint shown in the formulas 27-35 is satisfied under the value +.>

Is a feasible region of (2).

In the first place

In the course of the multiple iterations, inGiven->

The optimal solution is obtained by the lower optimal scheduling scheme>

. Next, fix +.>

In the following

Is to find a new +.>

As a next iteration +.>

. In this way, the loop is continued until the termination condition is satisfied. Note that due to->

To open the set, to ensure that a feasible solution can be taken, the closed set +.>

As->

Of (1), wherein->

，/>

For a small number, choose +.>

. Therefore, in each iteration process, the method is from +.>

A new feasible solution is selected.

Specifically, the solving the distributed robust joint opportunity constraint model based on the CVaR approximation based on the iterative lifting solving algorithm includes:

generating a plurality of constraint factor vectors in advance;

Wherein, the optimal solution obtained by each iteration represents the processing starting time of all furnace times and casting times, and the optimal value represents the total flowing time.

In this embodiment, in order to avoid the algorithm iteration process from sinking into local minima, a plurality of constraint factor vectors are selected, and each constraint factor vector is iteratively solved. And stopping the iterative calculation of the current constraint factor vector after the algorithm execution meets the iteration ending condition, wherein the iteration ending condition comprises the following steps: the algorithm iteration number reaches the maximum iteration number upper limit, the number of times that the improvement of the objective function value in the iteration process is smaller than the fixed threshold value in the continuous iteration process reaches the maximum continuous number upper limit, and the constraint factor vector values obtained in the two adjacent iteration processes are the same.

Illustratively, as shown in fig. 3, the complete flow of the iterative lifting solution algorithm includes steps S1 to S11:

step S1: inputting parameters: given parameters in a distribution function set of uncertain process times, including a support set

Mean vector- >

And covariance matrix->

The method comprises the steps of carrying out a first treatment on the surface of the Given a fixed threshold +.>

Maximum iteration number upper limit->

And a maximum number of consecutive times upper limit

；

Step S2: initializing: to avoid the algorithm iteration process being trapped in local minima, generateKInitial constraint factor vector

，/>

Wherein, the method comprises the steps of, wherein,Kis a positive integer;

step S3: let constraint factor vector

Initial optimum->

，/>

Continuous times->

Wherein->

Is a sufficiently large number;

step S4: if it is

Continuing to execute step S5, otherwise jumping to stepS9, performing step S9;

step S5: first, theiIn the course of the multiple iterations, according to a given

Value, solving the transformed semi-normal constraint problem to obtain the optimal value of the problem +.>

And optimal solution->

If->

Then->

Otherwise let->

；

Step S6: fixing

Take the value, look for belonging to the set +.>

And makes the semi-positive constraint shown in formulas 27-35 feasible +.>

；

Step S7: if it is

Step S9 is skipped, otherwise step S8 is continuously executed;

step S8: if it is

Jump to step S9, otherwise let +.>

Jumping to step S4;

step S9:recording constraint factor vectors

Corresponding optimum value->

And optimal solution->

；

Step S10: if it is

Let->

And jumping to the step S3, otherwise continuing to execute the step S11;

step S11: output parameters:

optimal value +. >

And its corresponding optimal solution->

。

For the distributed robust joint opportunity constraint problem of steelmaking continuous casting scheduling, if the optimal value of the problem is bounded, for the iterative lifting solution algorithm, if the problem is initially

If feasible, the algorithm is a falling algorithm and ends in a finite step, i.e. there is always +.>

Wherein->

Indicate->

Multiple iteration processAnd the algorithm terminates after a finite step and returns to the upper bound of the problem.

In the embodiment, with the shortest total flow time as an optimization target and the furnace processing time as a random variable, a distributed robust joint opportunity constraint model of a steelmaking continuous casting scheduling problem is constructed, correlation among constraint conditions is considered, the distributed robust joint opportunity constraint model is converted into a distributed robust joint opportunity constraint model based on CVaR approximation according to CVaR approximation and a dual theory, the obtained deterministic optimization problem is not convex, an iterative lifting solving algorithm is designed, and the distributed robust joint opportunity constraint model based on the CVaR approximation is solved, so that the steelmaking continuous casting scheduling scheme is obtained. Because the uncertainty of the furnace processing time is considered in the embodiment, the obtained steelmaking continuous casting scheduling scheme is more in line with the actual situation, the casting interruption phenomenon in the steelmaking continuous casting process can be greatly reduced, and the stability of the production process is improved.

In an alternative embodiment, if each constraint in the distributed robust joint opportunity constraint satisfies the independence assumption and the probability of being satisfied is known, the constraint is equivalent to a plurality of distributed robust independent joint opportunity constraints, so the method of solving the distributed robust joint opportunity constraints independent of each other in the constraint in the embodiment is to approximately convert the distributed robust independent opportunity constraints to solve the distributed robust independent opportunity constraints.

Specifically, when the constraints in the distributed robust joint opportunity constraint model are independent of each other, the method further includes step S401 and step S402:

step S401: and aiming at the condition that the constraint conditions are mutually independent, converting the distributed robust joint opportunity constraint model into a distributed robust joint opportunity constraint model based on an independence assumption.

Specifically, converting an objective function in the distributed robust joint opportunity constraint model into a general representation form; and (3) converting the distributed robust joint opportunity constraint in the distributed robust joint opportunity constraint model into a distributed robust independent opportunity constraint by giving the establishment probability of each constraint condition.

The method for converting the distributed robust joint opportunity constraint in the distributed robust joint opportunity constraint model into the distributed robust independent opportunity constraint by giving the establishment probability of each constraint condition comprises the following steps:

1) Giving an independence assumption.

For the distributed robust joint opportunity constraint, i.e., any of the constraints shown in equation 10

Random vector

And->

Are independent of each other. The random vectors in many production scheduling model constraints conform to the assumptions described above, such as a hybrid flow shop scheduling problem.

2) And (3) providing a transformation method of a distributed robust joint opportunity constraint model with independent constraints.

Under the condition that the independence assumption is satisfied, the probability that each constraint is satisfied in the distributed robust joint opportunity constraint shown in the formula 12 is also independent, so the distributed robust joint opportunity constraint can be written as follows:

(equation 36)

Thus, the feasible domains corresponding to the following two constraints are equivalent, namely:

(equation 37)

The equivalent relationship between the independence assumption and the above formula 37 is given in the present embodiment

In the fixed case, the multiple distributed robust independent opportunity constraints are equivalent to the distributed robust joint opportunity constraints. Namely:

(equation 38)

Obviously, probability distribution vectors

The change of the value can lead to the change of a feasible domain, so that the distributed robust joint opportunity constraint model can be equivalently converted into the following method for searching the optimal probability distribution +. >

Corresponding optimal solution->

Is a problem of (a). The distributed robust joint opportunity constraint model based on the independence assumption is expressed as:

(equation 39)

(equation 40)/(>

(formula 41)

(equation 42)

indicating the start-up time of each heat and cast,/-for each heat>

Representation->

Is (are) feasible domain->

Representing an uncertain heat processing time random vector, < ->

Support set of->

，/>

And->

Respectively indicate->

Upper and lower bounds of>

Representation->

In uncertain distribution->

Total flow-through time,/>

Representing distribution(s)>

Representing the upper limit function>

Representing a minimum function,/->

Expressed in uncertain distribution->

Lower probability limit for the establishment of lower events +.>

Representing the probability distribution factor.

Step S402: and solving the distributed robust joint opportunity constraint model based on the independence assumption based on the iterative lifting solving algorithm to obtain a steelmaking continuous casting scheduling scheme under the constraint independent condition.

In this embodiment, the constraint of the distributed robust joint opportunity constraint model based on the independence assumption is non-convex, and it is difficult to directly solve. Note that for the constraint shown in equation 40, if the probability distribution vector is fixed

The constraint can be equivalently converted into +.>

The distributed robust independent opportunity constraint can be converted into a linear programming problem of conservative approximation by using a linear programming approximation method, and then the problem is solved by adopting a traditional mode. Therefore, the present embodiment is implemented by continuously updating +.>

And the values of the (4) are fixed, and the distributed robust joint opportunity constraint model based on the independence assumption is converted into a distributed robust independent opportunity constraint model.

Specifically, the solving the distributed robust joint opportunity constraint model based on the independence assumption based on the iterative lifting solving algorithm includes:

generating a plurality of probability distribution vectors in advance;

In this embodiment, in order to avoid the algorithm iteration process from sinking into local minima, a plurality of probability distribution vectors are selected, and each probability distribution vector is subjected to iterative solution. And stopping the iterative calculation of the current probability distribution vector after the algorithm execution meets the iteration ending condition, wherein the iteration ending condition comprises the following steps: the algorithm iteration times reach the maximum iteration times upper limit, and the times of the improvement of the objective function value in the continuous iteration process, which is smaller than the fixed threshold value, reach the maximum continuous times upper limit.

Illustratively, as shown in fig. 4, the complete flow of the iterative lifting solution algorithm includes steps C1 to C10:

step C1: inputting parameters: given parameters in a distribution function set of uncertain process times, including a support set

Mean vector->

And covariance matrix->

Maximum iteration number upper limit->

And a maximum number of consecutive times upper limit

；

Step C2: initializing: to avoid the algorithm iteration process being trapped in local minima, generate KIndividual probability distribution vectors

，/>

Wherein, the method comprises the steps of, wherein,Kis a positive integer;

step C3: let probability distribution vector

Initial optimum->

，/>

Continuous times->

Wherein->

Is a sufficiently large number;

step C4: if it is

Continuing to execute the step C5, otherwise jumping to the step C8;

step C5: first, theiIn the course of the multiple iterations, according to a given

The values, approximate transformation is performed on the distributed robust independent opportunity constraint in the formula 40, and the optimal value of the problem is obtained through solving>

And optimal solution->

If->

Then->

Otherwise let->

；

Step C6:

take the value to get each constraint in equation 40 at the current solution +.>

Maximum probability that the following can be true and the corresponding parameter +.>

Thereby calculating +.>

The value of (i.e.)>

Wherein->

Is an adjustment function;

step C7: if it is

Jump to step C8, otherwise let +.>

Jumping to the step C4;

step C8: recording probability distribution vectors

Corresponding optimum value->

And optimal solution->

；

Step C9: if it is

Let->

And jumping to the step C3, otherwise continuing to execute the step C10;

step C10: output parameters：

Optimal value +.>

And its corresponding optimal solution->

。

In the implementation, aiming at the situation that the constraints are mutually independent, the distributed robust joint opportunity constraint is converted into the distributed robust independent opportunity constraint by giving the establishment probability of each constraint. Furthermore, the method provided by the implementation can be applied to an application scene of an independent constraint problem, such as a mixed flow shop scheduling problem.

In an embodiment of the invention, the processing time of the heat is considered as a random variable within a certain distribution set. The common steelmaking continuous casting model is modified based on the method, so that the steelmaking continuous casting model is more reasonable, and a distributed robust joint opportunity constraint model is provided for determining the start processing time of each casting time and each furnace time in the steelmaking continuous casting process. And a supporting set in a polyhedral form is introduced into a distribution function set based on accurate moment information, and a modeling and conversion method of a distributed robust joint opportunity constraint model under the distribution function set is provided for the first time. In addition, under the condition that each constraint has an independence assumption, a transformation method of a distributed robust joint opportunity constraint model is provided; under the condition that the constraints have correlation, a more general transformation method of the distributed robust joint opportunity constraint model is given based on CVaR approximation and dual theory. According to two different conditions of independent relation and correlation between constraint conditions, different iteration lifting methods are designed for solving.

It should be noted that, the technical solutions in the above embodiments may also be applied to various production scheduling scenarios where other constraint conditions are associated and independent, and the technical solutions in the above embodiments may be implemented by programming.

For example, a certain steel company in China is selected as a practical case, and the effect analysis of the steelmaking continuous casting scheduling method of the distributed robust joint opportunity constraint model provided by the implementation of the invention is as follows:

the embodiment is a steelmaking continuous casting scheduling problem with uncertain processing time, and the performance index is selected as the total flow time and the casting interruption condition. According to actual production conditions and the requirement of simplifying the distributed robust joint opportunity constraint model, only three main stages, namely steelmaking, refining and continuous casting, are considered in the model; assuming that all heats follow the same process, namely steelmaking, refining and continuous casting; since the order of the heats must be consistent with the downstream process order, it is assumed that the particular machine, the order of the casts, and the heats on each caster are determined. According to actual production data, determining all parameters required by a model, establishing a distributed robust joint opportunity constraint model as shown in formulas 1-10, considering the inter-constraint relation, converting the joint opportunity constraint in the model into a semi-positive constraint through CVaR approximation and dual theory methods one by one as shown in formulas 4-9, and finally obtaining an approximate optimal scheduling scheme through an iterative lifting solution algorithm as shown in formulas 27-35.

Experiments are carried out based on two months of actual production data of certain steel company in China, and 5200 effective production records are shared, wherein each record contains information such as furnace number, processing route, steel grade, processing time of each stage and the like. These records are used to estimate the mean and variance of the processing time. Because the production records of some special steels are few, the exact cutting of the estimated heat processing time is very difficult in the actual production process, so the method is suitable for adopting a distributed robust joint opportunity constraint model to formulate a daily scheduling schedule and determining the starting processing time of each heat.

In this embodiment, one of all possible processing times of a certain heat is randomly selected as the actual processing time, and then the production is performed according to a given schedule, and if the heat is not started on time, all subsequent processes need to be delayed, resulting in a cut-off. Repeating the above process until all the furnace times are completed, and completing the steelmaking continuous casting production process. In this example, the above experiment was repeated 10 times, and the average total flow-through time and the average number of times of casting off were taken as evaluation indexes of the final model. The actual production system consists of three converters, three refining furnaces and three continuous casting machines, and the processing time of one furnace on three machines in the same stage is the same. And (3) assuming that all machining time are mutually independent, determining the starting machining time of the heat given by the machining position and the machining sequence of the heat, and obtaining a heat scheduling time table, so as to compare the total flow time and the casting interruption times of a robust scheduling scheme and a deterministic scheduling scheme, wherein the deterministic scheduling scheme is obtained by solving a deterministic model which is required to be established by each constraint. The results are shown in tables 1 and 2.

Table 1 deterministic model and distributed robust joint opportunity constraint model

At different positions

Performance comparison under value (Heat collection 1)

Table 2 deterministic model and distributed robust joint opportunity constraint model

At different positions

Performance comparison under value (Heat set 2)/(Fu)>

Tables 1 and 2 respectively show deterministic models

And distributed robust joint opportunity constraint model +.>

Different +.>

Performance of the values. It can be seen from tables 1 and 2 that the average total flow time of the robust scheduling scheme follows +.>

The decrease in value increases and the incidence of interruption of the casting time is increased with + ->

The decrease in value decreases, which indicates that an improvement in the robustness of the scheduling scheme requires a loss of other production performance. The robust scheduling scheme sacrifices a small amount of production performance (i.e., increases the total throughput time) in exchange for a substantial increase in robustness compared to the deterministic scheduling scheme. Deterministic scheduling schemes will lead on average to about 4 break-gate situations, whereas for robust schemes, when +.>

The number of time-to-break casting has been reduced to an average of 0.04 times, with an average total flow-through time of only about 12% increase. It should be noted that other additional costs caused by the outage problem are not taken into account, where the production performance penalty only accounts for the increase in total flow-through time. The robust joint opportunity constraint model trades for stability and continuity of the production process by sacrificing a small number of production performance metrics to some extent. In actual production, the cost reduction due to the increase in production stability tends to be more significant than the performance loss portion of the robust joint opportunity constraint model. Thus, in an uncertain production environment, a robust joint opportunity constraint model is a better choice than a deterministic model.

In summary, the distributed robust joint opportunity constraint model can reduce the casting breaking times in the steelmaking continuous casting production process, does not bring great performance loss, and can achieve better trade-off between production performance and production stability. Therefore, the steelmaking continuous casting scheduling method of the distributed robust joint opportunity constraint model can effectively improve the stability of the production process and simultaneously maintain the production efficiency.

The embodiment of the invention also provides a steelmaking continuous casting scheduling device of the distributed robust joint opportunity constraint model, as shown in fig. 5, fig. 5 is a schematic structural diagram of the steelmaking continuous casting scheduling device of the distributed robust joint opportunity constraint model, and the device comprises:

the model building module 51 is used for building a distributed robust joint opportunity constraint model of steelmaking continuous casting scheduling problem by taking the shortest total flow time as an optimization target and the furnace processing time as a random variable;

the model conversion module 52 is configured to convert the distributed robust joint opportunity constraint model into a distributed robust joint opportunity constraint model based on CVaR approximation according to CVaR approximation and a dual theory, taking into consideration correlation between constraint conditions;

The problem solving module 53 is configured to solve the distributed robust joint opportunity constraint model based on CVaR approximation based on an iterative lifting solving algorithm, to obtain a steelmaking continuous casting scheduling scheme, where the steelmaking continuous casting scheduling scheme includes: all heats and start-up times for the runs.

In an alternative embodiment, the apparatus further comprises:

the second model conversion module is used for converting the distributed robust joint opportunity constraint model into a distributed robust joint opportunity constraint model based on an independence assumption aiming at the condition that the constraint conditions are mutually independent;

and the second problem solving module is used for solving the distributed robust joint opportunity constraint model based on the independence assumption based on the iterative lifting solving algorithm to obtain a steelmaking continuous casting scheduling scheme under the constraint independent condition.

In an alternative embodiment, the model building module includes:

the parameter determining module is used for determining parameters and decision variables of the distributed robust joint opportunity constraint model;

the uncertain parameter module is used for taking uncertain heat processing time as an uncertain parameter of the distributed robust joint opportunity constraint model, wherein the uncertain parameter is not known in specific distribution but belongs to a distribution function set with a support set and known moment information;

The function determining module is used for determining an objective function of the distributed robust joint opportunity constraint model, and the objective function takes the minimum total flow time as an optimization target;

a constraint determining module, configured to determine constraint conditions of the distributed robust joint opportunity constraint model, where the constraint conditions include: the distribution set constraint to which the process time is subject and the feasibility constraint of the scheduling scheme are not determined.

In an alternative embodiment, the constraint determination module includes:

a first constraint determination sub-module for determining an uncertain process time constraint comprising: the uncertain processing time belongs to a distribution function set determined by a support set, a mean value vector and a covariance matrix;

a second constraint determination submodule for determining a heat continuity constraint, comprising: on the same continuous casting machine, when a certain heat finishes casting, the subsequent heat reaches the continuous casting machine and can start to process;

a third constraint determination sub-module for determining a single run start machining time constraint, comprising: the starting processing time of each casting time is more than or equal to the preparation time, and the starting processing time of each casting time is more than or equal to the completion time of the first furnace time of the casting time in the last working procedure plus the transportation time;

A fourth constraint determination submodule for determining adjacent casting start machining time constraints, including: two adjacent casting times on the same continuous casting machine, wherein the starting processing time of the next casting time is more than or equal to the finishing time plus the preparation time of the previous casting time;

a fifth constraint determination submodule for determining a heat start machining time constraint, including: in addition to the continuous casting machine, two adjacent heats on the same machine, and the starting processing time of the subsequent heat needs to be more than or equal to the finishing time of the previous heat;

a sixth constraint determination submodule for determining a start processing time constraint of adjacent processes in the same heat, including: in two adjacent processes in the same furnace, the starting processing time of the next process is more than or equal to the finishing time plus the transportation time of the last process.

In an alternative embodiment, the model transformation module includes:

a first function conversion module, configured to convert an objective function in the distributed robust joint opportunity constraint model into a general representation;

the first constraint conversion module is used for converting the distributed robust joint opportunity constraint approximation in the distributed robust joint opportunity constraint model into a semi-positive constraint through CVaR approximation and a dual theory.

In an alternative embodiment, the problem solving module includes:

the first parameter generation module is used for generating a plurality of constraint factor vectors in advance;

the first iterative calculation module is used for solving an optimal solution and an optimal value of the distributed robust joint opportunity constraint model based on CVaR approximation according to the value of each constraint factor vector;

the first updating calculation module is used for updating the value of the constraint factor vector according to the optimal solution and the optimal value, and continuously solving the distributed robust joint opportunity constraint model based on CVaR approximation with the updated value of the constraint factor vector to obtain a new optimal solution and an optimal value;

and the first result output module is used for obtaining the optimal solution and the optimal value corresponding to the constraint factor vector after the iteration finishing condition is met, and selecting the final optimal solution and the optimal value from the optimal solution and the optimal value corresponding to the constraint factor vectors.

In an alternative embodiment, the second model transformation module includes:

the second function conversion module is used for converting the objective function in the distributed robust joint opportunity constraint model into a general representation form;

The second constraint conversion module is used for converting the distributed robust joint opportunity constraint in the distributed robust joint opportunity constraint model into the distributed robust independent opportunity constraint by giving the establishment probability of each constraint condition.

In an alternative embodiment, the problem solving module includes:

the second parameter generation module is used for generating a plurality of probability distribution vectors in advance;

the second iterative calculation module is used for carrying out approximate transformation on the distributed robust joint opportunity constraint model based on the independence assumption according to the value of each probability distribution vector, and obtaining the optimal solution and the optimal value of the steelmaking continuous casting scheduling problem through solving;

the second updating calculation module is used for calculating the maximum probability and corresponding parameters which can be established under the optimal solution, updating the value of the probability distribution vector according to the parameters, and continuously calculating a new optimal solution and an optimal value by using the updated probability distribution vector;

and the second result output module is used for obtaining the optimal solution and the optimal value corresponding to the probability distribution vector after the iteration ending condition is met, and selecting the final optimal solution and the optimal value from the optimal solution and the optimal value corresponding to the probability distribution vectors.

In this specification, each embodiment is described in a progressive manner, and each embodiment is mainly described by differences from other embodiments, and identical and similar parts between the embodiments are all enough to be referred to each other.

Embodiments of the present invention are described with reference to flowchart illustrations and/or block diagrams of methods and apparatus according to embodiments of the invention. It will be understood that each flow and/or block of the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing terminal device to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing terminal device, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.

These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.

These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.

While preferred embodiments of the present invention have been described, additional variations and modifications in those embodiments may occur to those skilled in the art once they learn of the basic inventive concepts. It is therefore intended that the following claims be interpreted as including the preferred embodiment and all such alterations and modifications as fall within the scope of the embodiments of the invention.

Finally, it is further noted that relational terms such as first and second, and the like are used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Moreover, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or terminal that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or terminal. Without further limitation, an element defined by the phrase "comprising one … …" does not exclude the presence of other like elements in a process, method, article or terminal device comprising the element.

The invention provides a steelmaking continuous casting scheduling method and device of a distributed robust joint opportunity constraint model, and specific examples are applied to illustrate the principle and implementation mode of the invention, and the description of the examples is only used for helping to understand the method and core ideas of the invention; meanwhile, as those skilled in the art will have variations in the specific embodiments and application scope in accordance with the ideas of the present invention, the present description should not be construed as limiting the present invention in view of the above.

Claims

1. A steelmaking continuous casting scheduling method of a distributed robust joint opportunity constraint model is characterized by comprising the following steps:

based on an iterative lifting solving algorithm, solving the distributed robust joint opportunity constraint model based on CVaR approximation to obtain a steelmaking continuous casting scheduling scheme, wherein the steelmaking continuous casting scheduling scheme comprises: starting processing time of all furnace times and casting times;

The objective function of the distributed robust joint opportunity constraint model is expressed as:

representing the upper limit function>

Representing a minimum function,/->

Indicating desire(s)>

Representing the aggregate of all runs, +.>

Represents all heat sets in the kth casting,/-for>

Representing distribution(s)>

Continuous casting machine with a machining run k +.>

Representing the heat on a continuous casting machine for processing the heat kiIn the order of (a),

at the beginning of the first heat representing the run kBetween (I) and (II)>

Representing the processing time of heat i on the continuous casting machine for processing heat k, +.>

Representing the total processing time of all heats before the ith heat in the kth casting,/->

Indicating the finishing time of the ith heat in the heat k,

representing the sum of the finishing times of all heats in run k,/>

Representing the sum of the finishing processing time of all furnace times in all casting times;

the uncertain heat processing time constraint of the distributed robust joint opportunity constraint model is expressed as:

representing an indefinite heat treatment time belonging to a supported set +.>

Mean vector->

And covariance matrix->

The set of determined distribution functions, />

Representing the mean;

the furnace continuity constraint of the distributed robust joint opportunity constraint model comprises: on the same caster, when a certain heat finishes casting, the subsequent heat has arrived at the caster and can start working, expressed as:

is a mathematical expression of opportunity constraint, and represents that the probability of event establishment is not lower than +.>

，

，/>

Indicating the finishing time of the heat i immediately preceding the heat,/->

Representing the start-up time of heat i on the direct-to-direct-succession machine of the continuous casting machine for processing heat k,/>

Representing the processing time of heat i on the direct succession of the continuous casting machine for processing heat k, +.>

Representing the furnace number i from processing castingThe transport time of the direct succession machine of the secondary k continuous casting machine to the continuous casting machine, +.>

Representing the time of the heat i reaching the continuous casting machine;

the single casting start machining time constraint of the distributed robust joint opportunity constraint model comprises: the start processing time of each casting pass needs to be equal to or greater than the preparation time, expressed as:

representing the preparation time of adjacent casting times;

the start processing time of each casting time is equal to or greater than the completion time of the last process of the first furnace time of the casting time plus the transportation time, expressed as:

representing the first heat +.>

Starting processing time on the direct succession of the continuous casting machine for processing the run k, +.>

Representing the first heat +.>

The processing time on the directly preceding machine of the continuous casting machine for processing run k,

representing the first heat +.>

The transit time from the directly preceding machine of the continuous casting machine for processing run k to the continuous casting machine,

the completion time of the last process of the first heat of the casting k is added with the transportation time;

the adjacent casting start processing time constraint of the distributed robust joint opportunity constraint model comprises the following steps: two adjacent casting times on the same continuous casting machine, the starting processing time of the next casting time is more than or equal to the finishing time plus the preparation time of the previous casting time, and the method is expressed as follows:

representing the start-up time of the next shot adjacent to shot k on the same caster,

representing the sum of the completion time of a run k and the preparation time of an adjacent run;

the furnace start machining time constraint of the distributed robust joint opportunity constraint model comprises the following steps: in addition to the continuous casting machine, two adjacent heats on the same machine, the start processing time of the subsequent heat needs to be greater than or equal to the completion time of the previous heat, expressed as:

representing the start-up time of the next heat of heat i on machine j, +.>

Representing the processing time of heat i on machine j,/->

Indicating the start-up time of heat i on machine j,/->

Representing the difference between the start-up times of heat i and the immediately subsequent heat on machine j,/->

A machine set representing all processing runs i;

the processing time constraint of the same heat adjacent procedure of the distributed robust joint opportunity constraint model comprises the following steps: in two adjacent processes in the same furnace, the starting processing time of the next process needs to be more than or equal to the finishing time plus the transportation time of the last process, and the process is expressed as follows:

indicating the start processing time of the beginning of heat i on the machine immediately following machine j, +.>

Representing the transit time from machine j to the directly following machine.

2. The steelmaking continuous casting scheduling method of a distributed robust joint opportunity constraint model of claim 1, further comprising:

3. The method for steelmaking continuous casting scheduling by using a distributed robust joint opportunity constraint model according to claim 1, wherein the method for constructing the distributed robust joint opportunity constraint model for steelmaking continuous casting scheduling by using the shortest total flow time as an optimization target and the heat processing time as a random variable comprises the following steps:

the uncertain furnace processing time is taken as an uncertain parameter of the distributed robust joint opportunity constraint model, the specific distribution of the uncertain parameter is unknown, but the uncertain parameter belongs to a distribution function set with a support set and known moment information;

and determining constraint conditions of the distributed robust joint opportunity constraint model, wherein the constraint conditions of the distributed robust joint opportunity constraint model are used for constraining the feasibility of a distribution set and a scheduling scheme obeyed by uncertain furnace processing time.

4. The steelmaking continuous casting scheduling method of a distributed robust joint opportunity constraint model according to claim 3, wherein the constraint conditions of the distributed robust joint opportunity constraint model comprise:

5. The steelmaking continuous casting scheduling method of a distributed robust joint opportunity constraint model according to claim 1, wherein the converting the distributed robust joint opportunity constraint model into a distributed robust joint opportunity constraint model based on CVaR approximation according to CVaR approximation and dual theory comprises:

6. The steelmaking continuous casting scheduling method of the distributed robust joint opportunity constraint model according to claim 1, wherein the solving the distributed robust joint opportunity constraint model based on CVaR approximation based on the iterative lifting solving algorithm comprises:

generating a plurality of constraint factor vectors in advance;

7. The steelmaking continuous casting scheduling method of a distributed robust joint opportunity constraint model according to claim 2, wherein said converting the distributed robust joint opportunity constraint model into a distributed robust joint opportunity constraint model based on an independence assumption comprises:

8. The steelmaking continuous casting scheduling method of a distributed robust joint opportunity constraint model according to claim 2, wherein the solving the distributed robust joint opportunity constraint model based on the independence assumption based on the iterative lifting solving algorithm comprises:

Generating a plurality of probability distribution vectors in advance;

9. A steelmaking continuous casting scheduling apparatus of a distributed robust joint opportunity constraint model, the apparatus comprising:

The problem solving module is used for solving the distributed robust joint opportunity constraint model based on CVaR approximation based on an iterative lifting solving algorithm to obtain a steelmaking continuous casting scheduling scheme, wherein the steelmaking continuous casting scheduling scheme comprises: starting processing time of all furnace times and casting times;

representing the upper limit function>

Representing a minimum function,/->

Indicating desire(s)>

Representing the aggregate of all runs, +.>

Represents all heat sets in the kth casting,/-for>

Representing distribution(s)>

Continuous casting machine with a machining run k +.>

The order of heat i on the continuous casting machine that processes heat k is shown,

indicating the start-up time of the first heat of run k, < >>

Indicating the finishing time of the ith heat in the heat k,

representing the sum of the finishing times of all heats in run k,/>

representing an indefinite heat treatment time belonging to a supported set +.>

Mean vector->

And covariance matrix->

Defined set of distribution functions->

Representing the mean;

，

，/>

Indicating the finishing time of the heat i immediately preceding the heat,/->

Representing the transport time of heat i from the directly preceding machine of the continuous casting machine processing heat k to the continuous casting machine, +>