Multi-objective optimization of strip laminar cooling system based on feature library and gene reconstruction technology

Qi-jiu ZHANG, Tie-jun SUN, Kai-bao WANG, Yu-feng ZHANG

(1Office of Research Affairs, Beihua University, Jilin 132013,China)(2College of Electrical and Information Engineering, Beihua University, Jilin 132021,China)(3School of Mechanical Engineering, Beihua University, Jilin 132021,China)

Abstract: : In order to solve the problem of two-dimensional multi-objective optimization of the given cooling path and the target coiling temperature in the rough tuning region of the laminar cooling system of hot rolled strip steel, a multi-objective optimization genetic algorithm based on the feature library and gene reconstruction technology is proposed to lock the optimal opening and closing feature library of the header in the roughing zone. In this algorithm, the intersection of Pareto front faces in previous generations is used to build a feature library, from which the optimal characteristics of header opening and closing are extracted and embedded into the next generation population, which can effectively inhibit the roam and randomness of population evolution. The dynamic competition mechanism is adopted in the feature base, which makes the individual population present more ideal parallel search characteristics in the global optimization space. The random rounding strategy of the feature library guarantees the uniformity of Pareto front plane distribution in space and improves the ability of the system to control the equilibrium of two dimensional multi-objective. Finally, gene reconstruction technology is a powerful engine to drive the algorithm to converge to the global optimal solution group, and it is an effective measure to improve the control accuracy of the system. The simulation program based on MFC is compiled, and the simulation results verify the effectiveness and advancement of the multi-objective optimization strategy.

Key words: Pareto frontier, Feature library, Multi-objective optimization, Gene recombination technology

Industrial products development and the quality improvement often involve optimization problems. If there are at least two indexes to be optimized and they need to be considered comprehensively, they are multi-objective optimization problems. There is not an optimal solution in the global search space, but only a compromise solution set to balance each goal, namely Pareto optimal set, also known as non-dominated set[1].

The laminar cooling system of hot rolled strip is a typical multi-objective optimization problem. The two optimization objectives that need to be considered comprehensively are: given cooling rate and target coiling temperature [2]. Due to the complexity of the physical process of laminar cooling system and the lag of parameter detection, the strip cooling modes commonly used by domestic enterprises at present, such as front-end intensive cooling, back-end intensive cooling and uniform cooling, are all inclined to consider the accuracy of the target coiling temperature, while ignoring the control of the strip cooling process. The large deviation between the temperature drop curve and the given cooling rate could lead to a decrease of strip quality [3- 4].

In this paper, a multi-objective optimization genetic algorithm based on the feature library and gene reconstruction technology is proposed by data feature mining on the intersection of Pareto front. The algorithm considers not only the given cooling rate curve, but also the control accuracy based on the target crimp temperature, aiming to explore a new way to further improve the quality of strip steel. The feature library built from the intersection of Pareto front is used to obtain the better opening and closing mode of headers, which are embedded into the next population, inherited and employed to guide the evolution direction. The dynamic survival mechanism of gene library is conducive to all-round spatial search; the random rounding function of gene library ensures the uniform distribution of Pareto front in the global search space, and improves the system’s multi-objective performance. The technology of gene recombination ensures the control accuracy of the system for the objective function. The simulation program by MFC is written to verify the advancement of the multi-objective optimization strategy.

1 Multi-objective optimization problem based on mathematical description

Fig.1 is the process flow diagram of the laminar cooling system of 1 750 mm hot rolling in a steel plant. Since the temperature drop of strip steel should be 200～300 ℃ in a short time before the final stand of finishing mill to coiling, efficient water spray facilities should be set up on the upper and lower sides of the roller table. It can be seen from Fig.1 that the cooling process of strip steel is composed of four parts: water-cooled coarse and fine adjustment area and air-cooling area (2 sections).

Fig.1 Laminar cooling process flow diagram

The upper and lower sides of the 132-meter-long roller table are equipped with water spray header controlled by valves. 18 pairs of water spray header are evenly arranged on the upper and lower sides of the roller table in the coarse adjustment area, and 6 pairs of water spray headers are evenly arranged on the upper and lower sides of the roller table in the fine adjustment area. The opening and closing mode of the header in the coarse adjustment area can be changed, the water spray quantity of each header is constant, and the opening and closing mode of the header in the fine adjustment area is fixed (full open). The water spray quantity of each header is adjustable. The temperature detectors are placed at the last stand of the finishing mill and in front of the coiler. It can be seen that there are 236kinds of opening and closing modes of headers in coarse tuning area. With such a huge search space, conventional mathematical methods can not optimize the best opening and closing mode of headers.

Based on this, we abstract the rough tuning region of laminar cooling into a multi-objective optimization problem: a decision variable (36 dimensions) composed of 36 manifolds, a 2-dimensional extreme objective function composed of a given cooling rate and a target coiling temperature, which is specifically described as follows:

(1)

Among them,α=(α35,α32,…α1,α0)∈Λ?Rnis the 36-dimensional decision variable,Λis the 36-dimensional decision space,ε=(ε1,ε2)∈Δ?R2is the 2-dimensional target vector,Δis the 2-dimensional target space, and two mapping functions from the header opening and closing mode (decision space) to the multi-objective (target space) are defined as the target functionΩ(α), wheref1(α) is the physical heat transfer equation of strip cooling,f2(β) is the given cooling path equation, and inequalityλi(α)≤0(i=1,2,…,x) is the initial strip of strip laminar cooling,μj(α)=0(j=1,2,…,y) is the boundary condition of strip laminar cooling.

Here, the following concepts are clarified:

Undetermined feature: if ?α∈Λ, ifαis applicable to the formula (1) of initial and constraint conditions,αis called undetermined feature.

Undetermined feature set: the set composed of all undetermined features inΛis called undetermined feature set, andΛfis recorded as, andΛf?Λ.

Pareto feature dominant: letαi,αj∈Λfsayαiis Pareto feature dominant compared withαj, if and only if ?m=1,2,fm(αi)≤fm(αj)∧?n=1,2,fn(αi)αj, it is also calledαidominatingαj.

(2)

Pareto optimal feature (non-dominant feature): let an undetermined featureα*∈Λfbe Pareto optimal feature if and only if

(3)

Pareto optimal feature group (non-dominant feature group): the so-called Pareto optimal feature group, that is, the set of all individuals with Pareto optimal feature, is recorded as

(4)

Pareto front: the surface formed by mapping all decision variables corresponding to the opening and closing mode of headers inΓ*to the 2D target vector is called Pareto front, which is recorded as

Γ**={Ω(α*)=(f1(α*),f2(α*))T|α*∈Γ*}

(5)

2 Pareto frontier

For the minimum problem of multi-objective optimization, the lower edge of the search area constitutes the Pareto front[5]; for the 2-dimensional objective function, the Pareto front is a curve, the 3-dimensional objective function is a surface, and the above 3-dimensional objective function is a hypersurface. As shown in Fig.2, the curve formed by X1, X2, X3, X4, and X5 constitutes the Pareto frontier of 2D multi-objective function optimization problem, and their corresponding decision variablesα*∈Λfare the optimal features; points X6, X7, X8, x9 and X10 are in the middle and upper part of the search area, and their corresponding decision variables are non-guiding features, and they are in a dominant position, more or less subject to Pareto frontier Control of optimal features on the surface[5].

Fig.2 Pareto frontier based on two-dimensional objective function multi-objective problem

In this paper, the core idea of a multi-objective genetic algorithm is to map out the best open and closed feature group[6]of the coarse-tuning area header through the iterative change of Pareto front in the evolution process. Therefore, it is of great practical significance to study the characteristics of Pareto front to provide direction for constructing the best feature groups of the past dynasties. In the optimization process of the algorithm, there will be intersections between the Pareto fronts of previous generations; because of the inherent characteristics of Pareto fronts, the intersection must contain useful information relative to multi-objective optimization problems.

3 Key Ideas of multi-objective genetic algorithm

3.1 Population initialization

3.2 Establishment of feature library

If the number of non-dominated features corresponding to the intersection of the front of thetgeneration Parteo is m, then m non-dominated features are selected into the feature library and recorded as the feature libraryΠ=(ε0,ε1,…εm-1)T, then the similarity rate of the same bit in the feature library can be expressed as follows:

(6)

3.3 Extraction of better features based on feature library

Set the superior feature carrier of the feature library asΠ**[36], and carry out features according to the following rules: ①m<5, do not extract the feature library; ②Π*[j]≥0.8(j=0,2,…35), assign the state of the jth header of the superior feature bodyΠ**[36] as “1”, as the effective bit; ③Π*[j]≤0.2(j=0,1,…,35), assign the state of the jth header of the superior feature bodyΠ**[36] as “0”, as the effective bit; ④ 0.8≤Π*[j]≥0.2(j=0,2,…,35), do not extract the superior feature.

(8)

Then the definition distance of the better feature is 6, the mode order is 2, and the * bit is set to “0”.

3.4 Embedding of better features

3.5 Dynamic competition mechanism of feature base

The capacity of the feature library should meet the following requirements: ① to prevent the deviation of evolution direction, the scale of the feature library should not be too small, andM>5 should be guaranteed; ② to ensure the global and convergence of the optimization process, the scale of the feature library should not be too large. In the middle and late stage of population evolution, with the alternation of time and space in Pareto frontier, the number of decision variables contained in spatial intersection increases, that is, the scale of feature pool becomes larger; the largest scale of feature pool (the number of decision variables in storage)ωmaxis taken as 25% of the population scale; If the scale of feature library is too large, the mechanism of survival of the fittest should be used to optimize the feature library.

The so-called dynamic competition mechanism of the feature base is to calculate the deviation of each decision variable in the feature base by the least square method after weightingf1(α) andf2(α) according to the strip steel of different specifications and steel grades, and finally eliminate the decision variable with large deviation according to the set scale of the gene base. The deviation can be expressed as follows:

(9)

Among them,φis the total number of decision variables in storage,Tdis the target coiling temperature,fs(τ) is the given cooling rate,Λ1、Λ2is the weight matrix, which reflects the target solution group’s degree of preference for multi-target; after eliminating the decision variables corresponding to the large deviation ofλ-ωmaxvalues in ∑E[φ], the feature library is composed of the remainingωmaxdecision variables.

3.6 Random rounding strategy of feature library

(10)

It can be seen from equation (10) that by using the random rounding strategy of gene pool and the embedding operation of better features, not only the spatial distribution of the Parteo frontier in the evolution process is uniform, but also the spatial distribution of the Parteo frontier corresponding to the target cluster is uniform. This ensures not only the diversity of the previous generations of Parteo frontier but also the flexibility of the system to select the target cluster.

3.7 Gene reconstruction technology

When the algorithm is close to convergence, the decision variables with different weights in the population are logically operated with the solidified bits inDNAI**,DNAII**andDNAIII**respectively. If the solidified bit is “0”, then “operation”; if the solidified bit is “0”, then process the “and” operation; if the solidified bit is “1”, then process the “or” operation. Therefore, the gene reconstruction segment is transplanted into the population to control the evolution trend of the target solution group in multi-dimensional space, thus eliminating degradation and The occurrence of random roaming strongly drives the population to approach the real Pareto optimal model group with global properties, thus ensuring the control accuracy of the system relative to each performance index to be optimized, which is also called gene reconstruction technology.

4 Multi-objective genetic algorithm based on feature library and gene reconstruction technology optimization

Combined with the embedding operation of feature base, dynamic competition mechanism, random selection strategy of better features and gene reconstruction technology, and referring to the population classification system of non-dominated sorting, a multi-objective genetic algorithm based on the optimization of feature base and gene reconstruction technology is constructed. Referring to the population classification system of non-dominated sorting proposed in reference 8, the specific steps of algorithm implementation are as follows:

Step1: Population Initialization

Step4: build feature libraryΟ=(ε1,ε2,…εn)T;

If the number of intersections of Pareto frontier is small,n<5, the program goes to Step 9;

Step5: build GENEI library, GENEII library and GENEIII library, getGENEI*,GENEII*andGENEIII*;

Step7: randomly selectStand inherit the better features through embedding operation;

Step9: ift

The pseudo-code of the algorithm is as follows:

BEGIN

fort=1;t

ift>1

St→Random fetch strategy → Embedding operation

ifn≥5

ifωmax≥n≥5

else ifn>ωmax

Building gene poolGENEI*、GENEII*和GENEIII*

if m>5

Gene segment reconstruction →GENEI**、GENEII**andGENEIII**

Output the optimal target solution group

END

5 Simulation

Fig.3 Laminar cooling temperature curve of strip based on multi-objective optimization strategy

Fig.4 Optimal opening and closing mode of rough tuning area header given by multi-objective optimization strategy

Fig.5 Strip laminar cooling temperature curve based on conventional GA multi-objective optimization strategy

It can be observed from Fig.5, conventional GA based on multi-objective optimization of the strip laminar cooling process, regardless of the strip surface point, center, and the temperature of the interior point, and given the temperature of the cooling path far, its average temperature curve and a given cooling path curve fitting are very poor, in the process of two-dimensional multi-objective optimization, only to meet the control precision of the coiling temperature, strip steel product quality needs to be further improved.

It can be seen from Fig.3 that the deviation between the actual coiling temperature and the target coiling temperature of the strip is controlled at ±10 ℃, and the given cooling rate curve is well tracked no matter from the point of view of the temperature drop process of the surface point, the inner point, and the center point, or from the changing trend of the average temperature of the strip. It shows that the algorithm of the best opening and closing mode set of collectors can control the cooling process of strip steel.

Table 1 Pareto frontier solution sets of 100, 400 and 700 generations

Table 2 Variance and mean of multi-objective optimization simulation results

The following conclusions can be summarized from Table 2:

6 Conclusion

In this paper, a multi-objective genetic algorithm based on the optimization of feature library and gene reconstruction technology is proposed to search the optimal open and closed pattern group of the coarse tuning area header in the global space. In this algorithm, the intersection of Pareto front is used to build the feature library, from which the better open and closed feature of headers is obtained, and it is embedded into the next generation population, which overcomes the degradation phenomenon in the process of population evolution. The dynamic competition mechanism introduced in feature base contributes to construct and maintain the best open and closed mode group of headers; the random rounding strategy of the feature library focuses on the balance and consideration ability of the objective solution group to the multi-objective, which improves the generality of the system. In addition, at the final stage of population evolution, gene reconstruction technology strongly controls the evolution direction of the target solution group in multi-dimensional space, which makes it quickly approach the real Pareto optimal pattern group, thus the accuracy of the system is significantly improved for multi-objective optimization performance indicators. The simulation results show that the multi-objective optimization strategy proposed in this paper not only ensures the control accuracy of the target coiling temperature, but also achieves a good fit between the cooling process and the given cooling rate, and its effect is obviously superior to the conventional cooling mode of strip steel. It not only improves the microstructure and mechanical properties of the strip, but also provides technical support for the research and development of high-end new steel with high added value.