CN101829438A - Method for optimizing chromatograph operating parameters of simulated mobile bed - Google Patents

Abstract

The invention discloses a method for optimizing chromatograph operating parameters of a simulated mobile bed. According to the method, the target preference requirement of a chromatograph production process of the simulated mobile bed is introduced for guiding the optimization direction to optimize the purity and production rate of a simulated mobile bed product. Compared with an experimental optimizing method, the method saves a large amount of operating time and economic cost; compared with a common single-target optimizing method, the method more accords with the fact that the weight relationship between a plurality of production targets or targets in the practical production process of the simulated mobile bed; and compared with a common multi-target optimizing method, the method adds the production target preference of the simulated mobile bed according to real process, so that the obtained optimizing results are positioned within a target preference range, the pertinence of the optimizing results is improved and better working points are acquired.

Description

A kind of method for optimizing chromatograph operating parameters of simulated mobile bed

Technical field

The present invention relates to the SMBC technical field, relate in particular to a kind of method for optimizing chromatograph operating parameters of simulated mobile bed that high request isolation field such as fine chemistry industry, chiral drug resolution are closed that is applied to.

Background technology

Simulation moving-bed (Simulated Moving Bed, abbreviation SMB) technology is as the main representative of continuous chromatography, have production efficiency height, organic solvent consumption less, mass transfer force is big, be convenient to advantage such as automatic continuous production, being new generation of green chemical separation technology in the world, also is an important research direction of process industry greenization, automation.Its range of application is also constantly expanded from fields such as traditional petrochemical industry, the descriscent bio-pharmaceuticals of carbohydrate branch, fine chemistry industries.

In the practical application of SMB technology, the main focus of people is how to determine suitable operating condition at different chromatographic separation processes, make the separating effect of whole system not only can satisfy the requirement of product quality, and save cost as much as possible, enhance productivity.But its operation mechanism complexity, the parameter that influences separating effect is numerous, lacks the optimum operation condition that effective method is comparatively determined actual device all the time.

A few generic operation parameter optimization methods commonly used at present are respectively: experimental technique, deltic method, single goal optimization method and general Multipurpose Optimal Method.The method practical application of experiment is stronger, but time cost and financial cost are relatively large, and the applicability of this method is relatively poor, is difficult to generalize; The triangle theory has important directive significance to the SMB searching process, and it makes searching process be simplified.But this theory is based on the hypothesis of ideal state, and there is big gap in the resistance to mass tranfer between having ignored two with the actual separation process, can not be used for quantitative study.The single goal optimization method need carry out artificial weight setting to each productive target, and this weight setting method has very big subjective factor, also is unfavorable for real process, and the ability of searching optimum of this method is relatively poor; Though Multipurpose Optimal Method can be handled multi-objective problem preferably, but its total space to object space when being optimized is carried out optimizing, it is equally distributed at object space that thereby the Pareto that finally obtains separates, but the operating point number is less in the separate targets zone of real realistic production requirement, selects to bring big limitation to actual condition.

Summary of the invention

The objective of the invention is deficiency, a kind of method for optimizing chromatograph operating parameters of simulated mobile bed is provided at existing simulation moving-bed operation parameter optimization method technology.

Concrete technical scheme of the present invention is as follows:

(1) measures simulation moving-bed bed parameter;

(2) measure the chromatographic process adsorption isotherm;

(3) determine the SMBC model;

(4) simulation moving-bed model finds the solution;

(5) determine optimization aim and target preference;

(6) determine decision variable and constraints;

(7) optimizing process design.

The invention has the beneficial effects as follows:

1, broken through the limitation of conventional optimization method, effectively treatment of simulated mobile bed chromatic optimization problem multivariable, multiobject characteristics.

2, solved the shortcoming that experiment optimization method time loss is many, financial cost is big.The present invention not only can obtain the operating condition of separating property excellence, and can effectively reduce the optimizing cost.

3, optimizing process has more specific aim, by add the preference information of simulation moving-bed separate targets in searching process, makes the optimization result who finally obtains all be positioned at the preference zone, can supply the more range of choice of actual operator.

4, the optimization result is better, experiment showed, the SMBC operating condition that the present invention can be more excellent than additive method obtained performance index.

Description of drawings

Fig. 1 is the operation logic figure of apparatus of the present invention object;

Fig. 2 is the flow chart of finding the solution of Mathematical Modeling of the present invention;

Fig. 3 is an optimization method flow chart of the present invention;

Fig. 4 is the optimization method filial generation production process flow chart of band preference of the present invention;

Fig. 5 is that the target preference is provided with schematic diagram among the present invention;

Fig. 6 is the present invention and Multipurpose Optimal Method commonly used to the optimization of simulation moving-bed a certain production process comparison diagram as a result.

The specific embodiment

A kind of optimization method of method for optimizing chromatograph operating parameters of simulated mobile bed utilization band productive target preference is optimized the chromatogram operating condition, makes simulated moving bed product purity and productivity ratio reach best.

A kind of method for optimizing chromatograph operating parameters of simulated mobile bed of the present invention may further comprise the steps:

1, measures simulation moving-bed bed parameter

Simulation moving-bed bed parameter is meant and simulation moving-bed device design and the relevant parameter of separate object.Mainly comprise: cylinder distribution, cylinder length, column diameter, voidage, mass tranfer coefficient, diffusion coefficient and Peclet number.Cylinder distributes and is meant the cylinder number of each separated region in the structure drawing of device shown in Figure 1; Cylinder length and column diameter can record by the general measure instrument, as slide measure etc.; Voidage can obtain from the shop instruction of filling cylinder; Mass tranfer coefficient is generally measured by direct determination method and the stimulation-method of replying; Diffusion coefficient is measured by the time delay method.

2, measure the chromatographic process adsorption isotherm

The general bi-Langmuir thermoisopleth form that adopts of adsorption equilibrium relation, isothermal model parameter be by the experimental data acquisition of single chromatographic column, and assay method can be with static method or flow method.

3, determine the SMBC model

The present invention utilizes TMB model based on general speed theory as the Mathematical Modeling basis.Its Mathematical Modeling zero dimension form is as follows:

Material balance equation:

$\frac{1}{{\mathrm{Pe}}_j}\frac{d^2{C}_{i,j}}{d{x}^2}-\frac{d{C}_{i,j}}{\mathrm{dx}}-\frac{\mathrm{\ξ}{\mathrm{\α}}_j}{{\mathrm{\γ}}_j}{k}_f(q_{i,j}^{*}-q_{i,j})=0---\left(1\right)$

The interphase mass transfer equation:

$\frac{{\mathrm{dq}}_{i,j}}{\mathrm{dx}}+{\mathrm{\α}}_j(q_{i,j}^{*}-q_{i,j})=0---\left(2\right)$

Boundary condition:

z＝0， $C_{i,j}-\frac{1}{{\mathrm{Pe}}_j}\frac{d{C}_{i,j}}{\mathrm{dx}}=C_{i,j,0}---\left(3a\right)$

z＝L， $\frac{{\mathrm{dC}}_{i,j,z}}{\mathrm{dz}}=0,$ q _i，j，z＝q _i，j+1，0 (3b)

The eluent inlet:

Q _I＝Q _IV+Q _D， (4a)

$C_{A,I}^{\mathrm{in}}=\frac{Q_{\mathrm{IV}}{C}_{A,\mathrm{IV}}^{\mathrm{out}}+Q_D{C}_{A,D}}{Q_I},$ $C_{B,I}^{\mathrm{in}}=\frac{Q_{\mathrm{IV}}{C}_{B,\mathrm{IV}}^{\mathrm{out}}+Q_D{C}_{B,D}}{Q_I}---\left(4b\right)$

Extract liquid and extract mouth:

Q _II＝Q _I-Q _E， (4c)

$C_{A,\mathrm{II}}^{\mathrm{in}}=C_{A,I}^{\mathrm{out}},$ $C_{A,E}=C_{A,I}^{\mathrm{out}},$ $C_{B,\mathrm{II}}^{\mathrm{in}}=C_{B,I}^{\mathrm{out}},$ $C_{B,E}=C_{B,I}^{\mathrm{out}}---\left(4d\right)$

Material inlet:

Q _III＝Q _II+Q _F， (4e)

$C_{A,\mathrm{III}}^{\mathrm{in}}=\frac{Q_{\mathrm{II}}{C}_{A,\mathrm{II}}^{\mathrm{out}}+Q_F{C}_{A,F}}{Q_{\mathrm{III}}},$ $C_{B,\mathrm{III}}^{\mathrm{in}}=\frac{Q_{\mathrm{II}}{C}_{B,\mathrm{II}}^{\mathrm{out}}+Q_F{C}_{B,F}}{Q_{\mathrm{III}}}---\left(4f\right)$

Raffinate extracts mouth:

Q _IV＝Q _III-Q _R， (4g)

$C_{A,\mathrm{IV}}^{\mathrm{in}}=C_{A,\mathrm{III}}^{\mathrm{out}},$ $C_{A,R}=C_{A,\mathrm{III}}^{\mathrm{out}},$ $C_{B,\mathrm{IV}}^{\mathrm{in}}=C_{B,\mathrm{III}}^{\mathrm{out}},$ $C_{B,R}=C_{B,\mathrm{III}}^{\mathrm{out}}---\left(4h\right)$

The adsorption isotherm type is measured by step 2.

In the following formula: i is material to be separated component numbering, and j is the chromatographic column numbering, and C is the phase concentration that flows, and q is fixing phase concentration, q ^*For with the fixing mutually saturated adsorption concentration of mobile phase concentration balance, a is a number of mass transfer unit, ξ is a voidage, Pe is the Peclet number, γ _iBe velocity ratio, Q _DBe desorbing agent flow, Q _FBe feed rate, Q _EFor extracting flow quantity, Q _RBe raffinate flow, Q _I, Q _II, Q _III, Q _IVBe regional flow, τ is a time zero dimension variable, and x is an axial coordinate zero dimension variable.

Bring bed parameter, operating parameter and the adsorption isotherm form of process into the TMB model, can obtain at the particular procedure model form.

4, simulation moving-bed model finds the solution

Simulation moving-bed model find the solution flow chart as shown in Figure 2, at first use the asymmetric quadrature collocation method to axial (x direction) discretization of bed, be a series of Nonlinear System of Equations with model conversation; Next utilizes the MatlabFsolve function to find the solution Nonlinear System of Equations, obtains in the simulation moving-bed stable state bed mean concentration distribution everywhere.

5, determine optimization aim and target preference

The product of SMBC comprises takes out the strong absorbed component (supposing to be called A) that liquid taking port obtains and the weak absorbed component (supposing to be called B) of raffinate mouth acquisition.The objective of the invention is to make simulated moving bed product purity and productivity ratio to reach best.Product purity and productivity ratio are defined as follows:

$\mathrm{PureR}=100*\frac{C_R^A}{C_R^A+C_R^B}$

$\mathrm{ProductivityR}=\frac{Q_R{C}_R^A}{\mathrm{VS}}$

$\mathrm{PureE}=100*\frac{C_E^B}{C_E^A+C_E^B}$

$\mathrm{ProductivityE}=\frac{Q_E{C}_E^B}{\mathrm{VS}}$

Wherein, C _R ^A, C _E ^AThe concentration of absorbed component a little less than being respectively raffinate and extracting in the liquid, C _R ^B, C _E ^BBe respectively the concentration of strong absorbed component in raffinate and the extraction liquid, VS is a device cylinder cumulative volume.

The selection of optimization aim is determined according to the required extraction of substance of production process; The target preference is meant the requirement relevant with production process or product quality, and for example productivity ratio will reach certain more than the level, purity be at least percent what etc.

6, determine decision variable and constraints

Decision variable refers to that the present invention seeks the operating parameter that its value needs change in the simulation moving-bed best effort point process.Simulation moving-bed operating parameter comprises: input concentration, feed rate, eluent flow, raffinate flow, extract flow quantity, circulating fluid flow rate and switching time.Constraints is to need the restrictive condition that satisfies in the simulation moving-bed running, mainly comprises operating parameter span and some preset parameters.The span of operating parameter can be determined according to methods such as the actual separation ability of simulation moving-bed device, people's experience or measurings, its main purpose is to obtain relatively large feasible zone, searching process can be carried out in bigger space, help obtaining more feasible solution.

7, optimizing process design

7.1, simulation moving-bed optimization method flow process

A kind of flow chart of the Multipurpose Optimal Method with preference describes the optimization method design cycle below in conjunction with Fig. 3 as shown in Figure 3.

Step 1: parameter initialization.Create population P ₀With outside archives population W ₀, the individual number NIND in the population, outside population number OutNIND, operation algebraically Maxgen, decision variable number VNIND are set;

Step 2: calculate population P ₀In each individual desired value, according to ordering order and crowding parameter individual in the desired value dominance relation definition population.

Step 3: according to the ordering order of individuality and crowding distance to P _nPopulation carries out algorithm of tournament selection, obtains parent population P _n

Step 4: to parent population P _nIntersect and mutation operation, obtain progeny population Q _nThe probability of mutation operation if this individual preference target satisfies the preference requirement that sets, is then adopted less variation probability, otherwise is increased the punishment dynamics by individual preference target decision in the parent population.

Step 5: with P _nAnd Q _nMerge, obtain middle for population T _n

Step 6: to T _nIn individuality select, all are met individualities that preference requires deposit outside archives population W in _n

Step 7: according to the ordering order of individuality and crowding distance to T _nAnd W _nSelect operation, obtain NIND filial generation individuality as population P _N+1The member, choose simultaneously OutNIND individual as outside archives population W _N+1In the member.

Step 8: calculate iterations, if iterations forwards step 3 to less than maximum iteration time Maxgen, otherwise end loop shows W _nIn the optimization result.

In this process middle generation and outside population are sorted and fill population P of new generation _N+1Process as shown in Figure 4.At first to the centre for population R _nIn non-bad layer number add up, whether can be held fully to determine it by new population.If can, then all individualities of should be non-bad layer are filled into new population, and with them from R _nMiddle deletion, and continue to judge selection to remaining individuality; If could not would select to fill according to crowding distance.

7.2, the target setting preference

Production process target preference addition manner of the present invention is realized by choose outside population in optimization method.As shown in Figure 5, in generation in the middle of parent in the optimizing process and filial generation merging produce, to all individual targets in middle generation judge whether satisfy preference information then with definite its.If satisfy, then it copied to outside population, otherwise be left intact.

Describe the present invention below with reference to the accompanying drawings in detail, it is more obvious that purpose of the present invention and effect will become.

Embodiment

Embodiment with a certain chipal compounds a little less than the simulation moving-bed leaching process of enantiomer be example, utilize the present invention to seek the optimal point of operation of simulation moving-bed device, make production process obtain high raffinate purity and raffinate productivity ratio.Concrete implementation step is as follows:

(1) simulation moving-bed bed parameter is measured or is directly obtained in equipment supplier's specification by the measuring method that illustrates in the embodiment.

(2) adsorption isotherm adopts bi-Langmuir thermoisopleth form, and the thermoisopleth parameter is measured by the method that static method and flow method combine.

(3) as the Mathematical Modeling basis, the model equation concrete form is seen the present invention program's implementation step to present embodiment based on the TMB model of general speed theory.

(4) simulation moving-bed model find the solution flow chart as shown in Figure 2, utilization asymmetric quadrature collocation method is provided with in each separated region 16 of collocation point numbers; , be 288 nonlinear equations then with model conversation to axial (x direction) discretization of bed; Utilize Matlab Fsolve function to find the solution this Nonlinear System of Equations at last, obtain in the simulation moving-bed stable state bed mean concentration distribution everywhere.

(5), determine that optimization aim is maximum raffinate purity and maximum raffinate productivity ratio at the separation requirement of present embodiment; The target preference is that the purity of weak absorbed component in the raffinate is higher than 98%.

(6) between simulation moving-bed each performance variable coupled relation is arranged, in fact the free variable number of system is less than the performance variable number.Present embodiment is chosen switching time, eluent flow, raffinate flow and the feed rate decision variable as optimizing process.Constraints is constant for I district flow in the maintenance device shown in Figure 1, and the span of each decision variable is determined according to real process.

(7) population scale is 50 in the present embodiment, and outside population scale is 50, and iterations is 100 times, crossover probability is 0.75, whether the variation probability satisfies preference according to target requires to determine: if satisfy, then be set at 0.05, otherwise the variation probability is (98-Pure R)/100.

Fig. 6 has shown optimization method of the present invention and existing Multipurpose Optimal Method, and (as: the non-domination ordering genetic method of band elitism strategy is NSGA-II) to the optimization result of enantiomer a little less than the simulation moving-bed separating chiral compound.

As can see from Figure 6, the purity target zone that the NSGA-II method obtains is very wide, distribution is all arranged in 68%～100% interval, the overwhelming majority is not within the productive target claimed range in these operating points, but cause the number of reality operating point less, distribute and dilute, be unfavorable for choosing of operating point.The present invention optimizes as a result that moderate purity satisfies the requirement of productive target preference then all more than 98%, can provide enough alternative operating points to actual production process.From throughput objectives, satisfy purity requirement greater than 98% condition under, the peak performance that the present invention obtains reaches 1.88g/h/l, is higher than the 1.75g/h/l best result that the NSGA-II method obtains, satisfying the requiring under the prerequisite of product quality, production capacity has improved 7.43%.From the uniformity of Pareto angle distribution, obviously the result that obtains of the present invention is better, and its whole disaggregation evenly distributes at object space, and NSGA-II method moderate purity 95% to separate number less relatively, it is concentrated relatively to distribute.To sum up can get, the present invention can better handle the problem that improves simulated moving bed product purity and productivity ratio.

The foregoing description is used for the present invention that explains, rather than limits the invention, and in the protection domain of spirit of the present invention and claim, any modification and change to the present invention makes all fall into protection scope of the present invention.

Claims (6)

1. a method for optimizing chromatograph operating parameters of simulated mobile bed is characterized in that, may further comprise the steps:

(1) measures simulation moving-bed bed parameter.

(2) measure the chromatographic process adsorption isotherm.

(3) determine the SMBC model.

(4) simulation moving-bed model finds the solution.

(5) determine optimization aim and target preference.

(6) determine decision variable and constraints.

(7) optimizing process design.

2. according to the described method for optimizing chromatograph operating parameters of simulated mobile bed of claim 1, it is characterized in that in the described step (1), described simulation moving-bed bed parameter is meant and simulation moving-bed device design and the relevant parameter of separate object.Mainly comprise: cylinder distribution, cylinder length, column diameter, voidage, mass tranfer coefficient and Peclet number.

3. according to the described method for optimizing chromatograph operating parameters of simulated mobile bed of claim 1, it is characterized in that described step (3) is specially: utilize TMB model based on general speed theory as the Mathematical Modeling basis, its Mathematical Modeling zero dimension form is as follows:

Material balance equation:

$\frac{1}{{\mathrm{Pe}}_j}\frac{d^2{C}_{i,j}}{{\mathrm{dx}}^2}-\frac{d{C}_{i,j}}{\mathrm{dx}}-\frac{\mathrm{\ξ}{\mathrm{\α}}_j}{{\mathrm{\γ}}_j}{k}_f(q_{i,j}^{*}-q_{i,j})=0;$

The interphase mass transfer equation:

$\frac{{\mathrm{dq}}_{i,j}}{\mathrm{dx}}+{\mathrm{\α}}_j(q_{i,j}^{*}-q_{i,j})=0;$

Boundary condition:

z＝0， $C_{i,j}-\frac{1}{{\mathrm{Pe}}_j}\frac{d{C}_{i,j}}{\mathrm{dx}}=C_{i,j,0};$

z＝L， $\frac{d{C}_{i,j,z}}{\mathrm{dz}}=0,q_{i,j,z}=q_{i,j+\mathrm{1,0}};$

The eluent inlet:

Q _I＝Q _IV+Q _D，；

$C_{A,I}^{\mathrm{in}}=\frac{Q_{\mathrm{IV}}{C}_{A,\mathrm{IV}}^{\mathrm{out}}+Q_D{C}_{A,D}}{Q_I},$ $C_{B,I}^{\mathrm{in}}=\frac{Q_{\mathrm{IV}}{C}_{B,\mathrm{IV}}^{\mathrm{out}}+Q_D{C}_{B,D}}{Q_I};$

Extract liquid and extract mouth:

Q _II＝Q _I-Q _E，；

$C_{A,\mathrm{II}}^{\mathrm{in}}=C_{A,I}^{\mathrm{out}},$ $C_{A,E}=C_{A,I}^{\mathrm{out}},$ $C_{B,\mathrm{II}}^{\mathrm{in}}=C_{B,I}^{\mathrm{out}},$ $C_{B,E}=C_{B,I}^{\mathrm{out}};$

Material inlet:

Q _III＝Q _II+Q _F，；

$C_{A,\mathrm{III}}^{\mathrm{in}}=\frac{Q_{\mathrm{II}}{C}_{A,\mathrm{II}}^{\mathrm{out}}+Q_F{C}_{A,F}}{Q_{\mathrm{III}}},$ $C_{B,\mathrm{III}}^{\mathrm{in}}=\frac{Q_{\mathrm{II}}{C}_{B,\mathrm{II}}^{\mathrm{out}}+Q_F{C}_{B,F}}{Q_{\mathrm{III}}};$

Raffinate extracts mouth:

Q _IV＝Q _III-Q _R，；

$C_{A,\mathrm{IV}}^{\mathrm{in}}=C_{A,\mathrm{III}}^{\mathrm{out}},$ $C_{A,R}=C_{A,\mathrm{III}}^{\mathrm{out}},$ $C_{B,\mathrm{IV}}^{\mathrm{in}}=C_{B,\mathrm{III}}^{\mathrm{out}},$ $C_{B,R}=C_{B,\mathrm{III}}^{\mathrm{out}};$

The adsorption isotherm type is measured by step (2).

Wherein: i is material to be separated component numbering, and j is the chromatographic column numbering, and C is the phase concentration that flows, and q is fixing phase concentration, q ^*For with the fixing mutually saturated adsorption concentration of mobile phase concentration balance, α is a number of mass transfer unit, ξ is a voidage, Pe is the Peclet number, γ _iBe velocity ratio, Q _DBe desorbing agent flow, Q _FBe feed rate, Q _EFor extracting flow quantity, Q _RBe raffinate flow, Q _I, Q _II, Q _III, Q _IVBe regional flow, τ is a time zero dimension variable, and x is an axial coordinate zero dimension variable.

Bring bed parameter, operating parameter and the adsorption isotherm form of process into the TMB model, can obtain at the particular procedure model form.

4. according to the described method for optimizing chromatograph operating parameters of simulated mobile bed of claim 1, it is characterized in that described step (5) is specially: the product of SMBC comprises takes out the weak absorbed component B that strong absorbed component A that liquid taking port obtains and raffinate mouth obtain.The objective of the invention is to make simulated moving bed product purity and productivity ratio to reach best.Product purity and productivity ratio are defined as follows:

$\mathrm{PureR}=100*\frac{C_R^A}{C_R^A+C_R^B}$

$\mathrm{ProductivityR}=\frac{Q_R{C}_R^A}{\mathrm{VS}}$

$\mathrm{PureE}=100*\frac{C_E^B}{C_E^A+C_E^B}$

$\mathrm{ProductivityE}=\frac{Q_E{C}_E^B}{\mathrm{VS}};$

Wherein, C _R ^A, C _E ^AThe concentration of absorbed component a little less than being respectively raffinate and extracting in the liquid, C _R ^B, C _E ^BBe respectively the concentration of strong absorbed component in raffinate and the extraction liquid, VS is a device cylinder cumulative volume.

5. according to the described method for optimizing chromatograph operating parameters of simulated mobile bed of claim 1, it is characterized in that in the described step (6), described decision variable refers to seek the operating parameter that its value needs change in the simulation moving-bed best effort point process.Simulation moving-bed operating parameter comprises: input concentration, feed rate, eluent flow, raffinate flow, extract flow quantity, circulating fluid flow rate and switching time.Constraints is to need the restrictive condition that satisfies in the simulation moving-bed running.

6. according to the described method for optimizing chromatograph operating parameters of simulated mobile bed of claim 1, it is characterized in that described step (6) comprises optimizing process design procedure and target setting preference step, described optimizing process design procedure specifically comprises:

(A) parameter initialization is created population P ₀With outside archives population W ₀, the individual number NIND in the population, outside population number OutNIND, operation algebraically Maxgen, decision variable number VNIND are set.

(B) calculate population P ₀In each individual desired value, according to ordering order and crowding parameter individual in the desired value dominance relation definition population.

(C) according to the ordering order of individuality and crowding distance to P _nPopulation carries out algorithm of tournament selection, obtains parent population P _n

(D) to parent population P _nIntersect and mutation operation, obtain progeny population Q _nThe probability of mutation operation if this individual preference target satisfies the preference requirement that sets, is then adopted less variation probability, otherwise is increased the punishment dynamics by individual preference target decision in the parent population.

(E) with P _nAnd Q _nMerge, obtain middle for population T _n

(F) to T _nIn individuality select, all are met individualities that preference requires deposit outside archives population W in _n

(G) according to the ordering order of individuality and crowding distance to T _nAnd W _nSelect operation, obtain NIND filial generation individuality as population P _N+1The member, choose simultaneously OutNIND individual as outside archives population W _N+1In the member.

(H) calculate iterations, if iterations forwards step 3 to less than maximum iteration time Maxgen, otherwise end loop shows W _nIn the optimization result.

Realize by outside population by choosing in optimization method for described target setting preference step, parent in the optimizing process and filial generation merge produce in the middle of generation, all individual targets in middle generation are judged whether satisfy preference information then to determine it.If satisfy, then it copied to outside population, otherwise be left intact.

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