CN109325267A - A kind of application for high-dimensional chemical engineering data conjugate particles group algorithm process method - Google Patents
A kind of application for high-dimensional chemical engineering data conjugate particles group algorithm process method Download PDFInfo
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Abstract
The invention belongs to chemical engineering data processing technology fields, disclose a kind of application for high-dimensional chemical engineering data conjugate particles group algorithm process method.Conjugate direction method is combined processing high dimensional data with particle swarm algorithm by the present invention.When the certain step number of particle swarm algorithm iteration falls into local extremum and obtains locally optimal solution x*, using x* as initial value, it is solved with conjugate direction method, using particle swarm algorithm to the validity of low-dimensional optimization problem, more preferably current optimal solution x** newly will be obtained, so that algorithm be made to jump out local extremum；Under conditions of new extreme value, and with particle swarm algorithm to former problem solving, repeatedly until terminating.It is tested by classical test function, the results showed that this trial is effective.Algorithm is finally used for the Non-linear parameter estimation of SO2 catalytic oxidation kinetic model, obtains promising result.
Description
Technical field
The invention belongs to chemical engineering data processing technology field more particularly to a kind of application for high-dimensional chemical engineering data conjugate particles group's algorithms
Processing method.
Background technique
The rate of chemical reaction is usually related with the concentration of reactant, pressure, temperature and catalyst used etc., establishes
Rate process model, and then can be used for predicting and optimizing, it also can be used for furtheing investigate the intension of chemical reaction.Modeling can be from mechanism
It sets out；It may be based on experimental data, first the functional form of foundation mechanism reduced model, wherein the undetermined parameter still having, with sample
Estimated based on data, the often preferable selection of this semiempirical model of half mechanism.The sample that Chemical Problems obtain
Data are mostly high dimensional data, to carry out the optimization problem that parameter Estimation is just high-dimension function according to sample data.Population is calculated
Method can obtain good effect to the lower objective function of dimension, and then effect does not comply with one's wishes when the dimension of objective function is higher.
In conclusion problem of the existing technology is: chemical engineering data is mostly high dimensional data, and particle swarm algorithm is to solution
High-dimensional optimization easily falls into local extremum.
Summary of the invention
In view of the problems of the existing technology, the present invention provides a kind of application for high-dimensional chemical engineering data conjugate particles group's algorithm process
Method.
The invention is realized in this way a kind of application for high-dimensional chemical engineering data conjugate particles group algorithm process method includes following step
It is rapid:
Step 1, the certain step number of particle swarm algorithm iteration and fall into local extremum and locally optimal solution x* when, with x*
For initial value, it is solved with conjugate direction method；
Step 2 will obtain more preferably current optimal solution newly using particle swarm algorithm to the validity of low-dimensional optimization problem
X**, so that algorithm be made to jump out local extremum；
Step 3, under conditions of new extreme value, and with particle swarm algorithm to former problem solving, repeatedly until terminating.
Further, the basic particle group algorithm and its mathematical analysis are as follows:
If optimization problem is stated are as follows:
(1) basic particle group algorithm (PSO):
Particle swarm algorithm (PSO) [1~3] is to the bionical of the colonial organisms behavior such as flock of birds, and each bion is referred to as grain
Son, PSO will be searched for optimal solution by one group of particle in n-dimensional space, and the location of each particle indicates a solution vector, as intelligence
It can remember the optimal solution itself searched to energy body, and obtain the optimal solution that wholegrain subgroup is lived through, and thus instruct its movement,
Progressive alternate seeks obtaining optimal solution.
Remember i-th of particle jth for when position be xi(j), the optimal solution that itself and wholegrain subgroup are searched point
It Wei not pid(j) and pgd(j), its moving velocity vector is vi(j), then at+1 generation of jth, i-th of particle be will move to:
vi(j+1)=ω φ1vi(j)+η1φ2(pid(j)-xi(j))+η2φ3(pga(j)-xi(j)) (2)
xi(j+1)=xi(j)+vi(j+1) (3)
Wherein: ω, η1, η2It is control parameter of the value in [0,1], algorithm performance is had a major impact but is difficult
Determine value appropriate, φ1, φ2, φ3It is the random number in [0,1] section；Neighbour structures different simultaneously are for efficiency of algorithm and receipts
Hold back the influence of speed.
The algorithm concept is simple, it is easy to accomplish, thus developed quickly, international EVOLUTIONARY COMPUTATION research neck has been obtained rapidly
The approval in domain, and be used widely in engineering, but algorithm has the deficiency in the presence of easily sunken local extremum, it is especially excellent to higher-dimension
It is even more so to change function；There is the proposition much about the algorithm improvement strategy thus；Main improvement has: 1. improving control ginseng
Number；2. to particle state variable again assignment；3. in conjunction with other evolution algorithms；4. updated using new position or speed etc.
Formula；5. new groups' form etc..
(2) mathematical analysis of particle swarm algorithm
For particle swarm algorithm: if 1. only one particle of algorithm and be free of 1, (2) formula substitution (3) formula obtain:
xi(j+1)=xi(j)+(η1φ1+η2φ2)(pid(j)-xi(j))；
From this view, particle swarm algorithm is a kind of popularization of hill-climbing algorithm, is advanced every time towards optimal direction；2. from
Entire algorithm sees that it is considered as with direction pid(j)-xi(j) with direction pgd(j)-xi(j) weighting is as the direction of search；pgd
Leading action is played, each particle scans in respective a certain range；General primary, which is generally evenly distributed in, entirely to be searched
It is generally possible to obtain the optimal solutions of problem in rope domain, when so being not very high to objective function.And when the dimension of objective function is higher
When, if algorithm once falls into local extremum, due to the mutual restriction between each dimension variable, and if it is constant in several steps, such as
Step 1 is constant with step 2, i.e. pid(1)=pid(2), then:
xi(2)=xi(1)+(η1φ1+η2φ2)(pid(1)-xi(1))
xi(3)=xi(2)+(η1φ1+η2φ2)(pid(1)-xi(2))=xi(1)+k(pid(1)-xi(1))；
Wherein: k=2 (η1φ1+η2φ2)-(η1φ1+η2φ2)2, can be seen that from this, in pia(j) it in the case where constant, calculates
The direction of search of method be also it is constant, thus pgdIt would become hard to improve to some extent, therefore be only to be difficult to jump out local pole by algorithm itself
Value.To contain ω φ1vi(j) item, situation are also similar.For this to higher-dimension majorized function, algorithm easily falls into local extremum, only draws
Enter new mechanism, is allowed to jump out local extremum rapidly.More satisfied solution could finally be obtained.
Further, the conjugate direction method are as follows:
Conjugate direction method is to be proposed early in 1964 by Powell, the problem of to (1) formula, the basic step of this method
It is:
Step 201, an optional point A makees one-dimensional optimization along first reference axis, obtains B point as initial position.At this
Step only needs 1 one-dimensional optimizing；
Step 202, the one-dimensional optimization of a wheel is carried out one by one to a coordinate, the one-dimensional extreme value once obtained in the past every time is pointed out
Hair obtains C point by time one-dimensional optimize in this way, and the line of B and C are the conjugate directions that this wheel result obtains, will
Replace first coordinate direction andMake primary one-dimensional optimization in direction.N+1 optimizing is needed in this step；
Step 203, the one-dimensional optimization of every one wheel of progress will all obtain a conjugate direction, be substituted for an original use
Coordinate direction；
Step 204, by the 1 one-dimensional optimization of wheel, as a result obtain D point, need to make one-dimensional optimization number in total be: 1+ (n+1) (n-
1)=n2；
The property of conjugate direction method is: if the majorized function of formula (1) is quadratic function, D point be exactly in dimension space most
Advantage；If not quadratic function, then D point ratio A point can continue optimizing closer to optimum point by D point.
Further, the conjugate direction particle swarm algorithm are as follows:
(1) conjugate direction particle swarm algorithm (CDPSO)
Conjugate direction method guarantees to be better than original initial point by obtained point after once-through operation, initially clicks to get over
Good, then the point obtained is better, and algorithm gets over rapid convergence to globe optimum, can the initial value difficulty selection in optimization operation, usually with
Machine is chosen, this makes algorithm converge to optimum point to have to pass through prolonged operation.Particle swarm algorithm is random algorithm, algorithm
Initial point (particle), which is appointed, to be taken, and algorithm is analogous to hill-climbing algorithm, initial point more than one, cooperates between each point, institute
Declined quickly with algorithm in incipient stage target function value, rear target value decrease speed is slower and slower to a certain extent, finally may be used
Local extremum can be fallen into, especially even more so to higher-dimension majorized function, according to analysis above, at this moment algorithm is difficult by itself
Jump out local extremum, it is necessary to introduce new mechanism.For this purpose, improving particle swarm algorithm with conjugate direction method, fallen into particle swarm algorithm
When entering local extremum, using at this moment obtained Local Extremum as initial point, make once-through operation with conjugate direction method, obtained knot
Fruit is denoted as；According to conjugate direction method it is found that will be better than；Thus algorithm is made to jump out local extremum；Again using as wholegrain subgroup institute
The optimal solution searched, and calculated with particle swarm algorithm.Repeatedly, until meeting termination condition.
(2) particle swarm algorithm falls into the determination method of local extremum
Whether particle swarm algorithm has fallen into the general determination method of local extremum in the process of running, when algorithm is being run
In the process, within certain algebra (generally taking 10 generations or 20 generations), optimal value does not have the algorithm that is considered as of any change to fall into
Local extremum.
(3) conjugate direction particle swarm algorithm calculates step
For the optimization problem of formula (1), the key step of algorithm are as follows:
Step 301, the initial population that scale is is randomly generated；
Step 302, it calculates after certain algebra or calculates by PSO method to occurring within constant generations (20 generations)
Target value without improvement after, if optimal solution at this moment is x*；
Step 303, using x* as initial point, (1) formula is optimized with conjugate direction method, while to conjugate direction method institute
The One Dimension Optimization Problems of generation are still solved with particle swarm algorithm, due to only one-dimensional, so its initial point does not have to very much
(general 50), Simultaneous Iteration algebra is without very big (general 50).If finally obtaining result is x**；
Step 304, it checks whether and meets termination condition, be that current all particles are found most with x** if not meeting
It is excellent, it goes to step 2 and continues iteration；Otherwise terminate algorithm operation, export optimal solution.
Advantages of the present invention and good effect are as follows: conjugate direction method is combined processing higher-dimension with particle swarm algorithm by the present invention
Data.When the certain step number of particle swarm algorithm iteration falls into local extremum and obtains locally optimal solution x*, using x* as initial value, use
Conjugate direction method solves it, using particle swarm algorithm to the validity of low-dimensional optimization problem, by newly it is more preferably current most
Excellent solution x**, so that algorithm be made to jump out local extremum；Under conditions of new extreme value, and with particle swarm algorithm to former problem solving, such as
This is repeatedly until terminate.It is tested by classical test function, the results showed that this trial is effective.Finally by algorithm
For the Non-linear parameter estimation of SO2 catalytic oxidation kinetic model, promising result is obtained.
Detailed description of the invention
Fig. 1 is that the present invention implements the application for high-dimensional chemical engineering data conjugate particles group's algorithm process method flow diagram provided.
Fig. 2 is that the present invention implements the unexpected path profile of detection provided.
Specific embodiment
In order to make the objectives, technical solutions, and advantages of the present invention clearer, with reference to embodiments, to the present invention
It is further elaborated.It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention, it is not used to
Limit the present invention.
Application principle of the invention is further described with reference to the accompanying drawing.
As shown in Figure 1, it includes following step that the present invention, which provides a kind of application for high-dimensional chemical engineering data conjugate particles group algorithm process method,
It is rapid:
Step S101, the certain step number of particle swarm algorithm iteration and fall into local extremum and locally optimal solution x* when, with
X* is initial value, is solved with conjugate direction method to it；
Step S102, using particle swarm algorithm to the validity of low-dimensional optimization problem, by newly more preferably current optimal
X** is solved, so that algorithm be made to jump out local extremum；
Step S103, under conditions of new extreme value, and with particle swarm algorithm to former problem solving, repeatedly until knot
Beam.
Basic particle group algorithm provided by the invention and its mathematical analysis are as follows:
If optimization problem is stated are as follows:
(1) basic particle group algorithm (PSO):
Particle swarm algorithm (PSO) [1~3] is to the bionical of the colonial organisms behavior such as flock of birds, and each bion is referred to as grain
Son, PSO will be searched for optimal solution by one group of particle in n-dimensional space, and the location of each particle indicates a solution vector, as intelligence
It can remember the optimal solution itself searched to energy body, and obtain the optimal solution that wholegrain subgroup is lived through, and thus instruct its movement,
Progressive alternate seeks obtaining optimal solution.
Remember i-th of particle jth for when position be xi(j), the optimal solution that itself and wholegrain subgroup are searched point
It Wei not pid(j) and pgd(j), its moving velocity vector is vi(j), then at+1 generation of jth, i-th of particle be will move to:
vi(j+1)=ω φ1νi(j)+η1φ2(pid(j)-xi(j))+η2φ3(pgd(j)-xi(j)) (2)
xi(j+1)=xi(j)+vi(j+1)(3)
Wherein: ω, η1, η2It is control parameter of the value in [0,1], algorithm performance is had a major impact but is difficult
Determine value appropriate, φ1, φ2, φ3It is the random number in [0,1] section；Neighbour structures different simultaneously are for efficiency of algorithm and receipts
Hold back the influence of speed.
The algorithm concept is simple, it is easy to accomplish, thus developed quickly, international EVOLUTIONARY COMPUTATION research neck has been obtained rapidly
The approval in domain, and be used widely in engineering, but algorithm has the deficiency in the presence of easily sunken local extremum, it is especially excellent to higher-dimension
It is even more so to change function；There is the proposition much about the algorithm improvement strategy thus；Main improvement has: 1. improving control ginseng
Number；2. to particle state variable again assignment；3. in conjunction with other evolution algorithms；4. updated using new position or speed etc.
Formula；5. new groups' form etc..
(2) mathematical analysis of particle swarm algorithm
For particle swarm algorithm: if 1. only one particle of algorithm and be free of 1, (2) formula substitution (3) formula obtain:
xi(j+1)=xi(j)+(η1φ1+η2φ2)(pid(j)-xi(j))；
From this view, particle swarm algorithm is a kind of popularization of hill-climbing algorithm, is advanced every time towards optimal direction；2. from
Entire algorithm sees that it is considered as with direction pid(j)-xi(j) with direction pgd(j)-xi(j) weighting is as the direction of search；pgd
Leading action is played, each particle scans in respective a certain range；General primary, which is generally evenly distributed in, entirely to be searched
It is generally possible to obtain the optimal solutions of problem in rope domain, when so being not very high to objective function.And when the dimension of objective function is higher
When, if algorithm once falls into local extremum, due to the mutual restriction between each dimension variable, and if it is constant in several steps, such as
Step 1 is constant with step 2, i.e. pid(1)=pid(2), then:
xi(2)=xi(1)+(η1φ1+η2φ2)(pid(1)-xi(1))
xi(3)=xi(2)+(η1φ1+η2φ2)(pid(1)-xi(2))=xi(1)+k(pid(1)-xi(1))；
Wherein: k=2 (η1φ1+η2φ2)-(η1φ1+η2φ2)2, can be seen that from this, in pid(j) it in the case where constant, calculates
The direction of search of method be also it is constant, thus pgdIt would become hard to improve to some extent, therefore be only to be difficult to jump out local pole by algorithm itself
Value.To contain ω φ1vi(j) item, situation are also similar.For this to higher-dimension majorized function, algorithm easily falls into local extremum, only draws
Enter new mechanism, is allowed to jump out local extremum rapidly.More satisfied solution could finally be obtained.
Conjugate direction method provided by the invention are as follows:
Conjugate direction method is to be proposed early in 1964 by Powell, the problem of to (1) formula, the basic step of this method
It is:
Step 201, an optional point A makees one-dimensional optimization along first reference axis, obtains B point as initial position.At this
Step only needs 1 one-dimensional optimizing；
Step 202, the one-dimensional optimization of a wheel is carried out one by one to a coordinate, the one-dimensional extreme value once obtained in the past every time is pointed out
Hair obtains C point by time one-dimensional optimize in this way, and the line of B and C are the conjugate directions that this wheel result obtains, will
Replace first coordinate direction andMake primary one-dimensional optimization in direction.N+1 optimizing is needed in this step；
Step 203, the one-dimensional optimization of every one wheel of progress will all obtain a conjugate direction, be substituted for an original use
Coordinate direction；
Step 204, by the 1 one-dimensional optimization of wheel, as a result obtain D point, need to make one-dimensional optimization number in total be:
1+ (n+1) (n-1)=n2；
The property of conjugate direction method is: if the majorized function of formula (1) is quadratic function, D point be exactly in dimension space most
Advantage；If not quadratic function, then D point ratio A point can continue optimizing closer to optimum point by D point.
Conjugate direction particle swarm algorithm provided by the invention are as follows:
(1) conjugate direction particle swarm algorithm (CDPSO)
Conjugate direction method guarantees to be better than original initial point by obtained point after once-through operation, initially clicks to get over
Good, then the point obtained is better, and algorithm gets over rapid convergence to globe optimum, can the initial value difficulty selection in optimization operation, usually with
Machine is chosen, this makes algorithm converge to optimum point to have to pass through prolonged operation.Particle swarm algorithm is random algorithm, algorithm
Initial point (particle), which is appointed, to be taken, and algorithm is analogous to hill-climbing algorithm, initial point more than one, cooperates between each point, institute
Declined quickly with algorithm in incipient stage target function value, rear target value decrease speed is slower and slower to a certain extent, finally may be used
Local extremum can be fallen into, especially even more so to higher-dimension majorized function, according to analysis above, at this moment algorithm is difficult by itself
Jump out local extremum, it is necessary to introduce new mechanism.For this purpose, improving particle swarm algorithm with conjugate direction method, fallen into particle swarm algorithm
When entering local extremum, using at this moment obtained Local Extremum as initial point, make once-through operation with conjugate direction method, obtained knot
Fruit is denoted as；According to conjugate direction method it is found that will be better than；Thus algorithm is made to jump out local extremum；Again using as wholegrain subgroup institute
The optimal solution searched, and calculated with particle swarm algorithm.Repeatedly, until meeting termination condition.
(2) particle swarm algorithm falls into the determination method of local extremum
Whether particle swarm algorithm has fallen into the general determination method of local extremum in the process of running, when algorithm is being run
In the process, within certain algebra (generally taking 10 generations or 20 generations), optimal value does not have the algorithm that is considered as of any change to fall into
Local extremum.
(3) conjugate direction particle swarm algorithm calculates step
For the optimization problem of formula (1), the key step of algorithm are as follows:
Step 301, the initial population that scale is is randomly generated；
Step 302, it calculates after certain algebra or calculates by PSO method to occurring within constant generations (20 generations)
Target value without improvement after, if optimal solution at this moment is x*；
Step 303, using x* as initial point, (1) formula is optimized with conjugate direction method, while to conjugate direction method institute
The One Dimension Optimization Problems of generation are still solved with particle swarm algorithm, due to only one-dimensional, so its initial point does not have to very much
(general 50), Simultaneous Iteration algebra is without very big (general 50).If finally obtaining result is x**；
Step 304, it checks whether and meets termination condition, be that current all particles are found most with x** if not meeting
It is excellent, it goes to step 2 and continues iteration；Otherwise terminate algorithm operation, export optimal solution.
1, algorithm performance test and discussion
The performance test of 1.1 algorithms
Test 1 is with the broad sense Rastrigin function of 10 dimensions:
It is tested, the optimum point x* of the function is (0,0 ..., 0), optimal value f (x*)=0.
It is optimized respectively with PSO and CDPSO, parameter is set as ω1=0.53, η1=0.35, η2=0.45, initial grain
Subnumber 200,1000 generation of iterative algebra；Simultaneously when being optimized with CDPSO, as long as thering is 10 generation optimal values are constant to think to fall into
Local extremum；
It is still solved with particle swarm algorithm to One Dimension Optimization Problems caused by conjugate direction method, initial grain at this moment
Subnumber is 50, and iterative algebra is also 50.Acquired results are as shown in table 1, table 2.
Test 2 is with the broad sense Griewank function of 30 dimensions:
It being tested, the optimal solution * of the function is 0,0,0, optimal value * is 0.All parameters are as test 1.Due to
It is random algorithm, to each algorithm all independent operating 10 times.10 optimal values obtained by 10 operations are as shown in table 3.
The performance evaluation of 1.2 algorithms
Test above shows that PSO algorithm is easily trapped into local extremum when solving the majorized function of higher-dimension, ties up to 10
Broad sense Rastrigin function when optimizing, in 200 generations, just fell into local extremum later and can not jump out；And CDPSO can be very
Local extremum is jumped out well, this mainly passes through the effect for introducing conjugate direction method, and so that algorithm is jumped out Local Extremum in time,
Conjugate direction method is constantly used alternatingly in this way, enhances algorithm to the optimization performance of higher-dimension problem.
The PSO optimum results of table 1Rastrigin
The CDPSO optimum results of table 2Rastrigin
The optimum results of table 3Griewank
2, the application in SO2 oxidation reaction kinetics model parameter estimation
Document furthers investigate SO2 catalysis oxidation mechanism, derives its kinetic model are as follows:
In formula: r --- reaction rate；——O2, SO2, SO3Partial pressure.
k1=k01exp(-E1/RT)；k2=k02exp(-E2/RT)；k3=k03exp(-E3/RT)；
Estimation of 2.1 PSO and CDPSO to model parameter
Herein according to experimental data provided by document [6], using CDPSO to model parameter k01、k02、k03、E1、E2And E3
Estimated.To make comparisons, while parameter Estimation also is carried out using PSO.Parameter Estimation principle is to keep reaching for (6) formula minimum,
This is optimization object function.
In formula: M --- sample size,--- the experiment value and estimated value of i-th of sample.The parameter of two algorithms is set
It sets as performance test 1, due to being random algorithm, to each algorithm all independent operating 10 times, 10 obtained by 10 operations
Optimal value column are as shown in table 4.
2.2 interpretation of result
Table 4 statistics indicate that CDPSO is better than PSO, while acquired results and document [6] nonlinear optimization side Powell
Method and document [7] improved adaptive GA-IAGA (EGA) and document [8] carry out parameter with eugenic evolution differential evolution algorithm (MDE)
Resulting result is compared as shown in table 5 when estimation.
Table 5 further illustrates CDPSO for handling the validity of chemical industry high dimensional data.
If (t.systemv=t ' .systemv) so transduction pathway be reasonable unexpected state transition path otherwise
Transduction pathway is that unreasonable unexpected state transition path algorithm terminates；Otherwise return step 2；
State transduction pathway as shown in Figure 2 changes into empty set wherein gathering in the paths, and environment vector value does not change
Become, indicates that this path is a reasonable unexpected path.
Table 4PSO is compared with DPSO is to the optimum results of (17) formula
The comparison of the different optimization algorithm optimization resulting estimates of parameters of optimal models of table 5
The foregoing is merely illustrative of the preferred embodiments of the present invention, is not intended to limit the invention, all in essence of the invention
Made any modifications, equivalent replacements, and improvements etc., should all be included in the protection scope of the present invention within mind and principle.
Claims (4)
1. a kind of application for high-dimensional chemical engineering data conjugate particles group algorithm process method, which is characterized in that the application for high-dimensional chemical engineering data conjugation
Particle swarm algorithm processing method the following steps are included:
Step 1, the certain step number of particle swarm algorithm iteration and fall into local extremum and locally optimal solution x* when, be first with x*
Value, solves it with conjugate direction method；
Step 2 will obtain more preferably current optimal solution x** newly using particle swarm algorithm to the validity of low-dimensional optimization problem,
To make algorithm jump out local extremum；
Step 3, under conditions of new extreme value, and with particle swarm algorithm to former problem solving, repeatedly until terminating.
2. application for high-dimensional chemical engineering data conjugate particles group algorithm process method as described in claim 1, which is characterized in that described basic
Particle swarm algorithm and its mathematical analysis are as follows:
If optimization problem is stated are as follows:
(1) basic particle group algorithm: each bion is referred to as particle, and PSO will be searched in n-dimensional space optimal by one group of particle
Solution, the location of each particle indicate a solution vector, and as intelligent body, it can remember the optimal solution itself searched, and obtain
The optimal solution that wholegrain subgroup is lived through, thus instructs its movement, and progressive alternate seeks obtaining optimal solution；
Remember i-th of particle jth for when position be xi(j), the optimal solution that itself and wholegrain subgroup are searched is respectively
pid(j) and pgd(j), its moving velocity vector is vi(j), then at+1 generation of jth, i-th of particle be will move to:
vi(j+1)=ω φ1vi(j)+η1φ2(pid(j)-xi(j) η is counted2φ3(pgd(j)-xi(j)) (2)
xi(j+1)=xi(j)+vi(j+1) (3)
Wherein: ω, η1, η2It is control parameter of the value in [0,1], algorithm performance is had a major impact but is difficult to determine
Value appropriate, φ1, φ2, φ3It is the random number in [0,1] section；Neighbour structures different simultaneously is for efficiency of algorithm and convergence speed
The influence of degree；
(2) mathematical analysis of particle swarm algorithm
For particle swarm algorithm: if 1. only one particle of algorithm and be free of 1, (2) formula substitution (3) formula obtain:
xi(j+1)=xi(j)+(η1φ1+η2φ2)(pid(j)-xi(j))；
From this view, particle swarm algorithm is a kind of popularization of hill-climbing algorithm, is advanced every time towards optimal direction；2. from entire
Algorithm sees that it is considered as with direction pid(j)-xi(j) with direction pgd(j)-xi(j) weighting is as the direction of search；pgdIt rises and draws
Neck effect, each particle scan in respective a certain range；General primary is generally evenly distributed in entire region of search
Interior, it is generally possible to obtain the optimal solutions of problem when so being not very high to objective function；And when the dimension of objective function is higher, if
Algorithm once falls into local extremum, due to the mutual restriction between each dimension variable, and if constant in several steps, i.e. pid(1)=
pid(2), then:
xi(2)=xi(1)+(η1φ1+η2φ2)(pid(1)-·xi(1))
xi(3)=xi(2)+(η1φ1+η1φ2)(pid(1)-xi(2))=xi(1)+k(pid(1)-xi(1))；
Wherein: k=2 (η1φ1+η2φ2)-(η1φ1+η2φ2)2。
3. application for high-dimensional chemical engineering data conjugate particles group algorithm process method as described in claim 1, which is characterized in that the conjugation
Direction method are as follows:
Conjugate direction method is to be proposed early in 1964 by Powell, and the problem of to (1) formula, the basic step of this method is:
Step 201, an optional point A makees one-dimensional optimization along first reference axis, obtains B point as initial position.In this step
Need 1 one-dimensional optimizing；
Step 202, the one-dimensional optimization of a wheel is carried out one by one to a coordinate, the one-dimensional extreme point once obtained in the past every time sets out,
C point is obtained by time one-dimensional optimize in this way, the line of B and C are the conjugate directions that this wheel result obtains, willIt takes
Generation first coordinate direction andMake primary one-dimensional optimization in direction.N+1 optimizing is needed in this step；
Step 203, the one-dimensional optimization of every one wheel of progress will all obtain a conjugate direction, be substituted for the seat originally used
Mark direction；
Step 204, by the 1 one-dimensional optimization of wheel, as a result obtain D point, need to make one-dimensional optimization number in total be:
1+ (n+1) (n-1)=n2；
The property of conjugate direction method is: if the majorized function of formula (1) is quadratic function, D point is exactly the optimum point in dimension space；
If not quadratic function, then D point ratio A point continues optimizing closer to optimum point by D point.
4. application for high-dimensional chemical engineering data conjugate particles group algorithm process method as described in claim 1, which is characterized in that the conjugation
Direction particle swarm algorithm are as follows:
(1) conjugate direction particle swarm algorithm, initial point (particle), which is appointed, to be taken, and algorithm is analogous to hill-climbing algorithm, and initial point is not
Only one, cooperated between each point, thus algorithm incipient stage target function value decline quickly, to a certain extent after target
It is slower and slower to be worth decrease speed, local extremum may finally be fallen into, it is especially even more so to higher-dimension majorized function, use conjugate direction
Method improves particle swarm algorithm, when particle swarm algorithm falls into local extremum, using at this moment obtained Local Extremum as initial point,
Make once-through operation with conjugate direction method, obtained result；
(2) particle swarm algorithm falls into the determination method of local extremum
Whether particle swarm algorithm has fallen into the general determination method of local extremum in the process of running, when algorithm is in operational process
In, within certain algebra, optimal value does not have the algorithm that is considered as of any change to fall into local extremum；
(3) conjugate direction particle swarm algorithm calculates step
Step 301, the initial population that scale is is randomly generated；
Step 302, it is calculated after certain algebra or is calculated by PSO method to there is within constant generations target value without improvement
Later, if optimal solution at this moment is x*；
Step 303, using x* as initial point, (1) formula is optimized with conjugate direction method, while to produced by conjugate direction method
One Dimension Optimization Problems still solved with particle swarm algorithm, due to only one-dimensional, thus its initial point do not have to it is very much (general
50), Simultaneous Iteration algebra is without very big；If finally obtaining result is x**；
Step 304, check whether and meet termination condition, if not meeting, with x** be current all particles find it is optimal, turn
Continue iteration to step 2；Otherwise terminate algorithm operation, export optimal solution.
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