CN106228232A - A kind of dynamic multi-objective based on fuzzy reasoning Population forecast strategy teaching optimization method - Google Patents

Abstract

The invention discloses a kind of dynamic multi-objective based on fuzzy reasoning Population forecast strategy teaching optimization method, by random initializtion learner population；Use school grade based on all learners of policy update decomposed；Assess and update reference point, calculate the adaptive value of learner, the person that chooses Optimal Learning, and renewal learning person's neighborhood；Whole learner population is carried out environmental change detection；If environment changes, then the Population forecast strategy combined with one-step prediction according to fuzzy reasoning produces new learner population；Judge whether to meet stopping criterion for iteration.The present invention strengthens algorithm to the location of optimum Pareto disaggregation and tracking ability by the Population forecast strategy that fuzzy reasoning combines with one-step prediction, rapidly environmental change can be made a response, multiple target teaching optimizes Population Regeneration, solve and solve the optimum slow-footed problem of Pareto disaggregation, DMOPs has stronger adaptability and robustness.

Description

A kind of dynamic multi-objective based on fuzzy reasoning Population forecast strategy teaching optimization method

Technical field

The present invention relates to a kind of dynamic multi-objective based on fuzzy reasoning Population forecast strategy teaching optimization method, belong to dynamic State environment multiple-objection optimization technical field.

Background technology

Dynamic multi-objective optimization problem (Dynamic Multi-objective Optimization Problems, DMOPs) it is frequently problem in actual application, refers to object function, decision variable and ambient parameter, constraints etc. Change over time and the optimization problem that changes.The change of environment, causes current optimal solution to be not suitable with the environment of change, this Just require the dynamic optimization algorithm that design is relevant, the optimal solution before environmental change can not only be found, also want can be to environmental change after Disaggregation accurately follow the tracks of.In recent years, for dynamic environment optimization problem, dynamic evolution algorithm based on forecasting mechanism obtains Increasing concern.Branke etc., in dynamic duty scheduling problem, make algorithm adapt to new ring by external search neatly Border.Bosman discusses the problem of time correlation theoretically, draws and may have influence on not in the decision made sometime The conclusion of optimal value can be obtained, and give a kind of combination machine learning, statistical learning and the algorithm frame of evolutionary computation.Etc. the environment utilizing Markov Chain Forecast to be likely to occur in the future, utilize linear programming and nonlinear programming approach prediction In the moment that environment may change, in some periodically variable dynamical systems, obtain certain effect.For environmental model energy Represent with accurate mathematical model, and the Kalman filter method that noise is the system of Gaussian, Kalman filter and extension is used In the prediction to environment, nonrandom environment obtains certain effect.Zhou etc. propose a kind of based on Prediction dynamic State multi-objective Evolutionary Algorithm, uses the method being predicted colony's manifold and center, utilizes current diverse populations information Predict the colony in lower moment.Muruganantham etc. propose a kind of mixed method based on Predicting Technique, when environment is unchanged Use decomposition base (MOEA/D-DE) algorithm to carry out static optimization, when environmental change, use kalman filtering method to carry out pre- Survey.The genetic algorithms of dynamic multi-objective optimization utilizes k-means clustering algorithm, obtains series barycenter, carries out pre-to barycenter Survey, save amount of calculation.Dynamic multi-objective evolution algorithm based on the association of Pareto disaggregation with prediction utilizes gradient prediction method, When environmental change, disaggregation is predicted, utilizes super block correlating method to produce time series, utilize gradient method that disaggregation is entered Row prediction.Fuzzy technology played an important role in solving uncertain problem, as long as preferably rule base, mould can be obtained Paste technology just can play its advantage.Therefore, how to make good use of the information of history, future is inferred, to improving dynamic optimization Performance is particularly significant.

In dynamic multi-objective optimization, Optimization Algorithm is a key link in dynamic optimization, and excellent optimization is calculated Method can guarantee that dynamic optimization has higher performance.Teaching optimized algorithm, since within 2011, proposing, has set in function optimization, engineering The aspects such as meter have obtained preferable application, and it imitates the teaching process of class and designs, and shares knowledge by teacher, phase between student Study improves the average achievement of class mutually, and algorithm operating is simple, is not related to any parameter to be determined, keeps away in colony's renewal process Exempt from the dependence to parameter of some intelligent optimization methods.For optimization problems particularly dynamic multi-objective optimization problem, mesh Before there is no teaching optimized algorithm apply in this respect correlational study work report.Therefore, teaching optimized algorithm how is played Advantage, it is to avoid its inferior position, designs excellent algorithm, the performance to raising dynamic optimization method, has great importance.

Summary of the invention

In order to solve the deficiencies in the prior art, it is an object of the invention to provide a kind of based on fuzzy reasoning population The dynamic multi-objective teaching optimization method of predicting strategy.

For reaching above-mentioned purpose, the technology used in the present invention means are: a kind of based on fuzzy reasoning Population forecast strategy Dynamic multi-objective teaching optimization method, step includes:

First, learner population, then, the algorithm following iterative process of entrance: (1) random initializtion learner kind are initialized Group；(2) school grade based on all learners of policy update decomposed is used；(3) assess and update reference point, calculate study The adaptive value of person, the person that chooses Optimal Learning, and renewal learning person's neighborhood；(4) whole learner population is carried out environmental change Detection；(5) if environment changes, then the Population forecast strategy combined with one-step prediction according to fuzzy reasoning produces new Learner population.

Further, by using based on the strategy decomposed according to the religion stage with level-learning person more in described step (2) New formula updates the school grade of current learner；School grade according to the learner after updating is assessed and updates reference point, Calculate the adaptive value of learner, the size of adaptive value assess and the person that chooses Optimal Learning, and the size of foundation adaptive value is more New learner neighborhood；Whole learner population is carried out environmental change detection, and reappraise in all learner populations is best Learner, if the achievement of best learner changes, then it is assumed that environment changes, and once environment changes, then according to mould The Population forecast strategy that paste reasoning combines with one-step prediction produces new learner population, otherwise, it is determined whether meet iteration End condition；Wherein, the Population forecast strategy combined with one-step prediction according to fuzzy reasoning produces new learner population Refer to: learner population during Conservation environment change, update memory pond, and use fuzzy reasoning based on maximum entropy and one-step prediction The Population forecast strategy combined produces new learner population, returns step (3) and proceeds to calculate.

Further, described religion level-learning person more new formula, newX_i=X_i+r*(NTeacher_i-TF*NMean_i)+ r*(NTeacher_i-X_i),

Wherein, X_iAnd newX_iIt is respectively corresponding states before and after the study of i-th learner, Teacher_iIt it is i-th learner Best learner in the learner neighborhood of place, Mean_iBeing that the average in the learner neighborhood of i-th learner place is individual, r is Random vector, the element on every dimension is the random number in the range of [0,1], and TF is the religion factor, value 1 or 2；

Described level-learning person more new formula, Wherein, X_iAnd newX_iIt is respectively corresponding states before and after the study of i-th learner, X_jFor one that learner neighborhood randomly selects Learner is individual, and r is value random number on interval [0,1], f (X_i) and f (X_j) be respectively in current learner neighborhood The i-th adaptive value corresponding with jth learner.

Further, described assessment update reference point and refer to: comment according to the school grade of all learners after updating Estimate and update reference point；The formula of renewal reference point:Represent the maximum of i-th object function, z^*It is m maximal solution set, f_iX () is the i-th target function value of learner x, m is the number of object function.

Further, the formula of the adaptive value of described calculating learner is as follows:

Wherein, w=(w₁,w₂,L,w_m) it is that weights are vowed Amount.

Further, the learner population method that described generation is new is as follows:

Wherein, r is the random number of scope [0,1],

The learner population obtained is predicted for t+1 moment fuzzy reasoning based on maximum entropy,

Computing formula:

Wherein,

For time series X_iIt is under the jurisdiction ofFuzzy membership；

β value is set asK is rule number；

$d(X_i,X_k^c)=\left|\right|X_i-X_k^c|{|}^2;$

The learner population obtained for t+1 moment one-step prediction,

Wherein, C_t-1With C_tThe center of the final Pareto disaggregation searched when being respectively moment t-1 and moment t, randn For normal random number.

Further, described fuzzy membership function is asked for, and fuzzy inference rule is as follows:

$\begin{array}{cc}{C}_1:X_1^c=\[x_{t-M},L,x_{t-1},e_{t-M},L,e_{t-1}\]& Y_1^c=\[x_t,e_t\]\\ C_2:X_2^c=\[x_{t-M-1},L,x_{t-2},e_{t-M-1},L,e_{t-2}\]& Y_2^c=\[x_{t-1},e_{t-1}\]\\ \mathrm{......}& \\ C_K:X_K^c=\[x_{t-M-K+1},L,x_{t-K},e_{t-M-K+1},L,e_{t-K}\]& Y_K^c=\[x_{t-K+1},e_{t-K+1}\]\end{array}$

Wherein, x_t-iFor the learner population searched before the i & lt environmental change moment in past.

The invention has the beneficial effects as follows: the Population forecast strategy using fuzzy reasoning to combine with one-step prediction effectively solves The problem of tracking environmental change, uses the Population forecast side that fuzzy reasoning based on principle of maximum entropy combines with one-step prediction Method can be predicted with initial population during environmental change, and this Population forecast strategy can effectively solve quick tracking environmental The problem of change；The Pareto time series memory pond storage strategy of learner colony uses first in first out strategy；By decompose Multipurpose Optimal Method is incorporated in multiple target teaching Optimization Framework, provides a kind of new optimization side for solving multi-objective problem Method, the Population forecast strategy combined with one-step prediction not only by fuzzy reasoning is to strengthen algorithm to optimum Pareto disaggregation Location and the ability of tracking, it is possible to rapidly environmental change is made a response, and propose a kind of based on the multiple target decomposing base Teaching optimization method Population Regeneration, has preferable convergence and adaptability, solves that to solve optimum Pareto disaggregation speed slow Problem, DMOPs has stronger adaptability and robustness.

Accompanying drawing explanation

The invention will be further elaborated with embodiment below in conjunction with the accompanying drawings.

Fig. 1 is that the present invention solves the flow process of dynamic environment multi-objective optimization question based on the MOTLBO/D that FIOPPS predicts Figure；

Fig. 2 is the present invention in 20 tests of 3 test problems, and different Forecasting Methodologies based on MOTLBO/D obtain The average IGD performance chart obtained；

Fig. 3 is the present invention in 20 tests of 3 test problems, and different Forecasting Methodologies based on MOTLBO/D obtain The average IGD performance chart obtained；

Fig. 4 is the present invention in 20 tests of 3 test problems, and different Forecasting Methodologies based on MOTLBO/D obtain The average IGD performance chart obtained；

Fig. 5 is the present invention when obtaining minimum DIGD performance in for 20 tests of F1 test problem, based on The initial disaggregation distribution schematic diagram that the different Forecasting Methodologies of MOTLBO/D obtain at RIS；

Fig. 6 is the present invention when obtaining minimum DIGD performance in for 20 tests of F1 test problem, based on The final disaggregation distribution schematic diagram that the different Forecasting Methodologies of MOTLBO/D obtain at RIS；

Fig. 7 is the present invention when obtaining minimum DIGD performance in for 20 tests of F1 test problem, based on The initial disaggregation distribution schematic diagram that the different Forecasting Methodologies of MOTLBO/D obtain at FPS；

Fig. 8 is the present invention when obtaining minimum DIGD performance in for 20 tests of F1 test problem, based on The final disaggregation distribution schematic diagram that the different Forecasting Methodologies of MOTLBO/D obtain at FPS；

Fig. 9 is the present invention when obtaining minimum DIGD performance in for 20 tests of F1 test problem, based on The initial disaggregation distribution schematic diagram that the different Forecasting Methodologies of MOTLBO/D obtain at PPS；

Figure 10 is the present invention when obtaining minimum DIGD performance in for 20 tests of F1 test problem, based on The final disaggregation distribution schematic diagram that the different Forecasting Methodologies of MOTLBO/D obtain at PPS；

Figure 11 is the present invention when obtaining minimum DIGD performance in for 20 tests of F1 test problem, based on The initial disaggregation distribution schematic diagram that the different Forecasting Methodologies of MOTLBO/D obtain at FIOPPS；

Figure 12 is the present invention when obtaining minimum DIGD performance in for 20 tests of F1 test problem, based on The final disaggregation distribution schematic diagram that the different Forecasting Methodologies of MOTLBO/D obtain at FIOPPS；

Figure 13 is the present invention in 20 tests of F3 test problem, difference based on RE-MEDA and MOTLBO/D The average IGD performance chart that Forecasting Methodology obtains；

Figure 14 is the present invention in 20 tests of F3 test problem, difference based on RE-MEDA and MOTLBO/D The average IGD performance chart that Forecasting Methodology obtains；

Figure 15 is the present invention in 20 tests of F3 test problem, difference based on RE-MEDA and MOTLBO/D The average IGD performance chart that Forecasting Methodology obtains.

Detailed description of the invention

Embodiment 1

With reference to Fig. 1, a kind of dynamic multi-objective based on fuzzy reasoning Population forecast strategy teaching optimization method, concrete steps As follows: step 1, use random initializtion method to initialize learner population；

Step 2, updates the achievement of all learners according to religion level-learning person more new formula,

More new formula:

newX_i=X_i+r*(NTeacher_i-TF*NMean_i)+r*(NTeacher_i-X_i),

Wherein, X_iAnd newX_iIt is respectively corresponding states before and after the study of i-th learner, Teacher_iIt it is i-th learner Best learner (teacher) in the learner neighborhood of place, Mean_iIt it is the average in the learner neighborhood of i-th learner place Body, r is random vector, and the element on every dimension is the random number in the range of [0,1], and TF is the religion factor, value 1 or 2；

Step 3, assesses and updates reference point, calculates the adaptive value of learner, the person that chooses Optimal Learning, and according to adapting to Size renewal learning person's neighborhood of value；

Reference point more new formula:It is the maximum of i-th object function, z^*It is m maximum Solve set, wherein, f_iX () is the i-th target function value of learner x, m is the number of object function；The adaptive value of learner Formula:

$F\left(x\right)=\min g\left(x\right|w,z*)=\underset{i=\{1,2,Lm\}}{max}\left\{w_i\right|f_i\left(x\right)-z_i^{*}\},$

Wherein, w=(w₁,w₂,L,w_m) it is a weighted vector；

Step 4, updates the achievement of all learners, more new formula according to level-learning person more new formula:

$new{X}_i=\left\{\begin{array}{ccc}{X}_i+r\&times;(X_i-X_k)+r*({\mathrm{NTeacher}}_i-X_i)& if& f\left(X_i\right)<f\left(X_k\right)\\ X_i+r\&times;(X_k-X_i)+r*({\mathrm{NTeacher}}_i-X_i)& if& f\left(X_i\right)\&GreaterEqual;f\left(X_k\right)\end{array}\right.,$

Wherein, X_iAnd newX_iIt is respectively corresponding states before and after the study of i-th learner, X_jFor learner neighborhood selects at random The learner individuality taken, r is value random number on interval [0,1], f (X_i) and f (X_j) it is respectively current study The adaptive value that i-th in person's neighborhood is corresponding with jth learner；

Step 5, assesses and updates reference point, calculates the adaptive value of learner, the person that chooses Optimal Learning, and according to adapting to Size renewal learning person's neighborhood of value；

Reference point more new formula is as follows:It is the maximum of i-th object function, z^*It it is m Maximal solution set, wherein, f_iX () is the i-th target function value of learner x, m is the number of object function；

The formula of the adaptive value of learner:

$F\left(x\right)=\min g\left(x\right|w,z*)=\underset{i=\{1,2,Lm\}}{max}\left\{w_i\right|f_i\left(x\right)-z_i^{*}\},$

Wherein, w=(w₁,w₂,L,w_m) it is a weighted vector；

Step 6, carries out environmental change detection to whole learner population；Reappraise in all learner populations is best Learner, if the achievement of best learner changes, then it is assumed that environment changes, and once environment changes, then according to step Rapid 7 produce new initial learn person population；Otherwise, step 8 is performed；

Step 7, if environment changes, then the Population forecast strategy combined with one-step prediction according to fuzzy reasoning produces The learner population of tissue regeneration promoting, produces new learner population method as follows:

${\hat{x}}_{t+1}=r\&CenterDot;{\hat{V}}_{t+1}+(1-r)\&CenterDot;{\hat{U}}_{t+1},$

Wherein,

Build fuzzy rule,

For time series X_iIt is under the jurisdiction ofFuzzy membership,

$\&lsqb;{\hat{x}}_{t+1},{\hat{e}}_{t+1}\&rsqb;=\underset{k=1}{\overset{K}{\&Sigma;}}{\mathrm{\&mu;}}_k{Y}_k^c+\frac{1}{M-1}\underset{k=1}{\overset{K-1}{\&Sigma;}}(Y_{k+1}^c-Y_k^c),$

β value is set as

C_t-1,C_tThe center of the final Pareto disaggregation searched when being respectively moment t-1 and moment t, randn is normal state Random number；Step 8, it may be judged whether meet stopping criterion for iteration.

Described fuzzy membership function is asked for, and fuzzy inference rule is as follows:

$\begin{array}{cc}{C}_1:X_1^c=\&lsqb;x_{t-M},L,x_{t-1},e_{t-M},L,e_{t-1}\&rsqb;& Y_1^c=\&lsqb;x_t,e_t\&rsqb;\\ C_2:X_2^c=\&lsqb;x_{t-M-1},L,x_{t-2},e_{t-M-1},L,e_{t-2}\&rsqb;& Y_2^c=\&lsqb;x_{t-1},e_{t-1}\&rsqb;\\ \mathrm{......}& \\ C_K:X_K^c=\&lsqb;x_{t-M-K+1},L,x_{t-K},e_{t-M-K+1},L,e_{t-K}\&rsqb;& Y_K^c=\&lsqb;x_{t-K+1},e_{t-K+1}\&rsqb;\end{array}$

Wherein, x_t-iFor the learner population searched before the i & lt environmental change moment in past.

Embodiment 2

The emulation experiment of effect of the present invention.

1. simulated conditions: this example is at AMD A6-3620APU with Radeon HD Graphics 2.20GHz Under Windows 7 system, on Matlab2009a operation platform, completing the present invention and existing RIS, the emulation of FPS, PPS method is real Test.

2. emulation experiment content:

1, for comparing performance during FIOPPS Yu RIS, FPS and PPS solution DMOPs, we select in the present invention MOTLBO/D is as multi-objective optimization algorithm.In this experiment, for MOTLBO/D algorithm, group size is set to 50.In order to Reducing statistical error, each Forecasting Methodology operates independently from 20 times, and every 50 iteration environmental changes once, test 121 altogether Secondary change.For corresponding each individuality, Fuzzy Inference Model uses 5 cluster centres, and each cluster centre comprises 5 environment and becomes Position before change.

2, in this experiment, test problem F1 is the FDA1 coming from FDA test set, for this benchmark test problem, Decision variable and the quantity of target, and the border of search volume keeps constant in whole service, but PS and/or PF is in time Change.It addition, present linear relationship between decision variable.Test problem F2, for coming from DMOP test set DMOP1, is The expansion of FDA1.Test problem F3 takes from the UDF5 of UDF test set, presents non-between the decision variable of this benchmark test problem Linear relationship.

3, DIGD statistical result is compared: in this experiment, for assessing test performance the most in the same time, by the survey of each run Test result be divided into three phases (0 ＜ T≤40,40 ＜ T≤80,80 ＜ T≤120, each stage follow the tracks of respectively 40 secondary environments become Change.For in 20 times of 3 test problems tests, table 1 average (Mean) giving DIGD statistically, intermediate value (Median), first stage average (First Phase), second stage average (Second Phase) and phase III average (Third Phase).Result best in all properties index is to show with runic.

The 1 four kinds of Forecasting Methodologies of the table comparative result to 3 test problems

Table 1DIGD statistical result is compared

The result of table 1 shows: to F1, FIOPPS obtain the average (Mean) of DIGD, intermediate value (Median), the first stage Average (First Phase) is better than other three kinds of Forecasting Methodologies.In second and third stage, although the result of FIOPPS Yu PPS is very Close, but PPS obtains the average (Third Phase) of minimum DIGD.To F2 and F3, in all of 5 performance indications In, FIOPPS obtains best test performance.Statistical result shows, solves when changing for dynamic multi-objective optimization problem context The prediction of collection, FIOPPS method is a kind of new up-and-coming Forecasting Methodology.

4, average IGD performance curve compares: IGD performance when running for every kind of Forecasting Methodology of display, Fig. 2,3,4 give For in 20 times of 3 test problems tests, the average IGD performance curve that different Forecasting Methodologies based on MOTLBO/D obtain Figure.

From Fig. 2,3,4 it can be seen that in early days stage FIOPPS can ensure that the algorithm quick response to environmental change. Especially, between Optimal Decision-making variable during F3 in non-linear relation, the performance curve that FIOPPS obtains is best, and this also demonstrates The result obtained from table 1.

5, disaggregation distributivity compares: Fig. 5,6,7,8,9,10,11,12 are to give 20 surveys for 3 test problems When obtaining minimum DIGD performance in examination, different Forecasting Methodologies based on MOTLBO/D inscribe initial solution collection when varying environment changes With final disaggregation distribution schematic diagram.

From Fig. 5,6,7,8,9,10,11,12 it can be seen that the initial population that all Forecasting Methodologies obtain can find one The best initial solution so that initial population is comparatively close to real Pareto forward position, and in all of method, FIOPPS The initial population obtained has best disaggregation distributivity.From Fig. 3 it is also seen that, although all of Forecasting Methodology can be Obtain the most final disaggregation during t=105 and 110, but the final disaggregation obtained when t=100 is not fine.It addition, The final disaggregation that FIOPPS obtains advantage in convergence and distribution becomes apparent from.

6, the impact of MOEA optimized algorithm is compared: when solving dynamic multi-objective optimization problem, multi-objective optimization algorithm exists The most rapidly and efficiently follow the tracks of in Pareto optimal solution set and also played an important role.For the different multi-objective Algorithm pair of assessment The impact of Forecasting Methodology performance, we test RE-MEDA and MOTLBO/D algorithm pair based on PPS and FIOPPS Forecasting Methodology The optimization performance of 3 test functions.

Table 2 gives DIGD result and statistically compares.

Table 2MOTLBO/D and RM-MEDA algorithm DIGD statistical result is compared

The result of table 2 shows: for prediction algorithm RIS, be better than the performance of test function F1 and F3, RM-MEDA MOTLBO/D；To test function F2, in latter two stage, the performance of MOTLBO/D is better than RM-MEDA.For prediction algorithm FPS, to test function F1 and F3, in addition to the first stage, the performance of MOTLBO/D will be better than RM-MEDA；To test function The performance of F2, MOTLBO/D will be better than RM-MEDA.For prediction algorithm PPS and FIOPPS, to test function F1 and F2, The performance of MOTLBO/D will be better than RM-MEDA, and the performance of test function F3, RM-MEDA is better than MOTLBO/D.Statistics Result shows, for dynamic multi-objective optimization problem, MOTLBO/D algorithm is a challenging new optimization method.

Figure 13,14,15 give in 20 times of test problem tests, based on RE-MEDA and MOTLBO/D not The average IGD performance chart obtained with Forecasting Methodology.

The variation tendency of the performance curve from Figure 13,14,15 can be seen that RE-MEDA+FIOPPS obtains statistically Can preferably, this also demonstrates the conclusion of table 2.

The Population forecast strategy that the present invention uses fuzzy reasoning to combine with one-step prediction efficiently solves tracking environmental and becomes The problem changed, the change of environment, cause current optimal solution to be not suitable with the environment of change, it is the most excellent that this just requires that design is correlated with Change algorithm, the optimal solution before environmental change can not only be found, also want the disaggregation after environmental change accurately be followed the tracks of.So-called Follow the tracks of, it is simply that along with its change, learner colony changes the most therewith, when this just defines the Pareto of a kind of learner colony Between sequence.Time initial, learner colony randomly generates, along with the search one by one of learner colony is evolved, and these learners Colony can slowly draw close to preferable Pareto forward position.Along with the propelling of algorithm, the increase of environmental change number of times, learner group The Pareto disaggregation that body is corresponding constitutes a time series.Therefore, use fuzzy reasoning based on principle of maximum entropy and a step pre- Surveying the Population forecast method combined to be predicted with initial population during environmental change, this Population forecast strategy can have The problem solving the change of quick tracking environmental of effect.The Pareto time series memory pond storage strategy of learner colony: advanced First go out strategy；Propose a kind of side solving dynamic environment multi-objective optimization question based on the multiple target teaching optimized algorithm decomposed Method.The Multipurpose Optimal Method of decomposition is incorporated in multiple target teaching Optimization Framework, provides one for solving multi-objective problem Plant new optimization method.The method of the solution dynamic environment multi-objective optimization question of the present invention, not only by fuzzy reasoning and The step Population forecast strategy that combines of prediction is to strengthen algorithm to the location of optimum Pareto disaggregation and tracking ability, it is possible to rapidly Environmental change is made a response, and propose a kind of based on decompose base multiple target teaching optimization method Population Regeneration, tool There are preferable convergence and adaptability, solve and solve the optimum slow-footed problem of Pareto disaggregation, have stronger in DMOPs Adaptability and robustness.

Disclosed embodiment of this invention is the explanation to technical scheme, it is impossible to as to present invention Restriction, those skilled in the art's simple change on the basis of the present invention, the most within the scope of the present invention.

Claims (7)

1. dynamic multi-objective based on a fuzzy reasoning Population forecast strategy teaching optimization method, it is characterised in that step bag Include: first, initialization learner population, then, the algorithm following iterative process of entrance:

(1) random initializtion learner population；(2) school grade based on all learners of policy update decomposed is used；(3) Assess and update reference point, calculate the adaptive value of learner, the person that chooses Optimal Learning, and renewal learning person's neighborhood；(4) to whole Individual learner population carries out environmental change detection；(5) if environment changes, then tie mutually with one-step prediction according to fuzzy reasoning The Population forecast strategy closed produces new learner population.

Dynamic multi-objective based on fuzzy reasoning Population forecast strategy the most according to claim 1 teaching optimization method, its It is characterised by: by using based on the strategy decomposed according to the religion stage with level-learning person more new formula more in described step (2) The school grade of new current learner；Reference point is assessed and updated to school grade according to the learner after updating, calculates study The adaptive value of person, is assessed by the size of adaptive value and the person that chooses Optimal Learning, and according to the size renewal learning person of adaptive value Neighborhood；Whole learner population is carried out environmental change detection, reappraises the best learner in all learner populations, if The preferably achievement of learner changes, then it is assumed that environment changes, and once environment changes, then according to fuzzy reasoning and The Population forecast strategy that step prediction combines produces new learner population, otherwise, it is determined whether meet stopping criterion for iteration；Its In, the Population forecast strategy combined with one-step prediction according to fuzzy reasoning produces new learner population and refers to: Conservation environment Learner population during change, updates memory pond, and uses the kind that fuzzy reasoning based on maximum entropy combines with one-step prediction Group's predicting strategy produces new learner population, returns step (3) and proceeds to calculate.

Dynamic multi-objective based on fuzzy reasoning Population forecast strategy the most according to claim 2 teaching optimization method, its It is characterised by: described religion level-learning person more new formula,

newX_i=X_i+r*(NTeacher_i-TF*NMean_i)+r*(NTeacher_i-X_i),

Wherein, X_iAnd newX_iIt is respectively corresponding states before and after the study of i-th learner, Teacher_iIt it is i-th learner place Best learner in learner neighborhood, Mean_iBeing that the average in the learner neighborhood of i-th learner place is individual, r is random Vector, the element on every dimension is the random number in the range of [0,1], and TF is the religion factor, value 1 or 2；

Described level-learning person more new formula,

$new{X}_i=\left\{\begin{array}{ccc}{X}_i+r\&times;(X_i-X_k)+r*({\mathrm{NTeacher}}_i-X_i)& if& f\left(X_i\right)<f\left(X_k\right)\\ X_i+r\&times;(X_k-X_i)+r*({\mathrm{NTeacher}}_i-X_i)& if& f\left(X_i\right)\&GreaterEqual;f\left(X_k\right)\end{array}\right.,$

Wherein, X_iAnd newX_iIt is respectively corresponding states before and after the study of i-th learner, X_jFor what learner neighborhood randomly selected One learner individuality, r is value random number on interval [0,1], f (X_i) and f (X_j) it is respectively current learner neighbour The adaptive value that i-th in territory is corresponding with jth learner.

Dynamic multi-objective based on fuzzy reasoning Population forecast strategy the most according to claim 1 teaching optimization method, its Being characterised by, described assessment also updates reference point and refers to: assesses according to the school grade of all learners after updating and updates Reference point；The formula of renewal reference point:Represent the maximum of i-th object function, z^*It it is m Maximal solution set, f_iX () is the i-th target function value of learner x, m is the number of object function.

Dynamic multi-objective based on fuzzy reasoning Population forecast strategy the most according to claim 4 teaching optimization method, its Being characterised by, the formula of the adaptive value of described calculating learner is as follows:

$F\left(x\right)=\min g\left(x\right|w,z*)=\underset{i=\{1,2,Lm\}}{max}\left\{w_i\right|f_i\left(x\right)-z_i^{*}\},$

Wherein, w=(w₁,w₂,L,w_m) it is a weighted vector.

Dynamic multi-objective based on fuzzy reasoning Population forecast strategy the most according to claim 2 teaching optimization method, its It is characterised by: the new learner population of described generation utilizes below equation to calculate:

${\hat{x}}_{t+1}=r\&CenterDot;{\hat{V}}_{t+1}+(1-r)\&CenterDot;{\hat{U}}_{t+1},$

${\hat{V}}_{t+1}={\hat{z}}_{t+1}-{\hat{e}}_{t+1},$

Wherein, r is the random number of scope [0,1],

Predict the learner population obtained based on maximum entropy fuzzy reasoning for the t+1 moment,

$\&lsqb;{\hat{z}}_{t+1},{\hat{e}}_{t+1}\&rsqb;=\underset{k=1}{\overset{K}{\&Sigma;}}{\mathrm{\&mu;}}_k{Y}_k^c+\frac{1}{M-1}\underset{k=1}{\overset{K-1}{\&Sigma;}}(Y_{k+1}^c-Y_k^c),$

Wherein,For time series X_iIt is under the jurisdiction ofFuzzy membership,

β value is set asK is rule number；

$d(X_i,X_k^c)=\left|\right|X_i-X_k^c|{|}^2$

The learner population obtained for t+1 moment one-step prediction,

${\hat{U}}_{t+1}=x_t+(1+randn)*(C_{t-1}-C_t),$

Wherein, x_t-iFor the learner population C searched before the i & lt environmental change moment in past_t-1With C_tBe respectively moment t-1 with The center of the final Pareto disaggregation searched during moment t, randn is normal random number.

Dynamic multi-objective based on fuzzy reasoning Population forecast strategy the most according to claim 6 teaching optimization method, its Being characterised by, described fuzzy membership, it is as follows that function asks for fuzzy inference rule:

$\begin{array}{cc}{C}_1:X_1^c=\&lsqb;x_{t-M},L,x_{t-1},e_{t-M},L,e_{t-1}\&rsqb;& Y_1^c=\&lsqb;x_t,e_t\&rsqb;\end{array}$

$\begin{array}{cc}{C}_2:X_2^c=\&lsqb;x_{t-M-1},L,x_{t-2},e_{t-M-1},L,e_{t-2}\&rsqb;& Y_2^c=\&lsqb;x_{t-1},e_{t-1}\&rsqb;\end{array}$

……

$\begin{array}{cc}{C}_K:X_K^c=\&lsqb;x_{t-M-K+1},L,x_{t-K},e_{t-M-K+1},L,e_{t-K}\&rsqb;& Y_K^c=\&lsqb;x_{t-K+1},e_{t-K+1}\&rsqb;\end{array}$

Wherein, C_k(k=1,2 ..., K) represent kth rule, x_t-iFor the study searched before the i & lt environmental change moment in past Person population, e_t-iTime in the past i & lt environmental change time learner population forecast error.