CN111311638A - Dynamic multi-objective optimization method based on segmentation multi-directional prediction strategy - Google Patents
Dynamic multi-objective optimization method based on segmentation multi-directional prediction strategy Download PDFInfo
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Abstract
The invention discloses a dynamic multi-target optimization method based on a segmentation multi-directional prediction strategy, which can better predict the change of an optimal front edge aiming at the problem that the prediction error of a linear model is insufficient, ensure the prediction of the distribution change of the concavity and convexity of the optimal front edge and effectively compensate the distance error of direction prediction. It comprises the following steps: (1) describing the dynamic multi-target problem; (2) and (4) dividing the multi-directional prediction. The invention has the beneficial effects that: firstly, the searched optimal leading edge is segmented, the population is divided according to the segmentation result of the optimal leading edge, each part of the population is subjected to linear prediction, the description of the cloud model on uncertain time is used for reference, the prediction error is made up by entropy and super entropy, and the diversity of the population in the prediction process is ensured by adopting a deflection angle enhanced search strategy aiming at sudden nonlinear change possibly occurring in the dynamic problem.
Description
Technical Field
The invention belongs to the technical field of intelligent calculation and multi-objective optimization, and particularly relates to a dynamic multi-objective optimization method based on a segmentation multi-directional prediction strategy.
Background
In the process of detecting and tracking a high-speed target in the air, because the target has high speed, strong maneuvering capability and large flying area span, a single sensor is difficult to effectively and continuously detect and track, and the reasonable arrangement of a detection and tracking task and a time sequence by applying a multi-source heterogeneous sensor scheduling technology is very important. The scheduled resources mainly comprise space-based infrared sensors and foundation radar sensors, and the related sensor types comprise high-orbit infrared detection satellites, low-orbit infrared satellites, foundation P-band radars, foundation X-band radars and the like.
Since the aerospace high-speed target is a novel target, the problem of sensor resource scheduling for detecting and tracking the target is less researched at present. Satellite resource scheduling is similar to this problem, and both solution scheduling schemes are time-based resource allocation problems. However, the sensor resource has strict time constraint on the detection and tracking of the target, and if the sensor can only realize partial monitoring or no monitoring within a limited time, the task fails and there is no chance of secondary observation, which is a main difference from the general remote sensing or navigation satellite scheduling problem.
Due to different problem characteristics, the sensor resource scheduling problem is different from the traditional scheduling problem in the following 3 points:
(1) the task has no waiting time, and the target is not observed in a limited time, so that the target has no observation opportunity.
(2) The resource matching exists simultaneously in a one-to-many mode and a many-to-one mode, and the difficulty of coding and searching is increased due to inconsistent matching rules.
(3) The sensor observes time fragmentation, fragmentation time which does not accord with constraint conditions is easily generated in the searching process, and the searching difficulty is increased.
In view of the above problems, factors for constructing a resource scheduling model for detecting and tracking a Multi-source heterogeneous sensor for an aerospace high-speed target are considered, a Dynamic Multi-object Optimization (DMO) model can be used to realize real-time scheduling of Multi-source heterogeneous sensor resources, and a reliable sensor network is constructed for cooperative tracking of the aerospace high-speed target.
The Dynamic Multi-objective Optimization Problem (DMOP) not only shows the characteristics of the Multi-objective Optimization Problem such as Optimization objective conflict, high solution space dimensionality, etc., but also has the characteristics of Optimization objectives, conditional constraints, and time-varying decision space. The traditional optimization method is more limited and is difficult to meet the requirements of large-scale, high timeliness and complex NP problems of modern engineering and scientific research. Compared with the traditional method, the evolutionary method has low requirement on a problem model, high solving efficiency, high parallelism, self-organization, self-adaptation and other advantages, and is applied to a plurality of industrial application and research fields.
In an evolutionary algorithm for solving a dynamic multi-objective optimization problem, the simplest method is to maintain population diversity. DNSGA-II (Dynamic multi-objective optimization and decision-making used modified NSGA-II) proposed by Deb increases the adaptability of a population in a changing environment by using partial random initialization or random variation (K.Deb, U.B.Rao N, S.Karthik. Dynamic multi-objective optimization and decision-making used modified NSGA-II: a case determination on hydro-thermal power allocation. in: Proceedings of the 4th International Conference on evaluation Multi-Criterion optimization, Matsuma, Japan: spring policy 2007.803-817.) A zedo initialize a population changed in an environment by using three kinds of transfer initialization environments (IEEE.C.2011. evaluation. F.2011. evaluation. III. in. more. IEEE.3. evaluation of collection of samples, IEEE.3. evaluation of collection of environment; shang, L.C.Jiano, M.G.Gong, W.P.Ma.an animal clone for dynamic multi-objective optimization, journal of Software,2007,18(11):2700-2711.) is well established by using a method combining various immunization strategies to initialize population after environmental change. Since the change trend of the dynamic environment is unknown, the method tries to explore the unknown area to ensure that the dominant individual is present after the change. The method has the advantages of being capable of coping with various environment changes and has the defect that the searching advantage before the environment changes is difficult to continue after the environment changes, so that the method has strong environment adaptability and poor searching advantage maintaining capability.
Compared with the method for dealing with the environmental change by keeping the population diversity in the early stage, researchers begin to predict the population position of the environmental change at the next moment by statistically analyzing the non-dominated solution set before the environmental change for many times by using the historical information after the environmental change for many times. And predicting the population position of the environmental change at the next moment by statistically analyzing the non-dominated solution set before the environmental change for a plurality of times.
The idea mainly comprises two solving ideas: a memory strategy and a prediction strategy. The memory strategy stores a large amount of non-dominated solution set information, and the population position at the next moment is predicted by a rule, so that the method has a good effect on solving the dynamic problem of short periodicity, because the periodicity can be described by historical information, and the short represents that the storage space is small.
However, when the strategy is used for processing the problem of high environment change frequency or non-linear time variation, the strategy shows that the storage space consumption is large and the prediction is inaccurate. Compared with the memory strategy, the prediction strategy predicts the possible migration direction of the population by using a prediction theory (such as a linear regression model, an autoregressive model and the like) through statistical analysis of historical information. Hatzakis proposed a forward Prediction method (FPS) (I.Hatzakis, D.Wallace. dynamic Multi-objective optimization with evaluation algorithms: a forward-looking assessment. in: Proceedings of the 8th Annual Conference on Genetic and evaluation calculation. Washington, USA: ACM,2006.1201-1208.) using an autoregressive model to predict non-dominated solution migration locations, which is not well predicted due to incomplete statistical analysis of FPS historical information. Zhou proposes a Population Prediction Strategy (PPS) (a.m.zhou, y.c.jin, q.f.zhang. a Population Prediction Strategy for evaluation dynamic optimization. ieee Transactions on Cybernetics,2014,44(1):40-53), predicts the location of Population center migration using an autoregressive model, and then translates the entire Population using shape estimation. Compared with the FPS, the PPS has two advantages, one is that the historical information is further processed, namely the center position of the population is adopted for prediction; secondly, the shape estimation method has better effect than the individual population one by one prediction migration. However, the strategy of the autoregressive model has a fundamental disadvantage that a large amount of statistical information is needed to construct the model. If the prediction deviation increases for a plurality of times, the prediction error is amplified, and when the environment change rule changes, the fast adaptation is difficult.
The autoregressive model is a very common model for predicting the problem of regular change, but has the defects of slow response, large statistical data amount and the like, and although the linear model is simple, the defects of the autoregressive model can be effectively compensated through a simple diversity retention strategy. Wu proposes a Directed Search Strategy (DSS) (Y.Wu, Y.jin, X.Liu.associated Search Strategy for evaluation dynamic multijoint optimization. Soft Computing,2015,19(11):3221-3235.), and processes dynamic problems by using two strategies of population center prediction and horizontal Search, wherein the population center prediction adopts a linear prediction method, and the method has the advantages of less historical information and is faster than the adaptability of a multiple linear regression environment. The rows segment the optimal leading edge and predict the changes one by one using linear models (Miao Rong, Dunwei Gong, Yong Zhang, Yaochu Jin, Witold Pedrecz. multidirectional prediction approach for dynamic multi-objective prediction schemes. in: Intelligent Computing methods. ICIC2016. characteristics in Computer Science, vol 9773, spring, Chamber.). Li employs an autoregressive model to predict critical point predictions such as boundary points, inflection points, etc. of the optimal frontier, and then uses a linear model to predict non-dominant solution locations (Qingya Li, Juan Zou, Shengxiang Yang, Jinhua Zheng, Gan Ruan. A predictive basis on specific points for evaluation dynamic multi-objective optimization, Soft Computing,2018, (1):1-17.https:// doi. org/10.1007/s 00500-018-. Ruan adopts a linear model to predict the optimal leading edge position (Gan Ruan, Guo Yu, Jinhua Zheng, Juan Zou, Shengxiang Yang. the effect of diversity mail on prediction index multi-objective optimization. applied Soft Computing,2017(58):631 and 647), and in the aspect of diversity preservation, the extreme point of the previous generation is combined with the linear model to predict the population change. It should be noted that although the linear model is simple, there is always a prediction error in solving the dynamic problem of increasing or decreasing or more complicated changes, so the disclosure in the above prior art all adopts a diversity-preserving method to compensate the prediction error.
Disclosure of Invention
The invention aims to provide a dynamic multi-target optimization method based on a segmentation multi-directional prediction strategy, which can better predict the change of the optimal leading edge aiming at the problem that the prediction error of a linear model is insufficient, ensure the prediction of the distribution change of the concavity and convexity of the optimal leading edge and effectively compensate the distance error of direction prediction.
The technical scheme of the invention is as follows: the dynamic multi-objective optimization method based on the segmentation multi-directional prediction strategy comprises the following steps:
(1) describing the dynamic multi-target problem;
(2) and (4) dividing the multi-directional prediction.
The dynamic multi-target problem in the step (1) is described as follows:
wherein x is (x)1,...,xn)TIs a decision variable in an n-dimensional decision space, t is a time variable, g (x, t) and h (x, t) are an inequality constraint and an equality constraint, respectively, (f)1(x,t),f2(x,t),L,fm(x,t))TThe method is an objective function vector of a dynamic multi-objective optimization problem, an evaluation function F (x, t) is mapping from a decision space to a target space, and s.t. represents a constraint condition.
In the step (2), the optimal leading edge is firstly divided into a plurality of segments by the multi-directional partition prediction, the population of the decision space is divided according to the partition result, then, part of individuals are selected from each population, the optimal leading edge change direction is searched by adopting a deflection angle enhancement search strategy, and finally, the deflection angle enhancement search is adopted to perform supplementary search on the position of the optimal leading edge which is possibly deflected.
The step (2) specifically comprises the following steps:
(a) carrying out population segmentation;
(b) directional cloud prediction;
(c) performing deflection angle enhancement search;
(d) detecting the environment;
(e) and carrying out segmentation multi-directional cloud prediction strategy calculation.
The step (a) of carrying out population segmentation comprises the steps of selecting a boundary point as a first key point in the PF, then calculating the distance from each point to the boundary point, and selecting the point with the maximum distance as a second key point; calculating the distance between other individuals and the second key point, selecting a point with the maximum distance between one point and the two key points as a third key point, selecting m +1 key points by analogy in sequence, wherein m is the number of targets, selecting the key point with the closest distance from each individual to form m +1 fragments, and dividing a plurality of populations according to the division result of the PF.
Said step (b) of directed cloud prediction comprises,
the population size is N, the ith population PopiContaining KiIndividual, for a sub-population at time t, PopiThe center is described as follows:
wherein the content of the first and second substances,
represents all individuals of the population, the k-th individual is
n is the decision space dimension, Ci(t) represents the center position of the population at the moment t, |, represents the potential of the set;
predicting population migration vector d at t +1 moment by using positions of population center points at t moment and t-1 momenti(t) and the double migration error Δ (t) are as follows
di(t)＝Ci(t)-Ci(t-1) (3)
Δ(t)＝di(t)-di(t-1) (4)
Predicting the migration position of the population by using a normal cloud model, wherein the population moving direction is expected, and the Euclidean distance d of a moving vectori(t) is entropy, deviation delta (t) of two times of population moving directions is used as super-entropy, expectation, entropy and super-entropy are used for constructing a normal cloud generator, firstly, delta (t) is used as expectation, and | delta (t) |/N is used as standard deviation to generate normal random vectors En' -N (delta (t) |, | | delta (t) | Y)2/n2) Wherein En' ═ e (En)1',...,Enn') to a host; then by di(t) as expected, En' as standard deviation to generate a normal random vector v1～N(di(t),En'2) The predicted position y of the individual after the environmental change is expressed as follows:
y＝p+v1(5)
wherein p is the individual position before environmental change, v1Is the prediction direction.
Said step (c) of the declination-enhanced search comprises,
construct a perpendicular to di(t) generating a random vector of [ -1,1 []Random vector r ═ in the range (r)1,...,rn) The value of j dimension of r is arbitrarily selected as formula (6),
declination enhancement search direction vector e (t) ═ e1,...,en) Is calculated as follows
In the formula, θ is the size of the deflection angle, and represents the possible search range, and is calculated as follows:
enhancing search in determining declinationCord direction vector e (t) ═ (e)1,...,en) Then, using a normal cloud model to perform deviation angle search on the individuals, and using ei(t) is expected, and Δ (t) is the standard deviation difference to generate normal random vectors En x N (d)i(t),Δ(t)2) Wherein En ═ is (En)1*,...,EnnX); then with ei(t) generating a normal random vector v for standard deviation, En2～N(ei(t),En*2) The predicted position y of the deviation angle search to the individual is as follows:
y*＝y+v2(9)
wherein v is2Is the predicted direction after the offset angle search.
The environmental sensitivity factor ε (t) in step (d) is calculated as follows:
wherein H is the number of individuals randomly drawn from the population, F (x)jAnd t) represents an individual xjAnd in the target function vector at the time t, the proportion of the environment monitoring extraction population is 5%.
The step (e) of calculating the partition multi-directional cloud prediction strategy comprises the following steps:
step 1: randomly initializing a population;
step 2: utilization type (10)
Detecting whether the environment changes, and if so, turning to the step 3; otherwise, turning to the step 8;
and step 3: judging whether d (t-1) is 0 or not, and if d (t-1) ≠ 0, jumping to the step 5; otherwise, turning to the step 4;
and 4, step 4: randomly selecting Zeta × N individuals to evolve, and making d (t-1) ═ d (t);
and 5: dividing the population into m +1 parts, calculating the population center for each sub-population Popi by using the formula (2),
according to formula (3)
di(t)＝Ci(t)-Ci(t-1) (3)
Calculating the population moving direction d (t) of time t, selecting L1 multiplied by N individuals by using a 2-system tournament method, and predicting the predicted position by using a normal cloud model;
step 6: selecting N x (1-L1) individuals according to formulas (6) - (8) using a 2-ary tournament method
Declination enhancement search direction vector e (t) ═ e1,...,en) Is calculated as follows
In the formula, θ is the size of the deflection angle, and represents the possible search range, and is calculated as follows:
calculating deviation angle search vectors of the individuals, and predicting positions by using a cloud model;
and 7: carrying out boundary detection on the newly generated individuals;
and 8: calculating non-dominant sorting and N front-of-congestion distance reservation individuals;
and step 9: judging iteration termination conditions, and if the iteration termination conditions are met, jumping to the step 10; otherwise, turning to the step 2;
step 10: and outputting the population PS.
And 7, carrying out boundary detection on the newly generated individuals, and repairing the individuals beyond the decision space:
wherein x isiRepresenting the i-dimension, y, of the individual before x predictioniFor the predicted ith-dimension position of the individual, i ═ 1iAnd biThe lower and upper bounds of the ith dimension of the variable are decided separately.
The invention has the beneficial effects that: firstly, the searched optimal leading edge is segmented, the population is divided according to the segmentation result of the optimal leading edge, each part of the population is subjected to linear prediction, the description of the cloud model on uncertain time is used for reference, the prediction error is made up by entropy and super entropy, and the diversity of the population in the prediction process is ensured by adopting a deflection angle enhanced search strategy aiming at sudden nonlinear change possibly occurring in the dynamic problem.
Drawings
FIG. 1 is a schematic view of a directed cloud search;
FIG. 2 is a schematic diagram of a declination enhancement search;
FIG. 3 is a graph of the time variation of the IGD index in the JY1 test function of the 4 algorithms;
FIG. 4 is a graph of the time variation of the IGD index in the JY2 test function of the 4 algorithms;
FIG. 5 is a graph of the time variation of the IGD index in the JY3 test function of the 4 algorithms;
FIG. 6 is a graph of the time variation of the IGD index in the JY4 test function of the 4 algorithms;
FIG. 7 is a graph of the time variation of the IGD index in the JY5 test function of the 4 algorithms;
FIG. 8 is a graph of the time variation of the IGD index in the JY6 test function of the 4 algorithms;
FIG. 9 is a graph of the time variation of the IGD index in the JY7 test function of the 4 algorithms;
FIG. 10 is a graph of the time variation of the IGD index in the JY8 test function of the 4 algorithms.
In fig. 1, d (t) is a directional prediction direction d' (t) which is a possible cloud prediction direction, that is, the directional cloud prediction uses the direction d (t) as a main search direction, and searches the last offset direction Δ (t) with a certain probability.
Detailed Description
The invention is described in further detail below with reference to the figures and the embodiments.
The dynamic multi-objective optimization method based on the segmentation multi-directional prediction strategy specifically comprises the following steps:
(1) describing dynamic multi-objective optimization problem
The dynamic multi-objective optimization problem is described as follows:
wherein x is (x)1,...,xn)TIs a decision variable in an n-dimensional decision space, t is a time variable, g (x, t) and h (x, t) are an inequality constraint and an equality constraint, respectively, (f)1(x,t),f2(x,t),L,fm(x,t))TThe method is an objective function vector of a dynamic multi-objective optimization problem, an evaluation function F (x, t) is mapping from a decision space to a target space, s.t. represents a constraint condition, and m is the number of targets.
(2) Segmented multi-directional prediction
The method comprises the steps of firstly dividing the optimal leading edge into a plurality of segments, dividing the population of a decision space according to the division result, then selecting partial individuals in each population, searching the optimal leading edge change direction by adopting a deflection angle enhanced search method, and finally performing supplementary search on the position of the optimal leading edge which is possibly deflected by adopting deflection angle enhanced search.
The method specifically comprises the following steps:
(a) performing population segmentation
In the dynamic multi-objective optimization problem, the optimal leading edge may deflect and deform, in order to predict the change form of the Pareto optimal leading edge (PF) more accurately, the PF is divided into partial segments, each segment is predicted respectively, and compared with population center linear prediction, the method can judge PF deformation and nonlinear deviation more accurately.
First, in the PF, a boundary point is selected as a first key point, then the distance from each point to this boundary point is calculated, and the point with the largest distance is selected as a second key point. And calculating the distance between other individuals and the second key, selecting a point with the maximum distance between one point and two key points as a third key point, and selecting m +1 key points (m is the target number) by analogy. And each individual selects the key points with the closest distance to form m +1 fragments, and a plurality of populations are divided according to the division result of the PF.
The method is simple in calculation and low in complexity. Each time a key point is selected, the complexity of time is O (N), N is the size of the population, and the calculation complexity of the method is O (N (m +2)/2) or O (Nm). And the clustering method has the calculation complexity of O (N)2) The segmentation method can more simply segment the population and has low computational complexity.
(b) Directional cloud prediction
The population size is N, the ith population PopiContaining KiIndividual, for a sub-population at time t, PopiThe center is described as follows:
wherein the content of the first and second substances,
represents all individuals of the population, the k-th individual is
n is the decision space dimension, Ci(t) represents the population center position at time t, |, represents the potential of the set.
As shown in FIG. 1, a predicted population transition vector d at time t +1 is predicted using the positions of the population center points at time t and time t-1i(t) and the double migration error Δ (t) are as follows
di(t)＝Ci(t)-Ci(t-1) (3)
Δ(t)＝di(t)-di(t-1) (4)
And predicting the population migration position by using a normal cloud model. Setting the moving direction of the population as an expectation and the Euclidean distance d of the moving vectori(t) is entropy, and the deviation Delta (t) of the two population moving directions is used as super entropyExpectation, entropy and super entropy construct a normal cloud generator. Firstly, generating normal random vectors En' -N (delta (t) | | delta (t) | N as standard deviation by taking delta (t) as expectation and | | delta (t) |2/n2) Wherein En' ═ e (En)1',...,Enn') to a host; then by di(t) as expected, En' as standard deviation to generate a normal random vector v1～N(di(t),En'2). The predicted position y of the individual after the environmental change is expressed as follows:
y＝p+v1(5)
wherein p is the individual position before environmental change, v1Is the prediction direction.
(c) Declination-enhanced search
The directional cloud prediction includes error compensation of linear prediction, but the compensation is only effective for gradual regularity change. If the dynamic problem presents a backward reciprocating or non-gradual change, the direction of the directional cloud prediction is exactly opposite to or perpendicular to the direction of the change of the dynamic problem. Aiming at the problem, the invention provides deflection angle enhanced search, namely randomly selecting a part of individuals and searching towards each possible direction at a certain angle.
As shown in FIG. 2, first, a perpendicular d is constructedi(t) generating a random vector of [ -1,1 []Random vector r ═ in the range (r)1,...,rn) The value of j dimension of r is arbitrarily selected as formula (6).
Declination enhancement search direction vector e (t) ═ e1,...,en) The calculation is as follows.
In the formula, θ is the size of the deflection angle, and represents the possible search range, and is calculated as follows:
when determining the deflection angle enhancement search direction vector e (t) ═ (e)1,...,en) And then, carrying out deviation angle search on the individual by using a normal cloud model. With ei(t) is expected, and Δ (t) is the standard deviation difference to generate normal random vectors En x N (d)i(t),Δ(t)2) Wherein En ═ is (En)1*,...,EnnX); then with ei(t) generating a normal random vector v for standard deviation, En2～N(ei(t),En*2). The deviation angle search has the following predicted positions y for individual x:
y*＝y+v2(9)
wherein v is2Is the predicted direction after the offset angle search.
(d) Environmental detection
The sensitivity of the algorithm to the environment is very important, and the solution efficiency of the dynamic multi-objective optimization problem (DMOP) is reduced when the sensitivity is excessive or deficient. Furthermore, each objective function of DMOP does not necessarily change at the same time, and the magnitude of the change in different objective functions is also different. Therefore, the invention comprehensively considers the change of each objective function value and carries out normalization processing, and environment detection is realized by calculating an environment sensitivity factor epsilon (t), and the specific calculation is as follows:
h is the number of individuals randomly extracted from the population, and the random extraction mainly reduces the consumption of the environment detection on the calculation cost of the algorithm; f (x)jAnd t) represents an individual xjVector of the objective function at time t, F (x)jT-1) represents an individual xjThe vector of the objective function at time t-1, F (x)iAnd t) represents an individual xiVector of the objective function at time t, F (x)jT-1) represents an individual xiThe objective function vector at time t-1. Typically, the proportion of the population drawn for environmental monitoring is 5%.
(e) Performing a segmented Cloud Prediction policy (SCPS) calculation
The SCPS algorithm iterates within the basic dynamic MOEA algorithm framework. The basic dynamic MOEA algorithm framework mainly comprises two parts, namely dynamic prediction and static MOEA search. Since the present invention mainly studies the predicted performance of DMOEA, a classical NSGA-II was chosen as the static MOEA search.
The SCPS algorithm is described in detail as follows:
inputting: when the historical information is not collected sufficiently, the population proportion is initialized randomly to ζ, the center orientation prediction population proportion L1, the population size N, the environment change final time Tmax, t: ═ 0, and d (t-1): 0 are implemented.
And (3) outputting: pareto optimal solution set (PS).
Step 1: randomly initializing a population;
step 2: whether the environment is changed is detected by using the formula (10),
if the change occurs, turning to step 3; otherwise, turning to the step 8;
and step 3: judging whether d (t-1) is 0 or not, and if d (t-1) ≠ 0, jumping to the step 5; otherwise, turning to the step 4;
and 4, step 4: randomly selecting Zeta × N individuals to evolve, and making d (t-1) ═ d (t);
and 5: dividing the population into m +1 parts, calculating the population center for each sub-population Popi by using the formula (2),
calculating the population moving direction d (t) of the time t according to the formula (3),
di(t)＝Ci(t)-Ci(t-1) (3)
selecting L1 multiplied by N individuals by using a 2-system tournament method, and predicting the predicted position by using a normal cloud model;
step 6: selecting N x (1-L1) individuals using a 2-ary tournament method, calculating deviation angle search vectors of the individuals according to equations (6) - (8),
declination enhancement search direction vector e (t) ═ e1,...,en) The calculation is as follows.
In the formula, θ is the size of the deflection angle, and represents the possible search range, and is calculated as follows:
predicting a location using a cloud model;
and 7: carrying out boundary detection on the newly generated individuals;
and 8: calculating non-dominant sorting and N front-of-congestion distance reservation individuals;
and step 9: judging iteration termination conditions, and if the iteration termination conditions are met, jumping to the step 10; otherwise, turning to the step 2;
step 10: and outputting the population PS.
One-step prediction step 5 and deviation angle search step 6 based on cloud model in SCPS algorithm respectively select K at random1xN and Nx (1-K)1) Individual subjects were predicted. Since the predicted individuals are likely to exceed the decision space, step 7 is added to carry out boundary detection on newly generated individuals and repair the individuals exceeding the decision space:
wherein x isiRepresenting the i-dimension, y, of the individual before x predictioniFor the predicted ith-dimension position of the individual, i ═ 1iAnd biThe lower and upper bounds of the ith dimension of the variable are decided separately.
The effects of the present invention are explained as follows:
(1) testing functions
A new dynamic test function generator JY is constructed in the literature (shipping Jiang, marketing Yang. evolution dynamic multiple optimization: benchmark and algorithm composites. IEEETransaction on Cybernetics,2017,47(1):198 and 211.) the dynamic test function generated based on JY is related to a plurality of actual engineering problems, such as greenhouse system, hydropower scheduling, route guidance scheduling and the like. The test function has the characteristics of three types of common PF convex-concave conversion and dynamic problems, and the like, and also comprises the characteristics of non-monotonic dependence of decision variables (non-monotonic dependencies), PF discrete, multi-modal, and the like. Eight test functions (JY1-JY8) generated based on JY are used as the test functions of the invention, and the eight test functions JY1-JY8 are different in the change rule of PS and PF along with time, so that the performance of the SCPS algorithm can be better analyzed. All function dynamics are determined according to the variation time t, which is calculated as follows:
wherein n istTo vary the intensity, τtτ is the number of iterations for the frequency of the environmental change.
In order to better test the performance of the algorithm in the aspect of dynamic problem optimization, the environment change frequency and frequency of 3 groups of test functions are set, and (n, tau) are respectively (5,10), (10,10) and (10, 20). The comparison algorithm of the test selects MOEA/D (Qingfu Zhang, Hui Li. MOEA/D: A multiple objective evaluation algorithm on the comparison. IEEE Transactions on evaluation algorithm, 11(6):712-731), PPS (A.M.ZHou, Y.C.Jin, Q.F.Zhang. A amplification prediction algorithm for evaluation of multiple objective evaluation algorithms, 2014,44(1):40-53), MDP (Miao routing, Dunwei gravity, Yong Zhang, Yaochhu, Witodi simulation, multiple objective prediction algorithm, S.E.M.M.Zhang, S.C.M.C.J.The population size N of the comparison algorithm is 200, and the evolution termination time Tmax＝10。
(i)MOEA/D：T＝20；
(ii) PPS: the population center point remaining number M is 23, p is 3 by using a p-element linear regression model;
(iii) SCPS: zeta 0.2, the number of individuals K selected by the prediction model1＝0.5×N；
The dynamic multi-objective evolutionary algorithm has a great number of measurement indexes, selects an Inverted Generation Distance (IGD) as an evaluation standard of each iteration, and uses a Modified IGD (MIGD) as a comprehensive evaluation standard of each algorithm which runs for many times in each test function.
Wherein P x (t) represents a uniformly distributed ideal PF solution set at time t; p (t) represents a PF solution set solved by the algorithm;
represents the distance of the individual x from the solution set P (t); | P (t) | represents the potential of the set P (t).
The MIGD is used to evaluate the average IGD of the algorithm running over a period of time in the test function, as defined below:
where T represents a discrete set of time points and | T | represents the potential of T.
Table 1 shows the average MIGD index results of the 4 dynamic multi-objective evolutionary methods run 20 times in 8 test functions, bold boldface indicates the optimal values. As can be seen from table 1, SCPS has the optimized performance that shows better among 8 dynamic test problems, and only in the case of JY4 test problem (n, τ) ═ 5,10), the performance is slightly inferior to PPS. Among all the test problems, the four methods have stronger problem optimizing capability at JY1-JY5 and JY8, and the MIGD index reaches 10-2Magnitude, four parties are provedThe method can better track the dynamic leading edge. JY6 is a multimodal TypeIII dynamic problem with PS and PF changing along with time, not only the number of the optimal solutions changes, but also the distribution of the optimal solutions changes continuously, although the SCPS performance in the problem is superior to the other three algorithms, but the SCPS performance is not satisfactory on the MIGD index. JY7 is also a multimodal problem, the convex-concave distribution of its PF continuously changes, but JY7 is relatively simpler than JY6 because its local optimum number is fixed. Therefore, the four test functions have better performance than JY6 on JY 7. However, the standard deviation of the MIGD indexes of the four algorithms in the JY7 function is observed, so that the SCPS has better stability compared with the other three algorithms, and the accuracy of the solution result is higher.
To further analyze the dynamic optimization performance of the four algorithms, the IGD index versus time curves of the 8 sets of test function analysis algorithms were selected for the case of (n, τ) — (10, 20). Fig. 3-10 are graphs of IGD index versus time in the test function for 4 algorithms. It can be seen from the figure that the MOEA/D algorithm has a better optimizing performance on the static problem, but has insufficient optimizing capability on the dynamic problem in a limited time because of no dynamic prediction capability. The performance of the PPS is obviously due to MDP on the problems of JY2 and JY5, but the performance of the PPS is inferior to the MDP on the problems of JY7 and JY 8. Particularly JY7, the prediction of PPS obviously has larger error, and the error continuously increases. Of the 8 test functions, SCPS is apparently due to the other 3 methods.
TABLE 1 MIGD INDICATOR OF FOUR METHODS IN 8 TEST FUNCTIONS
By combining the average value and the IGD index trend graph comparison result analysis, it can be seen that the method provided by the invention has stable performance and better prediction capability, and can better predict the population which is uniformly distributed and is close to the position at the last moment.
Claims (10)
1. The dynamic multi-objective optimization method based on the segmentation multi-directional prediction strategy is characterized by comprising the following steps of:
(1) describing the dynamic multi-target problem;
(2) and (4) dividing the multi-directional prediction.
2. The method of claim 1, wherein the method comprises: the dynamic multi-target problem in the step (1) is described as follows:
wherein x is (x)1,...,xn)TIs a decision variable in n-dimensional decision space, t is a time variable, (f)1(x,t),f2(x,t),L,fm(x,t))TThe method is an objective function vector of a dynamic multi-objective optimization problem, an evaluation function F (x, t) is mapping from a decision space to a target space, and s.t. represents a constraint condition.
3. The method of claim 1, wherein the method comprises: in the step (2), the optimal leading edge is firstly divided into a plurality of segments by the multi-directional partition prediction, the population of the decision space is divided according to the partition result, then, part of individuals are selected from each population, the optimal leading edge change direction is searched by adopting a deflection angle enhancement search strategy, and finally, the deflection angle enhancement search is adopted to perform supplementary search on the position of the optimal leading edge which is possibly deflected.
4. The method for dynamic multi-objective optimization based on the segmented multi-directional prediction strategy as claimed in claim 3, wherein the step (2) comprises the following steps:
(a) carrying out population segmentation;
(b) directional cloud prediction;
(c) performing deflection angle enhancement search;
(d) detecting the environment;
(e) and carrying out segmentation multi-directional cloud prediction strategy calculation.
5. The method of claim 4 for dynamic multi-objective optimization based on a segmented multi-directional prediction strategy, characterized in that: the step (a) of carrying out population segmentation comprises the steps of selecting a boundary point as a first key point in the PF, then calculating the distance from each point to the boundary point, and selecting the point with the maximum distance as a second key point; calculating the distance between other individuals and the second key point, selecting a point with the maximum distance between one point and the two key points as a third key point, selecting m +1 key points by analogy in sequence, wherein m is the number of targets, selecting the key point with the closest distance from each individual to form m +1 fragments, and dividing a plurality of populations according to the division result of the PF.
6. The method of claim 4 for dynamic multi-objective optimization based on a segmented multi-directional prediction strategy, characterized in that: said step (b) of directed cloud prediction comprises,
the population size is N, the ith population PopiContaining KiIndividual, for a sub-population at time t, PopiThe center is described as follows:
wherein the kth individual is
n is the decision space dimension, Ci(t) represents the center position of the population at the moment t, |, represents the potential of the set;
predicting population migration vector d at t +1 moment by using positions of population center points at t moment and t-1 momenti(t) and the double migration error Δ (t) are as follows
di(t)＝Ci(t)-Ci(t-1) (3)
Δ(t)＝di(t)-di(t-1) (4)
Predicting the migration position of the population by using a normal cloud model, wherein the movement direction of the population is expected, and the movement vector isEuclidean distance of di(t) is entropy, deviation delta (t) of two times of population moving directions is used as super-entropy, expectation, entropy and super-entropy are used for constructing a normal cloud generator, firstly, delta (t) is used as expectation, and | delta (t) |/N is used as standard deviation to generate normal random vectors En' -N (delta (t) |, | | delta (t) | Y)2/n2) Wherein En' ═ e (En)1',...,Enn') to a host; then by di(t) as expected, En' as standard deviation to generate a normal random vector v1～N(di(t),En'2) The predicted position y of the individual after the environmental change is expressed as follows:
y＝p+v1(5)
wherein p is the individual position before environmental change, v1Is the prediction direction.
7. The method of claim 4 for dynamic multi-objective optimization based on a segmented multi-directional prediction strategy, characterized in that: said step (c) of the declination-enhanced search comprises,
construct a perpendicular to di(t) generating a random vector of [ -1,1 []Random vector r ═ in the range (r)1,...,rn) The value of j dimension of r is arbitrarily selected as formula (6),
declination enhancement search direction vector e (t) ═ e1,...,en) Is calculated as follows
In the formula, θ is the size of the deflection angle, and represents the possible search range, and is calculated as follows:
when determining the deflection angle enhancement search direction vector e (t) ═ (e)1,...,en) Then, using a normal cloud model to perform deviation angle search on the individualsCable with ei(t) is expected, and Δ (t) is the standard deviation difference to generate normal random vectors En x N (d)i(t),Δ(t)2) Wherein En ═ is (En)1*,...,EnnX); then with ei(t) generating a normal random vector v for standard deviation, En2～N(ei(t),En*2) The predicted position y of the deviation angle search to the individual is as follows:
y*＝y+v2(9)
wherein v is2Is the predicted direction after the offset angle search.
8. The method of claim 4, wherein the environmental sensitivity factor ε (t) in step (d) is calculated as follows:
wherein H is the number of individuals randomly drawn from the population, F (x)jAnd t) represents an individual xjAnd in the target function vector at the time t, the proportion of the environment monitoring extraction population is 5%.
9. The method of claim 4, wherein the computing of the partition multi-directional cloud prediction strategy in the step (e) comprises:
step 1: randomly initializing a population;
step 2: utilization type (10)
Detecting whether the environment changes, and if so, turning to the step 3; otherwise, turning to the step 8;
and step 3: judging whether d (t-1) is 0 or not, and if d (t-1) ≠ 0, jumping to the step 5; otherwise, turning to the step 4;
and 4, step 4: randomly selecting Zeta × N individuals to evolve, and making d (t-1) ═ d (t);
and 5: dividing the population into m +1 parts, calculating the population center for each sub-population Popi by using the formula (2),
according to formula (3)
di(t)＝Ci(t)-Ci(t-1) (3)
Calculating the population moving direction d (t) of time t, selecting L1 multiplied by N individuals by using a 2-system tournament method, and predicting the predicted position by using a normal cloud model;
step 6: selecting N x (1-L1) individuals according to formulas (6) - (8) using a 2-ary tournament method
Declination enhancement search direction vector e (t) ═ e1,...,en) Is calculated as follows
In the formula, θ is the size of the deflection angle, and represents the possible search range, and is calculated as follows:
calculating deviation angle search vectors of the individuals, and predicting positions by using a cloud model;
and 7: carrying out boundary detection on the newly generated individuals;
and 8: calculating non-dominant sorting and N front-of-congestion distance reservation individuals;
and step 9: judging iteration termination conditions, and if the iteration termination conditions are met, jumping to the step 10; otherwise, turning to the step 2;
step 10: and outputting the population PS.
10. The method of claim 9 for dynamic multi-objective optimization based on a segmented multi-directional prediction strategy, characterized by: and 7, carrying out boundary detection on the newly generated individuals, and repairing the individuals beyond the decision space:
wherein x isiRepresenting the i-dimension, y, of the individual before x predictioniFor the predicted ith-dimension position of the individual, i ═ 1iAnd biThe lower and upper bounds of the ith dimension of the variable are decided separately.
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