CN108960486A - Interactive set evolvement method based on grey support vector regression prediction adaptive value - Google Patents

Abstract

The invention discloses a kind of interactive set evolutionary computation methods based on grey support vector regression prediction adaptive value, the specific steps of which are as follows: system provides design environment for user, generates initial Advanced group species at random before evolution starts；By interactive interface, people carries out numerical Evaluation to Nc individual；System clusters population according to individual similarity, and estimation clusters interior non-user and evaluates individual fitness, and predicts adaptive value using grey support vector regression；Set individual of evolving is carried out by Pareto is dominant sequence according to diversity, distributivity uncertainty measure, and set individual of evolving is operated using adaptive crossover and mutation, the generation interim population of same size；Parent population and interim population are merged, select top n individual as progeny population；Finally, being equidistantly divided into Nc unit to progeny population, 1 individual is randomly selected from each unit, Nc individual is recommended into user altogether.

Description

An Interactive Ensemble Evolutionary Method for Predicting Fitness Value Based on Gray Support Vector Regression Machine

technical field

The invention belongs to the field of intelligent computing, in particular to an interactive ensemble evolutionary optimization method for predicting fitness values based on gray support vector regression machines, which is used for the selection of color matching schemes.

Background technique

The application of interactive evolutionary computing based on heuristic learning proposed in the 1990s to solve implicit index optimization problems needs to solve two basic problems: (1) how to effectively extract implicit knowledge; (2) how to solve implicit performance with high quality index.

For the first question, there are mainly two research strategies: one is to directly extract implicit knowledge through the human-computer interaction interface in the mode of evolution while interacting. This mainly focuses on the research on the way of assigning fitness values. For example, the second issue of the journal "Acta Automatica Sinica" published in 2014 "A proxy model for weighted multi-output Gaussian processes based on interval fitness value interactive genetic algorithm" uses interval numbers and other uncertain numbers to express The fitness value reflects the user's preference characteristics; the twelfth issue of the journal "Acta Electronics" published in 2017 "Interactive Genetic Algorithm for Non-user-assigned Adaptive Value Based on the Entropy Maximization Criterion" and the journal "Applied Intelligence" published in 2016 The third issue of "Predicting user's preferences using neural networks and psychology models" combines user browsing behaviors to express personalized needs, making up for the lack of knowledge expression of numerical fitness value preferences. Direct acquisition of implicit knowledge requires less computation and is simple, but it is highly subjective, has large information uncertainty, and has high noise content. The second is to obtain implicit knowledge indirectly, that is, to mine implicit knowledge during the evolution process and extract valuable preference information. The 6th issue of the journal "Journal of Zhengzhou University (Engineering)" published in 2017 ".Interactive Genetic Algorithm and Its Application Based on Possibility Conditional Preference Network" uses preference network to fit user preferences, estimate individual fitness value and guide search; Similarly, the journal "Automated Software Engineering" No. 3 "An Architecture based on interactive optimization and machine learning applied to the next release problem" published in 2017 uses neural networks to learn user preferences and estimate fitness values. The indirect acquisition of implicit knowledge is the in-depth mining of preference information, which enhances the search ability of the algorithm, but the modeling of the proxy model is relatively complicated, and the estimation error cannot be measured, which will still bring a lot of noise in the fitness value. The fitness value estimation/expression strategy that digs deeply into user behavior patterns is expected to improve the effect of implicit knowledge extraction or extract knowledge in more complex scenarios, but from the overall optimization performance, only relying on improving the intensity of implicit knowledge extraction to obtain algorithm performance has a certain effect. Very limited. For the second problem, it is mainly achieved through an efficient evolutionary strategy that reduces user fatigue. Using a large population size can improve the search ability of the algorithm, but this method needs to solve the problem of estimating the fitness value of a large number of unevaluated individuals. Using the agent model to perform evolutionary operations can reduce user workload and save time for users. For example, the 8th issue of the journal "Acta Electronics" published in 2014 "Interactive Genetic Algorithm for Selecting Evolutionary Individuals Based on Elite Sets" constructs individual elite sets, and selects individual categories similar to the elite set for direct genetic operations, reducing the burden on users. Combining the above ideas, using the evolutionary surrogate model in large-scale populations can significantly improve the performance of the algorithm.

In the above algorithm, how to design the population evolution strategy is very important, because the surrogate model will generate error accumulation, and controlling the error is a difficult problem to solve. If the ensemble evolution method is applied to large-scale population clustering evolution, the search efficiency can be improved; at the same time, if the surrogate model is used to re-evaluate the estimated fitness value of the existing large-scale population individuals, the accuracy of the fitness value can be improved. By learning from each other, it is expected to improve the performance of the current interactive evolutionary optimization algorithm. After reviewing relevant literature, there is no interactive ensemble evolutionary optimization method that uses gray support vector regression machine to predict fitness value. If a related efficient design system can be developed, it will not only promote color matching design, but also have great inspiration for other product designs.

Contents of the invention

The technical problem to be solved by the present invention is to overcome the shortcomings of existing fitness value estimation techniques, and provide an interactive evolutionary optimization method that reduces fitness value estimation errors, reduces user burden, enhances algorithm search capabilities, and improves evolutionary optimization quality.

Technical scheme of the present invention is:

First, a large-scale population is used to expand the search space, and a limited number of user-evaluated individuals are used as clustering centers for population clustering. Then, the fitness value of non-clustering center individuals in the cluster is estimated according to the individual similarity of personal browsing behavior, and the gray support vector regression model is used to further predict the individual fitness value to form a collective evolutionary individual. Finally, the ensemble evolutionary algorithm is implemented under the NSGA-II paradigm by adopting the ensemble evolutionary strategy and the self-adaptive cross-mutation operation. In order to realize the present invention, it is necessary to solve two main problems of individual fitness value prediction and ensemble evolution strategy design.

(1) Gray support vector machine fitness value prediction

The individual exact fitness value f(x _k (t)), x _k (t)∈x(t) is denoted as F ₀ =(f ₀ (x ₁ (t)),f ₀ (x ₂ (t)) ,…,f ₀ (x _N (t))), constitute the original sequence of individual fitness values. Then the 1-AGO sequence of F ₀ is F ₁ =(f ₁ (x ₁ (t)),f ₁ (x ₂ (t)),...,f ₁ (x _N (t))), In order to make the impact weight of the original data on the objective function consistent in each feature dimension, the original sequence is first normalized:

The normalized data sequence is F ₀ '=(f ₀ '(x ₁ (t)), f ₀ '(x ₂ (t)),..., f ₀ '(x _N (t))). Then, establish the 1-AGO sequence F ₁ of F ₀ '=(f ₁ '(x ₁ (t)), f ₁ '(x ₂ (t)),...,f ₁ '(x _N (t))) , Then the gray support vector model is recorded as:

In the formula: b is the bias item; ω is the weight. The 1-AGO transformation term f ₁ '(x _k (t)) represents the nonlinear mapping from the input space of individual fitness values to the high-dimensional feature space. The unknown parameters ω and b in the formula use the ε-insensitive loss function proposed by Vapnik, estimated from the training set in the high-dimensional feature space:

due to minimize The minimum deviation of ε can be guaranteed, and the gray support vector model can be written as the following convex optimization problem:

In the formula: Control the fitting accuracy of the model; C is a regularization constant, which controls the degree of punishment for samples exceeding the error. The above formula can be solved by Lagrange multiplier method:

The dual optimization model can be obtained:

In the formula, <f ₁ '( _xi (t)), f ₁ '(x _j (t))> represents the vector inner product. The present invention selects the kernel function K(f ₁ '( _xi (t)), f ₁ '(x _j (t)))=exp(-υ||f ₁ '( _xi (t)), f ₁ ' (x _j (t))||), υ＞0, υ is a kernel parameter. Substitute the kernel function into the above formula to obtain α _k , After and b, the gray support vector regression machine model is:

In the formula, is the predicted value of the gray support vector machine for the new input individual fitness value f ₁ '(x _new (t)).

Finally, restoring the predicted values to the original sequence scale yields:

After the population individuals are clustered and the fitness value is predicted, the individual subclasses x ₁ (t), x ₂ (t),…, x _Nc (t) formed are a set of individuals. Based on the idea of set evolution, it is natural that individuals Subclasses are treated as evolutionary individuals (collective evolutionary individuals).

(2) Ensemble evolution strategy

By selecting an appropriate performance index, the implicit performance index optimization can be transformed into the following general set decision variable optimization problem:

max F(X)＝(F ₁ (X),F ₂ (X),...,F _Id (X))

in, is the power set of the decision space S; X={x ₁ (t),x ₂ (t),…,x _Nc (t)} is the population composed of evolutionary individuals; F _d (X),d=1,2, ..., Id is the performance index of the population X; Id is the dimension of the optimized problem after transformation, and it is much smaller than Nc. Combining with the characteristics of implicit performance indicators, this section presents a new collective individual comparison measure, as follows.

Note that the jth evolutionary individual of the tth generation evolutionary population x(t) is Among them, x _j (t) is the central individual, and the individual fitness value is M=|x _j (t)| is the number of individuals included in the evolved individual x _j (t).

Using evolutionary individual similarity information entropy to describe diversity:

In the above formula, Among them, x _ir ,r=1,2,...,g are the r attributes of the individual, is the attribute value of x _ir . The greater the similarity μ( _xi (t), x _j (t)) between the central individual x _j (t) of x _j (t) and other evolutionary individuals, the greater the relationship between x _j (t) and other evolutionary individuals The more similar, the worse the diversity of the population, at this time, the smaller the F ₂ (X). Conversely, the larger the F ₂ (X) is, the more "loose" the evolutionary individuals of the population are, and the better the diversity of the population is.

The distribution is described by the following formula:

In the formula, d(x _j (t)) is the minimum crowding distance of x _j (t), d ^* is the average crowding distance of individuals in population evolution,

For evolutionary individuals with the same sequence value, the uncertainty is further described by the interval gray number gray scale:

The above formula regards the fitness value of the evolutionary individual x _j (t) as an interval gray number, and the evaluation uncertainty of x _j (t) can be described by the interval gray number gray scale, that is, the smaller the GF(X), the different evolutionary individual The less certain it is, and vice versa.

When x ₁ || _spar x ₂ , select x=arg min{GF(x ₁ ),GF(x ₂ )} as the winning individual. Through the above method, it is possible to compare the advantages and disadvantages of any two collective evolution individuals in the population.

(3) Adaptive set crossover and mutation probability

According to the characteristics of set evolution, this section gives adaptive set crossover and mutation operators. For the crossover probability within the same evolutionary individual, the adaptive crossover probability is used:

The above formula considers the relationship between the crossover operation in the evolution process and the individual diversity and uncertainty changes of ensemble evolution. That is, in order to enhance the search ability, the uncertainty of evolutionary individuals should be proportional to the crossover probability; in order to retain dominant individuals, the diversity of evolutionary individuals should be inversely proportional to the crossover probability, and the overall crossover probability should gradually decrease with evolution to strengthen the convergence of the algorithm ; and vice versa.

The mutation operation of collective evolutionary individuals adopts the single-point mutation method, and the adaptive mutation probability consists of P _m ¹ and P _m ² 2 parts:

The above formula embodies the relationship between the mutation operation and the diversity and convergence of evolutionary individuals. That is, in order to retain dominant individuals, diversity and convergence should be inversely proportional to mutation probability, and vice versa.

In the formula is the individual to be mutated in the evolved individual x _j (t) adaptation value. The above formula embodies the relationship between mutation operation and evolutionary individual fitness value. That is, in order to protect the dominant individuals from being destroyed, among the evolutionary individuals x _j (t) selected for the mutation operation, the individual with the greater fitness value has a lower probability of being mutated.

The evolutionary individual adaptive mutation probability P _m is:

The color individual coding method is: the RGB color mode obtains various colors by changing the three color attributes of red (R), green (G), and blue (B) and their superposition, and the value range of each color attribute is 0 ~255. RGB color individual chromosomes are coded in binary, with a code length of 24 bits. Among them, the first 8 bits represent the red attribute, the middle 8 bits represent the green attribute, and the last 8 bits represent the blue attribute. Each color attribute corresponds to a binary code ranging from 00000000 to 11111111 . The optimization target is a certain target color set in advance, and through evolutionary optimization, the user obtains a pair of color individuals that match the target color.

Advantage and positive effect of the present invention are:

1. The present invention uses a gray support vector machine to predict the individual fitness value of non-user evaluation, which greatly reduces the estimation error and reduces user fatigue compared with other fitness value estimation strategies;

2. The present invention adopts a new set evolution strategy to realize evolution, which obviously improves the search efficiency and optimization quality, and obtains good optimization effect when applied to the color matching problem.

Description of drawings

Fig. 1 is the general flowchart of the present invention;

Fig. 2 is a system interaction interface diagram of the present invention;

Fig. 3 is a schematic diagram of the search time comparison of the present invention;

Fig. 4 is a schematic diagram of evolutionary algebra comparison in the present invention.

Detailed ways

Referring to Fig. 1-Fig. 4, the implementation of the present invention will be described in further detail below. The following examples are only descriptive, not restrictive, and cannot limit the protection scope of the present invention.

Figure 1 shows an interactive ensemble evolution calculation process based on gray support vector regression machine to predict fitness value. The steps of this method are as follows:

Step 1. The interactive interface is composed of 3 parts. The first part is the evolution module located in the left half of the interface. This module presents 12 individuals (color blocks) to the user, and an adaptation value input text box is set under each individual. At the same time, the system records the user's evaluation time for each individual through the slider below the individual, which is used to calculate the uncertainty of the fitness value. For the convenience of comparison, a target color block is set on the periphery of the individual, and the distance value from the current individual is displayed. The second part is the evolution parameter and information statistics module located in the upper right part of the interface. Before evolution, the user can input the RGB color value by dragging the scroll bar to set the target color. In addition, this module also displays statistical information such as the start time of evolution, the current evolution algebra, the number of individuals evaluated by users, and the total time spent on evaluation. The third part is the command button module located at the lower right of the interface. The user clicks the "Start" button, the system initializes and generates an initial population; after the user evaluates the individual, clicks the "Next" button, and the system performs clustering and fitness value Evolutionary operations such as estimation and ensemble evolution generate the next generation of evolutionary populations. This process is looped until the termination condition is satisfied, and the evolution is terminated by clicking the "End" button.

The color individual coding method is: the RGB color mode obtains various colors by changing the three color attributes of red (R), green (G), and blue (B) and their superposition, and the value range of each color attribute is 0 ~255. RGB color individual chromosomes are coded in binary, with a code length of 24 bits. Among them, the first 8 bits represent the red attribute, the middle 8 bits represent the green attribute, and the last 8 bits represent the blue attribute. Each color attribute corresponds to a binary code ranging from 00000000 to 11111111 . The optimization target is a certain target color set in advance, and through evolutionary optimization, the user obtains a pair of color individuals that match the target color.

Step 2.

First, some individuals x _i (t), i=1, 2, ... Nc are selected as cluster center individuals, and the fitness value f( _xi (t)) is evaluated by the user. Then, calculate the similarity between other non-central individuals x _o (t) and each central individual in the population one by one according to the formula, and cluster the individuals according to the similarity, recorded as x _i (t)={ _xi (t)},i ∈{1,2,...Nc}. In this way, the population x(t) is finally divided into Nc subclasses, denoted as x ₁ (t), x ₂ (t),...,x _Nc (t). Then, calculate the weighted average of the similarity with each cluster center in each individual subclass, and estimate the fitness value of the non-central individual x _o (t). In order to reduce the estimation error of the fitness value, the estimated fitness value f(x _o (t)) of the non-central individual is predicted by the gray support vector regression machine, and the final fitness value of the non-central individual for subsequent evolution is obtained

Step 3.

The diversity, distribution and uncertainty measures are calculated sequentially for the ensemble evolutionary individuals.

Diversity measure:

Distribution measure:

In the formula, d(x _j (t)) is the minimum crowding distance of x _j (t), d ^* is the average crowding distance of individuals in population evolution,

Uncertainty measure:

The above formula regards the fitness value of the evolutionary individual x _j (t) as an interval gray number, and the evaluation uncertainty of x _j (t) can be described by the interval gray number gray scale, that is, the smaller the GF(X), the different evolutionary individual The less certain it is, and vice versa.

When x ₁ || _spar x ₂ , select x=arg min{GF(x ₁ ),GF(x ₂ )} as the winning individual. Through the above method, it is possible to compare the advantages and disadvantages of any two evolutionary individuals in the population.

Step 4.

The self-adaptive crossover and mutation operations are used for collective evolution individuals to generate temporary populations of the same size. Adaptive Crossover Probability:

The above formula considers the relationship between the crossover operation in the evolution process and the individual diversity and uncertainty changes of ensemble evolution. That is, in order to enhance the search ability, the uncertainty of evolutionary individuals should be proportional to the crossover probability; in order to retain dominant individuals, the diversity of evolutionary individuals should be inversely proportional to the crossover probability, and the overall crossover probability should gradually decrease with evolution to strengthen the convergence of the algorithm ; and vice versa.

The mutation operation of collective evolutionary individuals adopts the single-point mutation method, and the adaptive mutation probability is given by and Partial composition:

The above formula embodies the relationship between the mutation operation and the diversity and distribution of evolutionary individuals. That is, in order to retain dominant individuals, the diversity and distribution should be inversely proportional to the mutation probability, and vice versa.

In the formula is the individual to be mutated in the evolved individual x _j (t) adaptation value. In order to protect the dominant individual from being destroyed, among the evolutionary individuals x _j (t) selected for the mutation operation, the individual with a larger fitness value has a lower probability of being mutated.

The evolutionary individual adaptive mutation probability P _m is:

Step 5.

Merge the parent population and the temporary population, sort the merged population, and select the first N individuals as the offspring population; finally, divide the offspring population into Nc units at equal intervals, and randomly select one individual from each unit, A total of Nc individuals are recommended to the user.

Comparison between the present invention and the current algorithm

Combining "Probabilistic Conditional Preference Network Assisted Interactive Genetic Algorithm (PCPN-IGA)" and "Interactive Genetic Algorithms with Selecting Individuals Using Elite Sets" (Interactive Genetic Algorithms with Selecting Individuals Using Elite Set, IGA-SES) and other related algorithms are used as comparison algorithms to verify the effectiveness of the present invention in terms of search efficiency, optimization quality, and user fatigue relief.

The experimental results of the three methods are shown in Figure 4. As can be seen from Fig. 4, the present invention is obviously better than the comparison algorithm, specifically as follows:

a. In terms of search time, the present invention consumes the least time and improves search efficiency. The reason is that the present invention adopts the collective evolution strategy and the NSGA-II algorithm engine, which can make the population distribution more uniform, the diversity better, and the algorithm search efficiency improved. Adaptive crossover and mutation operations enhance the convergence of the algorithm. Although it takes a long time to compare the collective evolution of individuals, the overall search time is still shorter than that of the comparison algorithm.

b. In terms of evolution algebra, the present invention has the least evolution algebra, which not only improves search efficiency, but also reduces user fatigue. The reason is that the present invention uses the individual similarity based on user browsing behavior to estimate the individual fitness value, and at the same time uses the gray support vector regression machine to further predict the fitness value, which improves the precision of the fitness value, so the evolution direction is more in line with human preferences, and the algorithm convergence is accelerated .

The following table shows the mean value of the search results and the statistics of the number of exact matching users of the three methods. The data in the table were subjected to the Mann-Whitney U test at a significance level of 0.05. It can be seen from the table that the number of the present invention is the least in the two indicators of the number of evaluation individuals and the number of search individuals, and there is a significant difference with the comparative method. On the number of optimal solutions, although the number of the present invention is not significantly different from that of the comparison method, it is still the largest. This shows that the present invention can obtain the most satisfactory solutions with the relatively least number of evaluations (including evolution algebra). This reflects that the optimization efficiency of the present invention is the highest. The small number of searched individuals in the present invention is due to the small number of evolutionary algebras. Because the comparison method is also a large-scale population evolution with the same population size, the more evolutionary algebras, the more search individuals. Therefore, the comparison method has more search individuals, which does not mean that the search ability is better than the present invention. There are 3 users in the present invention, 2 users in IGA-SES and only 1 user in PCPN-IGA in terms of the number of users who obtain complete matching solutions. This shows that for the complex implicit performance index optimization problem of color matching, most users still obtain approximate solutions in the end. However, the present invention has the largest number of users who can obtain complete matching solutions, which reflects that the present invention has the best optimization performance. Through the above analysis, it can be seen that the search performance of the present invention is the best.

a. The present invention>IGA-SES>PCPN-IGA b. The present invention=IGA-SES=PCPN-IGA

The above are only preferred embodiments of the present invention, and are not intended to limit the present invention in any form. Any simple modifications, equivalent changes and modifications made to the above embodiments according to the technical essence of the present invention still belong to within the scope of the technical solutions of the present invention.

Claims (4)

1. An interactive set evolution method for predicting adaptive values based on a gray support vector regression is characterized by comprising the following steps: adopting a large-scale population expansion search space, and carrying out population clustering by taking a limited number of user evaluation individuals as a clustering center; then, estimating adaptive values of non-clustering center individuals in the clusters according to the individual similarity of the integrated individual browsing behaviors, and further predicting the individual adaptive values by adopting a gray support vector regression model to form a set evolution individual; finally, a set evolution strategy and self-adaptive cross variation operation are adopted to realize set evolution;

(1) adaptive value prediction for gray support vector machine

Individual adaptation value f for new inputs₁'(x_new(t)) the gray support vector machine predictor is:

(2) ensemble evolution strategy

Measure of diversity:

measure of distribution:

uncertainty measure:

(3) adaptive set intersection and mutation probabilities

Self-adaptive cross probability:

self-adaptive mutation probability:

2. the interactive set evolution method based on the grey support vector regression prediction adaptive value according to claim 1, characterized in that:

3. the interactive set evolution calculation method based on the prediction adaptive value of the gray support vector regression machine as claimed in claim 1, wherein: d (x)_j(t)) is x_j(t) a minimum crowding distance of,d^*the average crowding distance of individuals in population evolution,

4. the interactive set evolution method based on the grey support vector regression prediction adaptive value according to claim 1, characterized in that: adaptive mutation probability P_mByAnd2, the part is formed by the following steps,

in the formulaIs an evolved individual x_j(t) individuals to be mutatedThe adaptive value of (a).