CN114330108B - Multi-objective optimization method and system based on dominant information extraction - Google Patents

Abstract

The invention provides a multi-objective optimization method and a system based on dominant information extraction, and relates to the technical field of communication system design, wherein the method comprises the following steps of S1, extracting space dominant information and obtaining a space partition result; and step S2, extracting parameter space advantage information according to the acquired space partition result, fully applying the parameter information contained in the advantage individuals in different evolution stages, and step S3, selecting optimal individuals distributed in different areas according to the parameter information, and guiding the evolution process. The method can fully extract the advantage information in the calculation process, guide evolution, greatly improve the searching capability and multi-objective weighing capability of the algorithm, ensure that the algorithm can efficiently optimize the actual industrial production process and improve the economic benefit.

Description

Multi-objective optimization method and system based on dominant information extraction

Technical Field

The invention relates to the technical field of communication system design, in particular to a multi-objective optimization method and system based on dominant information extraction.

Background

With the development of society and the progress of technology, the production scale of industrial processes becomes larger and larger, the process flow becomes more and more complex, the contained constraint conditions become more and the degree of nonlinearity is increased. The complexity of the flow process presents a significant challenge to the requirements of actual production.

Proper noun interpretation:

the advantage information defines the information contained in the target space that is beneficial to evolving towards an individual approaching the optimal leading edge.

And defining the optimal evolution direction, namely defining the direction of the reference point and the central position.

And (3) defining and calculating the distances between all individuals in the subspace and the reference point in the optimal evolution direction, wherein the individual with the shortest distance among all the distances is the optimal individual in the subspace.

And the contribution value is defined as the percentage of the total individual number of the individual number with the positive difference value between the adaptation value of the parent individual and the adaptation value of the child individual in the subspace.

The intelligent group algorithm simulates the mutual collaboration behavior among biological groups in nature and the win-lose criterion existing among biological individuals, and has better global searching capability. The parallel operation of a plurality of solutions can be realized in one calculation process due to the occurrence of the group, and the group intelligent algorithm has higher calculation efficiency and stronger universality. And has obvious advantages in solving the problem of large-scale optimization. The result of a multi-objective algorithm solution is often not a single solution, but a solution set containing several solutions. The effect of solving the actual industrial production problem is greatly influenced by a calculation method, and how to fully extract the advantage information of the calculation process so as to accelerate the convergence speed of an optimization algorithm and improve the diversity of the population is a difficult problem which is not thoroughly solved.

The invention patent with publication number of CN112822058A discloses a multi-objective optimization design method based on an effective area, which adopts a bacterial foraging algorithm to jointly optimize a plurality of design objectives of a communication system by taking an optimization design objective function of the communication system as an adaptation value of bacterial trend movement. And swimming bacteria to a global optimal position in a set effective area by using self-adaptive step length and direction, continuously updating the flora by adopting dynamic retention proportion, and finally obtaining the optimal design scheme of the system by finding out the optimal demodulation of the flora. The patent uses a flora foraging algorithm to perform multi-objective optimization on a communication system, and the effective area designed in the initial stage in the method is based on experience. The individuals with the crowded distances arranged in front in the generated optimal solution set form an optimal pool, and then global optimal bacteria are randomly selected from the optimal pool, so that the operation has certain randomness and has higher requirement on priori knowledge of application objects.

The invention patent with publication number CN108564163B discloses an improved ant colony algorithm for solving the problem of multiple targets and traveling merchants, after a pheromone matrix is randomly initialized, the ant colony utilizes an improved state transition formula to combine with a round-robin selection algorithm to sequentially select the next distribution point until a feasible solution is constructed. And after the weighting scoring of the feasible solution, taking the scoring as a benchmark of the pheromone addition amount, and carrying out the pheromone addition of different amounts for multiple rounds by combining multiple characteristics of the sub-paths. The invention improves the ant colony algorithm, and the positive feedback mechanism of the whole optimizing process along with the increase of iteration times can lead the pheromone difference value on different paths to be continuously expanded, and guide the whole system to evolve to the optimal direction. This method has certain limitations in that no pheromone exists when the ant colony algorithm is not used.

Disclosure of Invention

Aiming at the defects in the prior art, the invention provides a multi-objective optimization method and system based on dominant information extraction.

According to the multi-objective optimization method and system based on the dominant information extraction, the scheme is as follows:

In a first aspect, a multi-objective optimization method based on dominant information extraction is provided, the method comprising:

S1, extracting space advantage information and obtaining a space partition result;

Step S2, extracting parameter space advantage information according to the acquired space partition result, and fully applying the parameter information contained in the advantage individuals in different evolution stages;

And step S3, selecting optimal individuals distributed in different areas according to the parameter information, and guiding the evolution process.

Preferably, the step S1 includes:

The adaptation value f obtained by calculation is normalized to be between 0 and 1, and the vector form is as follows:

Wherein, the Representing the adaptation value after normalization operation;

x represents a decision variable, x _i represents an ith decision variable;

n represents N decision variables;

m represents m objective functions, wherein i and j respectively represent a designated ith decision variable and a jth objective function;

f' (x _i) represents the set of adaptation values obtained by the ith decision variable x _i on all objective functions;

[. ] ^T represents a transpose of the set;

The maximum and minimum values of all objective functions in each dimension consist of:

And

T represents the selected t dimension;

rp _max consists of the maximum of one objective function and the minimum of the remaining functions;

rp _min consists of the minimum of all objective functions;

The vector angle between the fitness value f' and the reference point Rp _max is calculated using formula (3):

θ=arccos(f′(x),Rp_max)(3)

Wherein, the the expression. Norms of vectors;

calculating a vector angle beta between reference points:

β_(t,j)＝arccos(Rp_max,t,Rp_max,j),t∈{1,2,...,m},j∈{1,2,...,m},t≠j (5)

when the number of the objective functions exceeds two, randomly selecting reference points corresponding to the adaptive values of the two objective functions to calculate vector angles, (t, j) are the selected t, j objective functions;

according to the vector angle between the reference points and the vector angle between the adaptive value and the reference points obtained through calculation, each individual participating in evolution is endowed with a 0-1 label belonging to the individual by using a formula (6):

Sn _i represents the label of the ith decision variable, and the label set of all decision variables is represented by Sn;

Obtaining dominant individuals P _best contained in a sub-solution set obtained from each generation in the evolution process;

dividing a target space into n subspaces through formulas (1) - (6), wherein the population X is also divided into a plurality of corresponding sub-populations;

calculating the central position of each subspace by using a formula (7), wherein the directions of the reference points Rp _min and the central position are the optimal evolution directions of each subspace;

where T _k represents the center position and z _k represents the number of individuals in the kth ^th subspace.

Preferably, the step S1 further includes:

Calculating the distances between all individuals in the k ^th subspace and the reference point Rp _min in the optimal evolution direction;

Among all the distances obtained by the calculation, the individual having the shortest distance is defined as the optimal individual P _best,k in the subspace;

The number of all individuals in the kth ^th subspace is denoted by z _k;

d_i,k＝||f′(x_i,k)||cos(f′(x_i,k),T_k),k＝1,2,...,n,i＝1,2,...,z_k (8)

Where d _i,k denotes the distance between the ith individual and the reference point Rp _min in the optimal evolution direction in the kth subspace;

f' (x _i,k) denotes the adaptation value of the decision variable xi in the kth subspace;

preferably, the step S2 includes:

calculating the difference between the adaptation value of the parent individual and the adaptation value of the child individual by using the result of the spatial partitioning in the step S1 through a formula (10);

wherein k represents the k ^th th subspace;

z _k represents the number of individuals in the kth ^th subspace;

Δf _k,i represents the sum of the differences in the fitness values of the child individuals and the parent individuals in the kth ^th subspace;

Meanwhile, Δf _k,i with a positive real number as a reserved result is stored in a set V _k, k e {1,2,.. The n } and the corresponding parameters are stored in a set R _k, k e {1,2,.. The n };

establishing a hybrid Gaussian model according to data in a set Mu is the mean and σ ² is the variance:

calculating parameters required by Gaussian distribution by using formulas (14) - (15):

Wherein, the Representing the mean value of the dominant parameter information in the subspace;

Representing the mean value of the dominant parameter information in the kth ^th subspace;

r _k,j represents an individual whose jth sub-generation adaptation value is better than the parent adaptation value in the kth subspace;

representing the variance of the dominant parameter information in the kth ^th subspace;

the difference delta f _k,i between the adaptation value of the parent and the adaptation value of the child in the k ^th th subspace is the number of positive real numbers.

Preferably, the step S2 further includes:

When there are n subspaces, the dominant parameter distribution for each subspace is Different subspaces have dominant parameter models with different Gaussian distributions, and the difference information of parent and offspring stored in V _k and k epsilon {1,2,.. N } is used for judging the contribution value w of dominant parameters in the different subspaces to the whole population when the current generation is evolved;

The specific mathematical description is as follows:

w_k＝∑V_k/(∑V₁+∑V₂+...+∑V_n),k∈{1,2,...,n} (16)

w _k represents a numerical representation of the contribution of the dominant parameter in the kth subspace to the whole population;

V _k, k e {1,2,., n } represents the sum of fitness value differences of individuals whose offspring perform better than the parent in the entire population;

From building a dominant parametric model mixture gaussian model of the whole population, the mean and variance are generated using equations (17) and (18):

in a second aspect, there is provided a multi-objective optimization system based on dominant information extraction, the system comprising:

the module M1 is used for extracting space advantage information and acquiring a space partition result;

the module M2 extracts parameter space advantage information according to the acquired space partition result and fully applies the parameter information contained in the dominant individuals in different evolution stages;

and the module M3 is used for selecting optimal individuals distributed in different areas according to the parameter information and guiding the evolution process.

Preferably, the module M1 comprises:

The adaptation value f obtained by calculation is normalized to be between 0 and 1, and the vector form is as follows:

Wherein, the Representing the adaptation value after normalization operation;

x represents a decision variable, x _i represents an ith decision variable;

n represents N decision variables;

m represents m objective functions, wherein i and j respectively represent a designated ith decision variable and a jth objective function;

f' (x _i) represents the set of adaptation values obtained by the ith decision variable x _i on all objective functions;

[. ] ^T represents a transpose of the set;

The maximum and minimum values of all objective functions in each dimension consist of:

And

T represents the selected t dimension;

rp _max consists of the maximum of one objective function and the minimum of the remaining functions;

rp _min consists of the minimum of all objective functions;

The vector angle between the fitness value f' and the reference point Rp _max is calculated using formula (3):

θ=arccos(f′(x),Rp_max) (3)

Wherein, the the expression. Norms of vectors;

calculating a vector angle beta between reference points:

β_(t,j)＝arccos(Rp_max,t,Rp_max,j),t∈{1,2,...,m},j∈{1,2,...,m},t≠j (5)

when the number of the objective functions exceeds two, randomly selecting reference points corresponding to the adaptive values of the two objective functions to calculate vector angles, (t, j) are the selected t, j objective functions;

according to the vector angle between the reference points and the vector angle between the adaptive value and the reference points obtained through calculation, each individual participating in evolution is endowed with a 0-1 label belonging to the individual by using a formula (6):

Sn _i represents the label of the ith decision variable, and the label set of all decision variables is represented by Sn;

Obtaining dominant individuals P _best contained in a sub-solution set obtained from each generation in the evolution process;

dividing a target space into n subspaces through formulas (1) - (6), wherein the population X is also divided into a plurality of corresponding sub-populations;

calculating the central position of each subspace by using a formula (7), wherein the directions of the reference points Rp _min and the central position are the optimal evolution directions of each subspace;

where T _k represents the center position and z _k represents the number of individuals in the kth ^th subspace.

Preferably, the module M1 further comprises:

Calculating the distances between all individuals in the k ^th subspace and the reference point Rp _min in the optimal evolution direction;

Among all the distances obtained by the calculation, the individual having the shortest distance is defined as the optimal individual P _best,k in the subspace;

The number of all individuals in the kth ^th subspace is denoted by z _k;

d_i,k＝||f′(x_i,k)||cos(f′(x_i,k),T_k),k＝1,2,...,n,i＝1,2,...,z_k (8)

Where d _i,k denotes the distance between the ith individual and the reference point Rp _min in the optimal evolution direction in the kth subspace;

f' (x _i,k) denotes the adaptation value of the decision variable xi in the kth subspace.

Preferably, the module M2 comprises:

calculating the difference between the adaptation value of the parent individual and the adaptation value of the child individual by using the result of the spatial partitioning in the step S1 through a formula (10);

wherein k represents the k ^th th subspace;

z _k represents the number of individuals in the kth ^th subspace;

Δf _k,i represents the sum of the differences in the fitness values of the child individuals and the parent individuals in the kth ^th subspace;

Meanwhile, Δf _k,i with a positive real number as a reserved result is stored in a set V _k, k e {1,2,.. The n } and the corresponding parameters are stored in a set R _k, k e {1,2,.. The n };

establishing a hybrid Gaussian model according to data in a set Mu is the mean and σ ² is the variance:

calculating parameters required by Gaussian distribution by using formulas (14) - (15):

Wherein, the Representing the mean value of the dominant parameter information in the subspace;

Representing the mean value of the dominant parameter information in the kth ^th subspace;

r _k,j represents an individual whose jth sub-generation adaptation value is better than the parent adaptation value in the kth subspace;

representing the variance of the dominant parameter information in the kth ^th subspace;

the difference delta f _k,i between the adaptation value of the parent and the adaptation value of the child in the k ^th th subspace is the number of positive real numbers.

Preferably, the module M2 further comprises:

When there are n subspaces, the dominant parameter distribution for each subspace is Different subspaces have dominant parameter models with different Gaussian distributions, and the difference information of parent and offspring stored in V _k and k epsilon {1,2,.. N } is used for judging the contribution value w of dominant parameters in the different subspaces to the whole population when the current generation is evolved;

The specific mathematical description is as follows:

w_k＝∑V_k/(∑V₁+∑V₂+...+∑V_n),k∈{1,2,...,n} (16)

w _k represents a numerical representation of the contribution of the dominant parameter in the kth subspace to the whole population;

V _k, k e {1,2,., n } represents the sum of fitness value differences of individuals whose offspring perform better than the parent in the entire population;

From building a dominant parametric model mixture gaussian model of the whole population, the mean and variance are generated using equations (17) and (18):

Compared with the prior art, the invention has the following beneficial effects:

1. By adopting the space advantage information extraction method, the target space can be effectively partitioned, so that the sub-population has own search area, and meanwhile, the advantage information in different sub-spaces is extracted, the evolution of individuals is guided, and the convergence speed of a population intelligent algorithm is accelerated;

2. by adopting the space advantage information extraction method, the advantage parameter information contained in the advantage individuals in different evolution stages can be effectively stored and utilized, the optimal control parameters are provided for different stages of the group intelligent algorithm, and the performance of the algorithm is improved;

3. and establishing a parameter space associated with the original population space, realizing information interaction between the two spaces, and improving the autonomous adjustment capability of algorithm control parameters.

Drawings

Other features, objects and advantages of the present invention will become more apparent upon reading of the detailed description of non-limiting embodiments, given with reference to the accompanying drawings in which:

FIG. 1 is a flowchart of an algorithm;

Fig. 2 is a dominant information extraction process.

Detailed Description

The present invention will be described in detail with reference to specific examples. The following examples will assist those skilled in the art in further understanding the present invention, but are not intended to limit the invention in any way. It should be noted that variations and modifications could be made by those skilled in the art without departing from the inventive concept. These are all within the scope of the present invention.

The embodiment of the invention provides a multi-objective optimization method based on dominant information extraction, which can be applied to various multi-objective group intelligent algorithms, and aims to improve the capability of the algorithms for fully extracting dominant information in the calculation process, guide evolution, greatly improve the searching capability and multi-objective weighing capability of the algorithms, ensure that the algorithms can efficiently optimize the actual industrial production process and improve economic benefits. The industrial production process comprises at least ten or more control conditions such as temperature, raw material input amount, intermediate product content and the like, and at least two optimization targets such as yield, cost or profit and the like. Referring to fig. 1 and 2, the method specifically includes the following steps:

S1, extracting space advantage information and obtaining a space partition result;

first, the adaptive value f obtained by calculation is normalized to between 0 and 1, and the vector form is as follows:

Wherein, the Representing the adaptation value after normalization operation;

x represents a decision variable, x _i represents an ith decision variable;

n represents N decision variables;

m represents m objective functions, wherein i and j respectively represent a designated ith decision variable and a jth objective function;

f' (x _i) represents the set of adaptation values obtained by the ith decision variable x _i on all objective functions;

[. ] ^T represents a transpose of the set;

The reference point is used as a boundary in the target space division method, and the maximum value and the minimum value of all target functions in each dimension are formed by the following steps: And

T represents the selected t dimension;

rp _max consists of the maximum of one objective function and the minimum of the remaining functions;

rp _min consists of the minimum of all objective functions;

The vector angle between the fitness value f' and the reference point Rp _max is calculated using formula (3):

θ=arccos(f′(x),Rp_max) (3)

Wherein, the the expression. Norms of vectors;

calculating a vector angle beta between reference points:

β_(t,j)＝arccos(Rp_max,t,Rp_max,j),t∈{1,2,...,m},j∈{1,2,...,m},t≠j (5)

when the number of the objective functions exceeds two, randomly selecting reference points corresponding to the adaptive values of the two objective functions to calculate vector angles, (t, j) are the selected t, j objective functions;

according to the vector angle between the reference points and the vector angle between the adaptive value and the reference points obtained through calculation, each individual participating in evolution is endowed with a 0-1 label belonging to the individual by using a formula (6):

Sn _i represents the label of the ith decision variable, and the label set of all decision variables is represented by Sn;

Obtaining dominant individuals P _best contained in a sub-solution set obtained from each generation in the evolution process;

dividing a target space into n subspaces through formulas (1) - (6), wherein the population X is also divided into a plurality of corresponding sub-populations;

calculating the central position of each subspace by using a formula (7), wherein the directions of the reference points Rp _min and the central position are the optimal evolution directions of each subspace;

where T _k represents the center position and z _k represents the number of individuals in the kth ^th subspace.

Next, the distances of all individuals in the kth ^th subspace and the reference point Rp _min in the optimal evolutionary direction are calculated;

Among all the distances obtained by the calculation, the individual having the shortest distance is defined as the optimal individual P _best,k in the subspace;

The number of all individuals in the kth ^th subspace is denoted by z _k;

d_i,k＝||f′(x_i,k)||cos(f′(x_i,k),T_k),k＝1,2,...,n,i＝1,2,...,z_k (8)

Where d _i,k denotes the distance between the ith individual and the reference point Rp _min in the optimal evolution direction in the kth subspace;

f' (x _i,k) denotes the adaptation value of the decision variable xi in the kth subspace;

Step S2, extracting parameter space advantage information according to the acquired space partition result, and fully applying the parameter information contained in the advantage individuals in different evolution stages;

setting that each individual participating in evolution has own parameters and certain intelligence, and calculating the difference value of the adaptation value of the parent individual and the adaptation value of the child individual by using the result of the space partition in the step 1 through a formula (10);

wherein k represents the k ^th th subspace;

z _k represents the number of individuals in the kth ^th subspace;

Δf _k,i represents the sum of the differences in the fitness values of the child individuals and the parent individuals in the kth ^th subspace;

Meanwhile, Δf _k,i with a positive real number as a reserved result is stored in a set V _k, k e {1,2,.. The n } and the corresponding parameters are stored in a set R _k, k e {1,2,.. The n };

establishing a hybrid Gaussian model according to data in a set Mu is the mean and σ ² is the variance:

calculating parameters required by Gaussian distribution by using formulas (14) - (15):

Wherein, the Representing the mean value of the dominant parameter information in the subspace;

Representing the mean value of the dominant parameter information in the kth ^th subspace;

r _k,j represents an individual whose jth sub-generation adaptation value is better than the parent adaptation value in the kth subspace;

representing the variance of the dominant parameter information in the kth ^th subspace;

the difference delta f _k,i between the adaptation value of the parent and the adaptation value of the child in the k ^th th subspace is the number of positive real numbers.

When there are n subspaces, the dominant parameter distribution for each subspace isDifferent subspaces have dominant parameter models with different Gaussian distributions, and the difference information of parent and offspring stored in V _k and k epsilon {1,2,.. N } is used for judging the contribution value w of dominant parameters in the different subspaces to the whole population when the current generation is evolved;

The specific mathematical description is as follows:

w_k＝∑V_k/(∑V₁+∑V₂+...+∑V_n),k∈{1,2,...,n} (16)

w _k represents a numerical representation of the contribution of the dominant parameter in the kth subspace to the whole population;

V _k, k.epsilon.1, 2, the sum of n represents the sum of the difference in fitness values of individuals whose children perform better than the parent in the whole population, and the different subspaces are linked together according to their contribution.

From building a dominant parametric model mixture gaussian model of the whole population, the mean and variance are generated using equations (17) and (18):

And step S3, selecting optimal individuals distributed in different areas according to the parameter information, and guiding the evolution process.

The invention also provides a multi-objective optimization system based on the dominant information extraction, which comprises:

the module M1 is used for extracting space advantage information and acquiring a space partition result;

the module M2 extracts parameter space advantage information according to the acquired space partition result and fully applies the parameter information contained in the dominant individuals in different evolution stages;

and the module M3 is used for selecting optimal individuals distributed in different areas according to the parameter information and guiding the evolution process.

Specifically, the module M1 includes:

The adaptation value f obtained by calculation is normalized to be between 0 and 1, and the vector form is as follows:

Wherein, the Representing the adaptation value after normalization operation;

x represents a decision variable, x _i represents an ith decision variable;

n represents N decision variables;

m represents m objective functions, wherein i and j respectively represent a designated ith decision variable and a jth objective function;

f' (x _i) represents the set of adaptation values obtained by the ith decision variable x _i on all objective functions;

[. ] ^T represents a transpose of the set;

The maximum and minimum values of all objective functions in each dimension consist of:

And

T represents the selected t dimension;

rp _max consists of the maximum of one objective function and the minimum of the remaining functions;

rp _min consists of the minimum of all objective functions;

The vector angle between the fitness value f' and the reference point Rp _max is calculated using formula (3):

θ=arccos(f′(x),Rp_max) (3)

Wherein, the the expression. Norms of vectors;

calculating a vector angle beta between reference points:

β_(t,j)＝arccos(Rp_max,t,Rp_max,j),t∈{1,2,...,m},j∈{1,2,...,m},t≠j (5)

when the number of the objective functions exceeds two, randomly selecting reference points corresponding to the adaptive values of the two objective functions to calculate vector angles, (t, j) are the selected t, j objective functions;

according to the vector angle between the reference points and the vector angle between the adaptive value and the reference points obtained through calculation, each individual participating in evolution is endowed with a 0-1 label belonging to the individual by using a formula (6):

Sn _i represents the label of the ith decision variable, and the label set of all decision variables is represented by Sn;

Obtaining dominant individuals P _best contained in a sub-solution set obtained from each generation in the evolution process;

dividing a target space into n subspaces through formulas (1) - (6), wherein the population X is also divided into a plurality of corresponding sub-populations;

calculating the central position of each subspace by using a formula (7), wherein the directions of the reference points Rp _min and the central position are the optimal evolution directions of each subspace;

where T _k represents the center position and z _k represents the number of individuals in the kth ^th subspace.

Calculating the distances between all individuals in the k ^th subspace and the reference point Rp _min in the optimal evolution direction;

Among all the distances obtained by the calculation, the individual having the shortest distance is defined as the optimal individual P _best,k in the subspace;

The number of all individuals in the kth ^th subspace is denoted by z _k;

d_i,k＝||f′(x_i,k)||cos(f′(x_i,k),T_k),k＝1,2,...,n,i＝1,2,...,z_k (8)

d_min,k＝min(d_1,k,d_2,k,d_3,k,...,d_zk,k); (9)

Where d _i,k denotes the distance between the ith individual and the reference point Rp _min in the optimal evolution direction in the kth subspace;

f' (x _i,k) denotes the adaptation value of the decision variable xi in the kth subspace;

The module M2 includes:

Calculating the difference between the adaptation value of the parent individual and the adaptation value of the child individual by using the result of the space partition in the step 1 through a formula (10);

wherein k represents the k ^th th subspace;

z _k represents the number of individuals in the kth ^th subspace;

Δf _k,i represents the sum of the differences in the fitness values of the child individuals and the parent individuals in the kth ^th subspace;

Meanwhile, Δf _k,i with a positive real number as a reserved result is stored in a set V _k, k e {1,2,.. The n } and the corresponding parameters are stored in a set R _k, k e {1,2,.. The n };

establishing a hybrid Gaussian model according to data in a set Mu is the mean and σ ² is the variance:

calculating parameters required by Gaussian distribution by using formulas (14) - (15):

Wherein, the Representing the mean value of the dominant parameter information in the subspace;

Representing the mean value of the dominant parameter information in the kth ^th subspace;

r _k,j represents an individual whose jth sub-generation adaptation value is better than the parent adaptation value in the kth subspace;

representing the variance of the dominant parameter information in the kth ^th subspace;

the difference delta f _k,i between the adaptation value of the parent and the adaptation value of the child in the k ^th th subspace is the number of positive real numbers.

When there are n subspaces, the dominant parameter distribution for each subspace isDifferent subspaces have dominant parameter models with different Gaussian distributions, and the difference information of parent and offspring stored in V _k and k epsilon {1,2,.. N } is used for judging the contribution value w of dominant parameters in the different subspaces to the whole population when the current generation is evolved;

The specific mathematical description is as follows:

w_k＝∑V_k/(∑V₁+∑V₂+...+∑V_n),k∈{1,2,...,n} (16)

w _k represents a numerical representation of the contribution of the dominant parameter in the kth subspace to the whole population;

V _k, k e {1,2,., n } represents the sum of fitness value differences of individuals whose offspring perform better than the parent in the entire population;

From building a dominant parametric model mixture gaussian model of the whole population, the mean and variance are generated using equations (17) and (18):

Next, the present invention will be described in more detail.

The following description of the technical solution of the present invention will be made in detail with reference to specific examples, where objective functions of a multi-objective industrial process are set as costs, yields. Suitable population intelligent algorithms are exemplified by differential evolution algorithms.

The multi-objective optimization method based on the dominant information extraction is shown with reference to fig. 1 and 2, and comprises the following specific steps:

1. Determining an optimization target of a control system:

a mathematical model is established according to the requirements in an actual industrial control system, control conditions are used as independent variables, cost and yield are used as objective functions, and a mathematical formula is described as follows:

F(x)=[minf₁(x),...,minf_m(x)],x∈χ

x_min≤x≤x_max (19)

Where x= (x ₁,x₂,...,x_n) the range of decision variables is defined between x _min＝(x_1,min,x_2,min,...x_n,min. The objective function F (x) defines m mapping functions from the decision space to the objective space, and typically, the objective function contains several constraints:

Wherein g _j (x) represents the j-th inequality constraint;

h _j (x) represents the jth equality constraint;

p, q represent the number of inequality and equality constraints contained in the multiple objective function, respectively.

2. And (3) controlling an optimization process:

taking a differential evolution algorithm as an example, the method comprises the following steps:

S1 initializing

Randomly generating an original population S, setting the population size as N, setting the maximum evolution algebra G _max, the current generation G in the evolution process, the number N of subintervals, the adaptation value F (x) of the original population, and the normalized adaptation value

S2 evolution of population

According to the optimization function in S1, the objective function value is calculated, the advantage information is extracted by adopting the method, firstly, the adaptive value f obtained through calculation is normalized to be between 0 and 1, and the vector form is as follows:

The reference points are used as boundaries in the object space division method, are not randomly generated, but are composed of the maximum value and the minimum value of all object functions in each dimension: And

Rp _max consists of the maximum of one objective function and the minimum of the remaining functions, rp _min consists of the minimum of all objective functions.

The vector angle between the fitness value f' and the reference point Rp _max is calculated using formula (23):

θ=arccos(f′(x),Rp_max) (23)

calculating a vector angle beta between reference points:

β_(t,j)＝arccos(Rp_max,t,Rp_max,j),t∈{1,2,...,m},j∈{1,2,...,m},t≠j (25)

And when the number of the objective functions exceeds two, randomly selecting reference points corresponding to the adaptive values of the two objective functions to calculate vector angles. (t, j) is the selected t, j objective function. According to the vector angle between the reference points and the vector angle between the adaptive value and the reference points obtained by calculation, each individual participating in evolution is given a 0-1 tag belonging to the individual using the formula (26):

Where n is the number of subspaces.

Through S1 and S2, the target space is divided into n subspaces, the population X is also divided into a plurality of corresponding sub-populations, the central position of each subspace is calculated by using a formula (27), the direction defining the reference point Rp _min and the central position is the optimal evolution direction of each subspace, and T _k represents the central position.

The distances of all individuals in the k ^th th subspace and the reference point Rp _min in the optimal evolutionary direction are calculated. The individual having the shortest distance among all the distances obtained by the calculation is defined as the optimal individual P _best,k in the subspace. The number of all individuals in the kth ^th subspace is denoted by z _k.

d_i,k＝||f′(x_i,k)||cos(f′(x_i,k),T_k),k＝1,2,...,n,i＝1,2,...,z_k (28)

Simultaneously selecting dominant individuals x _best,k in each subinterval;

Mutation strategy:

DE/best/2:

and calculating the adaptive value of the body objective function after the mutation operation, and selecting the population.

Selection operation:

If it is Dominance ofThenWill be retained in population S ^G. If it isDominance ofThenCan replaceStored in population S ^G. If it isAndNot mutually dominate, thenAndWill be stored in population S ^G. N individuals are selected by non-dominant solution sorting and crowding distance sorting to maintain the population size, and a next generation population S ^G+1 is generated.

S3, parameter space advantage information extraction method

The parameters of the group intelligent algorithm play an important role in the calculation effect of the algorithm. Calculating the difference between the adaptation value of the parent individual and the adaptation value of the child individual by the formula (31),

Where k represents the k ^th th subspace, z _k represents the number of individuals in the k ^th th subspace, and Δf _k,i represents the sum of the differences in the fitness values of the child and parent individuals in the k ^th th subspace. Meanwhile, Δf _k,i whose reserved result is a positive real number is stored in set V _k, k e {1,2,..n } and its corresponding parameters are stored in set R _k, k e {1,2,..n }. Establishing a hybrid Gaussian model according to data in a setMu is the mean and σ ² is the variance:

calculating parameters required by Gaussian distribution by using formulas (35) - (36):

Wherein, the Representing the mean value of the dominant parameter information in the kth ^th subspace; representing the variance of the dominant parameter information in the kth ^th subspace; the difference delta f _k,i between the adaptation value of the parent and the adaptation value of the child in the k ^th th subspace is the number of positive real numbers.

When there are n subspaces, the dominant parameter distribution for each subspace isDifferent subspaces have dominant parameter models with different gaussian distributions, and the difference information of parent and offspring stored in V _k, k epsilon {1,2,.. N } is used for judging the contribution value w of the dominant parameters in the different subspaces to the whole population when the current generation is evolved. The specific mathematical description is as follows:

w_k＝∑V_k/(∑V₁+∑V₂+...+∑V_n),k∈{1,2,...,n} (37)

V _k, k e {1,2,..n } represents the sum of fitness value differences for individuals whose children perform better than their parents in the entire population. And according to the contribution degree of the different subspaces, the different subspaces are connected together. From building a dominant parametric model mixture gaussian model for the whole population, the mean and variance are generated using equations (38) and (39):

And S4, updating the evolution algebra, if G=G _max, ending the whole evolution process, and if G does not reach G _max, repeating S2-S4.

The embodiment of the invention provides a multi-objective optimization method and a multi-objective optimization system based on dominant information extraction, which aim at solving the problem that the multi-objective problem has multiple dimensions and is not unique, and provides a method for extracting space dominant information, so that the utilization rate of effective information in an objective space is improved;

Aiming at the problem that the group intelligent algorithm has different requirements on parameters in different evolutionary stages, a method for extracting the parameter space advantage information is provided, so that the parameter information contained in the dominant individuals in different evolutionary stages can be fully applied, and the performance of the algorithm is improved;

Aiming at the problem that a large number of non-dominant solutions exist when solving the multi-objective problem, the optimal individuals distributed in different areas are selected to guide the evolution process, so that the computation complexity of a group intelligent algorithm is reduced, and the convergence speed is increased.

Those skilled in the art will appreciate that the invention provides a system and its individual devices, modules, units, etc. that can be implemented entirely by logic programming of method steps, in addition to being implemented as pure computer readable program code, in the form of logic gates, switches, application specific integrated circuits, programmable logic controllers, embedded microcontrollers, etc. Therefore, the system and the devices, modules and units thereof provided by the invention can be regarded as a hardware component, and the devices, modules and units for realizing various functions included in the system can be regarded as structures in the hardware component, and the devices, modules and units for realizing various functions can be regarded as structures in the hardware component as well as software modules for realizing the method.

The foregoing describes specific embodiments of the present application. It is to be understood that the application is not limited to the particular embodiments described above, and that various changes or modifications may be made by those skilled in the art within the scope of the appended claims without affecting the spirit of the application. The embodiments of the application and the features of the embodiments may be combined with each other arbitrarily without conflict.

Claims (8)

1. The multi-objective optimization method based on the dominant information extraction is characterized by comprising the following steps of:

S1, extracting space advantage information and obtaining a space partition result;

Step S2, extracting parameter space advantage information according to the acquired space partition result, and fully applying the parameter information contained in the advantage individuals in different evolution stages;

step S3, selecting optimal individuals distributed in different areas according to the parameter information, and guiding the evolution process;

The step S1 includes:

The adaptation value f obtained by calculation is normalized to be between 0 and 1, and the vector form is as follows:

Wherein, the Representing the adaptation value after normalization operation;

x represents a decision variable, x _i represents an ith decision variable;

n represents N decision variables;

m represents m objective functions, wherein i and j respectively represent a designated ith decision variable and a jth objective function;

f' (x _i) represents the set of adaptation values obtained by the ith decision variable x _i on all objective functions;

[. ] ^T represents a transpose of the set;

The maximum and minimum values of all objective functions in each dimension are Rp _max＝(f₁ ^min,K,f_t ^max,K f_m ^min), t +.m, t +.1, 2, k, m and Rp _min＝(f₁ ^min,f₂ ^min,K f_m ^min), t +.m, t +.1, 2, k, m;

t represents the selected t dimension;

rp _max consists of the maximum of one objective function and the minimum of the remaining functions;

rp _min consists of the minimum of all objective functions;

The vector angle between the fitness value f' and the reference point Rp _max is calculated using formula (3):

θ=arccos(f′(x),Rp_max) (3)

Wherein, the the expression. Norms of vectors;

calculating a vector angle beta between reference points:

β_(t,j)＝arccos(Rp_max,t,Rp_max,j),t∈{1,2,K,m},j∈{1,2,K,m},t≠j (5)

when the number of the objective functions exceeds two, randomly selecting reference points corresponding to the adaptive values of the two objective functions to calculate vector angles, (t, j) are the selected t, j objective functions;

according to the vector angle between the reference points and the vector angle between the adaptive value and the reference points obtained through calculation, each individual participating in evolution is endowed with a 0-1 label belonging to the individual by using a formula (6):

Sn _i represents the label of the ith decision variable, and the label set of all decision variables is represented by Sn;

Obtaining dominant individuals P _best contained in a sub-solution set obtained from each generation in the evolution process;

dividing a target space into n subspaces through formulas (1) - (6), wherein the population X is also divided into a plurality of corresponding sub-populations;

calculating the central position of each subspace by using a formula (7), wherein the directions of the reference points Rp _min and the central position are the optimal evolution directions of each subspace;

where T _k represents the center position and z _k represents the number of individuals in the kth ^th subspace.

2. The multi-objective optimization method based on dominant information extraction of claim 1, wherein the step S1 further comprises:

Calculating the distances between all individuals in the k ^th subspace and the reference point Rp _min in the optimal evolution direction;

Among all the distances obtained by the calculation, the individual having the shortest distance is defined as the optimal individual P _best,k in the subspace;

The number of all individuals in the kth ^th subspace is denoted by z _k;

d_i,k＝||f′(x_i,k)||cos(f′(x_i,k),T_k),k＝1,2,K,n,i＝1,2,K,z_k (8)

Where d _i,k denotes the distance between the ith individual and the reference point Rp _min in the optimal evolution direction in the kth subspace and f' (x _i,k) denotes the fitness value of the decision variable xi in the kth subspace.

3. The multi-objective optimization method based on dominant information extraction according to claim 2, wherein the step S2 comprises:

calculating the difference between the adaptation value of the parent individual and the adaptation value of the child individual by using the result of the spatial partitioning in the step S1 through a formula (10);

wherein k represents the k ^th th subspace;

z _k represents the number of individuals in the kth ^th subspace;

Δf _k,i represents the sum of the differences in the fitness values of the child individuals and the parent individuals in the kth ^th subspace;

meanwhile, Δf _k,i with a positive real number as a reserved result is stored in a set V _k, k epsilon {1,2, K, n }, and corresponding parameters are stored in a set R _k, k epsilon {1,2, K, n };

establishing a hybrid Gaussian model according to data in a set Mu is the mean and σ ² is the variance:

calculating parameters required by Gaussian distribution by using formulas (14) - (15):

Wherein, the Representing the mean value of the dominant parameter information in the subspace;

Representing the mean value of the dominant parameter information in the kth ^th subspace;

r _k,j represents an individual whose jth sub-generation adaptation value is better than the parent adaptation value in the kth subspace;

representing the variance of the dominant parameter information in the kth ^th subspace;

the difference delta f _k,i between the adaptation value of the parent and the adaptation value of the child in the k ^th th subspace is the number of positive real numbers.

4. The multi-objective optimization method based on dominant information extraction as claimed in claim 3, wherein said step S2 further comprises:

When there are n subspaces, the dominant parameter distribution for each subspace is Different subspaces have dominant parameter models with different Gaussian distributions, and the difference information of parent and offspring stored in V _k and k E {1,2, K and n } is used for judging the contribution degree w of dominant parameters in different subspaces to the whole population when the current generation is evolved;

The specific mathematical description is as follows:

w_k＝∑V_k/(∑V₁+∑V₂+K+∑V_n),k∈{1,2,K,n} (16)

w _k represents a numerical representation of the contribution of the dominant parameter in the kth subspace to the whole population;

V _k, the sum of k E {1,2, K, n } represents the sum of the fitness value differences of individuals whose offspring perform better than the parent in the whole population;

From building a dominant parametric model mixture gaussian model of the whole population, the mean and variance are generated using equations (17) and (18):

5. a multi-objective optimization system based on dominant information extraction, comprising:

the module M1 is used for extracting space advantage information and acquiring a space partition result;

the module M2 extracts parameter space advantage information according to the acquired space partition result and fully applies the parameter information contained in the dominant individuals in different evolution stages;

the module M3 is used for selecting optimal individuals distributed in different areas according to the parameter information and guiding the evolution process;

The module M1 includes:

The adaptation value f obtained by calculation is normalized to be between 0 and 1, and the vector form is as follows:

Wherein, the Representing the adaptation value after normalization operation;

x represents a decision variable, x _i represents an ith decision variable;

n represents N decision variables;

m represents m objective functions, wherein i and j respectively represent a designated ith decision variable and a jth objective function;

f' (x _i) represents the set of adaptation values obtained by the ith decision variable x _i on all objective functions;

[. ] ^T represents a transpose of the set;

The maximum and minimum values of all objective functions in each dimension are Rp _max＝(f₁ ^min,K,f_t ^max,K f_m ^min), t +.m, t +.1, 2, k, m and Rp _min＝(f₁ ^min,f₂ ^min,K f_m ^min), t +.m, t +.1, 2, k, m;

t represents the selected t dimension;

rp _max consists of the maximum of one objective function and the minimum of the remaining functions;

rp _min consists of the minimum of all objective functions;

The vector angle between the fitness value f' and the reference point Rp _max is calculated using formula (3):

θ=arccos(f′(x),Rp_max) (3)

Wherein, the the expression. Norms of vectors;

calculating a vector angle beta between reference points:

β_(t,j)＝arccos(Rp_max,t,Rp_max,j),t∈{1,2,K,m},j∈{1,2,K,m},t≠j (5)

when the number of the objective functions exceeds two, randomly selecting reference points corresponding to the adaptive values of the two objective functions to calculate vector angles, (t, j) are the selected t, j objective functions;

according to the vector angle between the reference points and the vector angle between the adaptive value and the reference points obtained through calculation, each individual participating in evolution is endowed with a 0-1 label belonging to the individual by using a formula (6):

Sn _i represents the label of the ith decision variable, and the label set of all decision variables is represented by Sn;

Obtaining dominant individuals P _best contained in a sub-solution set obtained from each generation in the evolution process;

dividing a target space into n subspaces through formulas (1) - (6), wherein the population X is also divided into a plurality of corresponding sub-populations;

calculating the central position of each subspace by using a formula (7), wherein the directions of the reference points Rp _min and the central position are the optimal evolution directions of each subspace;

where T _k represents the center position and z _k represents the number of individuals in the kth ^th subspace.

6. The multi-objective optimization system based on dominant information extraction of claim 5, wherein the module M1 further comprises:

Calculating the distances between all individuals in the k ^th subspace and the reference point Rp _min in the optimal evolution direction;

Among all the distances obtained by the calculation, the individual having the shortest distance is defined as the optimal individual P _best,k in the subspace;

The number of all individuals in the kth ^th subspace is denoted by z _k;

d_i,k＝||f′(x_i,k)||cos(f′(x_i,k),T_k),k＝1,2,K,n,i＝1,2,K,z_k (8)

Where d _i,k denotes the distance between the ith individual and the reference point Rp _min in the optimal evolution direction in the kth subspace;

f' (x _i,k) represents the adaptation value of the decision variable xi in the kth subspace.

7. The multi-objective optimization system based on dominant information extraction of claim 6, wherein the module M2 comprises:

calculating the difference between the adaptation value of the parent individual and the adaptation value of the child individual by using the result of the spatial partitioning in the step S1 through a formula (10);

wherein k represents the k ^th th subspace;

z _k represents the number of individuals in the kth ^th subspace;

Δf _k,i represents the sum of the differences in the fitness values of the child individuals and the parent individuals in the kth ^th subspace;

meanwhile, Δf _k,i with a positive real number as a reserved result is stored in a set V _k, k epsilon {1,2, K, n }, and corresponding parameters are stored in a set R _k, k epsilon {1,2, K, n };

establishing a hybrid Gaussian model according to data in a set Mu is the mean and σ ² is the variance:

calculating parameters required by Gaussian distribution by using formulas (14) - (15):

Wherein, the Representing the mean value of the dominant parameter information in the subspace;

Representing the mean value of the dominant parameter information in the kth ^th subspace;

r _k,j represents an individual whose jth sub-generation adaptation value is better than the parent adaptation value in the kth subspace;

representing the variance of the dominant parameter information in the kth ^th subspace;

the difference delta f _k,i between the adaptation value of the parent and the adaptation value of the child in the k ^th th subspace is the number of positive real numbers.

8. The multi-objective optimization system based on dominant information extraction of claim 7, wherein the module M2 further comprises:

When there are n subspaces, the dominant parameter distribution for each subspace is Different subspaces have dominant parameter models with different Gaussian distributions, and the difference information of parent and offspring stored in V _k and k E {1,2, K and n } is used for judging the contribution degree w of dominant parameters in different subspaces to the whole population when the current generation is evolved;

The specific mathematical description is as follows:

w_k＝∑V_k/(∑V₁+∑V₂+K+∑V_n),k∈{1,2,K,n} (16)

w _k represents a numerical representation of the contribution of the dominant parameter in the kth subspace to the whole population;

V _k, the sum of k E {1,2, K, n } represents the sum of the fitness value differences of individuals whose offspring perform better than the parent in the whole population;

From building a dominant parametric model mixture gaussian model of the whole population, the mean and variance are generated using equations (17) and (18):