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

Abstract

The present invention provides a multi-objective optimization method and system based on advantage information extraction, relating to the technical field of communication system design. The method comprises: step S1: extracting spatial advantage information and obtaining spatial partitioning results; step S2: extracting parameter space advantage information based on the obtained spatial partitioning results, and fully utilizing the parameter information contained in the advantaged individuals at different evolutionary stages; and step S3: selecting the optimal individuals distributed in different regions based on the parameter information to guide the evolution process. The present invention can fully extract advantage information during the calculation process to guide evolution, greatly improving the algorithm's search capability and multi-objective trade-off capabilities, enabling the algorithm to efficiently optimize actual industrial production processes and improve economic benefits.

Description

Technical Field

[0001] The present invention relates to the technical field of communication system design, and in particular to a multi-objective optimization method and system based on advantage information extraction. Background Art

[0002] With the development of society and the advancement of technology, the scale of industrial processes has become larger and larger, and the process flows have become more complex, with more constraints and increasing nonlinearity. This complexity of process technology has posed a huge challenge to the requirements of actual production.

[0003] Explanation of proper nouns:

[0004] Advantage information: defines the information contained in the target space that is beneficial to the evolution of individuals approaching the optimal frontier.

[0005] Optimal evolution direction: defines the direction between the reference point and the center position.

[0006] Optimal individual: Define the distance between all individuals in the calculation subspace and the reference point in the optimal evolutionary direction. The individual with the shortest distance among all distances is the optimal individual in the subspace.

[0007] Contribution value: defines the percentage of individuals in the subspace whose fitness value between the parent individual and the offspring individual is positive to the total number of individuals.

[0008] Swarm intelligence algorithms simulate the collaborative behavior of biological groups in nature and the survival of the fittest principles that exist among individual organisms, demonstrating excellent global search capabilities. The presence of a swarm allows for the parallel computation of multiple solutions within a single computational process, resulting in high computational efficiency and versatility. This approach also offers significant advantages in solving large-scale optimization problems. Multi-objective algorithms often yield not a single solution but a set of solutions encompassing several. The effectiveness of solving practical industrial production problems is significantly influenced by the computational methods used. Exploiting the optimal information from the computational process to accelerate the convergence of optimization algorithms and increase population diversity remains a challenge that has yet to be fully addressed.

[0009] The invention patent with publication number CN112822058A discloses a multi-objective optimization design method based on the effective area. It adopts the bacterial foraging algorithm to take the communication system optimization design objective function as the fitness value of the bacterial tendency movement to jointly optimize multiple design objectives of the communication system. The bacteria use adaptive step size and direction to swim to the global optimal position in the set effective area, and at the same time use dynamic retention ratio to continuously update the bacterial colony. Finally, the optimal design scheme of the system is obtained by finding the best reconciliation solution of the bacterial colony. This patent uses a bacterial colony foraging algorithm to perform multi-objective optimization of the communication system. The effective area designed in the initial stage of the method is based on experience. In the generated optimal solution set, the individuals with the highest crowding distance are selected to form the optimal pool, and then the global optimal bacteria are randomly selected from it. This operation has a certain degree of randomness and requires a high level of prior knowledge of the application object.

[0010] The invention patent, publication number CN108564163B, discloses an improved ant colony algorithm for solving the multi-objective multi-traveling salesman problem. After randomly initializing the pheromone matrix, the ant colony uses an improved state transition formula combined with a round-robin selection algorithm to sequentially select the next delivery point until a feasible solution is constructed. The feasible solution is weighted and scored, and this score is used as a benchmark for the amount of pheromone added. Multiple rounds of pheromone additions are performed in varying amounts, taking into account multiple characteristics of the sub-paths. This invention improves the ant colony algorithm. As the number of iterations increases throughout the optimization process, a positive feedback mechanism will continuously expand the pheromone differences on different paths, guiding the entire system to evolve in the optimal direction. This method has certain limitations; pheromones are not present when the ant colony algorithm is not used. Summary of the Invention

[0011] In view of the defects in the prior art, the present invention provides a multi-objective optimization method and system based on advantage information extraction.

[0012] According to a multi-objective optimization method and system based on advantage information extraction provided by the present invention, the scheme is as follows:

[0013] In a first aspect, a multi-objective optimization method based on advantage information extraction is provided, the method comprising:

[0014] Step S1: extracting spatial advantage information and obtaining spatial partitioning results;

[0015] Step S2: extracting parameter space advantage information based on the obtained spatial partitioning results, and making full use of the parameter information contained in the dominant individuals at different evolutionary stages;

[0016] Step S3: Based on the parameter information, the optimal individuals distributed in different areas are selected to guide the evolution process.

[0017] Preferably, the step S1 includes:

[0018] The calculated fitness value f is normalized to between 0 and 1, and the vector form is as follows:

[0019]

[0020]

[0021] in, Represents the fitness value after normalization operation;

[0022] x represents the decision variable, x i represents the i-th decision variable;

[0023] N means there are N decision variables;

[0024] m means there are m objective functions, where i and j represent the specified i-th decision variable and j-th objective function respectively;

[0025] f′(x i ) represents the i-th decision variable x i The set of fitness values ​​obtained on all objective functions;

[0026] [.] T Represents the transpose of a set;

[0027] The maximum and minimum values ​​of all objective functions in each dimension are composed of:

[0028] and

[0029]

[0030] t represents the selected tth dimension;

[0031] Rp max It consists of the maximum value of an objective function and the minimum value of the remaining functions;

[0032] Rp min It consists of the minimum values ​​of all objective functions;

[0033] Use formula (3) to calculate the adaptation value f′ and reference point Rp max The vector angle between:

[0034] θ=arccos(f′(x),Rp max )(3)

[0035]

[0036] Among them, ||.|| represents the norm of the vector;

[0037] Calculate the vector angle β between the reference points:

[0038] β (t,j) =arccos(Rp max,t ,Rp max,j ),t∈{1,2,...,m},j∈{1,2,...,m},t≠j (5)

[0039] When the number of objective functions exceeds two, the reference points corresponding to the fitness values ​​of two objective functions are randomly selected to calculate the vector angle, and (t, j) is the selected t, jth objective function;

[0040] According to the calculated vector angles between reference points and the vector angles between fitness value and reference points, each individual participating in the evolution is given a 0-1 label of its own using formula (6):

[0041]

[0042] Where n is the number of subspaces; Sn i represents the label of the i-th decision variable, and the label set of all decision variables is represented by Sn;

[0043] Obtain the dominant individual P contained in the sub-solution set obtained in each generation during the evolution process best ;

[0044] By using formulas (1) to (6), the target space is divided into n subspaces, and the population X is also divided into several corresponding subpopulations;

[0045] Use formula (7) to calculate the center position of each subspace, the reference point Rp min The direction with respect to the center position is the optimal evolution direction of each subspace;

[0046]

[0047] Among them, T k Indicates the center position, z k Represents the kth th The number of individuals in a subspace.

[0048] Preferably, the step S1 further includes:

[0049] Calculate the kth th All individuals in the subspace and the reference point Rp in the optimal evolution direction min distance;

[0050] Among all the distances calculated, the individual with the shortest distance is defined as the optimal individual P in the subspace. best,k ;

[0051] kth th The number of all individuals in the subspace is z k express;

[0052] d i,k =||f′(x i,k )||cos(f′(x i,k ),T k ),k=1,2,...,n,i=1,2,...,z k (8)

[0053]

[0054] Among them, d i,k Indicates the reference point Rp between the i-th individual and the optimal evolutionary direction in the k-th subspace min the distance between them;

[0055] f′(x i,k ) represents the fitness value of the decision variable xi in the kth subspace;

[0056] Preferably, the step S2 includes:

[0057] The result of spatial partitioning in step S1 is used to calculate the difference between the fitness value of the parent individual and the fitness value of the offspring individual through formula (10);

[0058]

[0059] Among them, k represents the kth th subspaces;

[0060] z k Represents the kth th The number of individuals in a subspace;

[0061] Δf k,i Represents the kth th The sum of the differences between the fitness values ​​of offspring individuals and parent individuals in the subspace;

[0062] At the same time, retain the Δf that is a positive real number k,i Stored in set V k ,k∈{1,2,...,n}, and its corresponding parameters are stored in the set R k ,k∈{1,2,...,n};

[0063] Build a Gaussian mixture model based on the data in the collection μ is the mean, σ 2 is the variance:

[0064]

[0065]

[0066]

[0067] Use formulas (14) and (15) to calculate the parameters required for Gaussian distribution:

[0068]

[0069]

[0070] in, Represents the mean of the dominant parameter information in the subspace;

[0071] Represents the kth th The mean of the dominant parameter information in the subspace;

[0072] R k,j Indicates that in the k-th subspace, the fitness value of the j-th offspring is better than that of the parent;

[0073] Represents the kth th The variance of the dominant parameter information in the subspace;

[0074] Represents the kth th The difference Δf between the fitness value of the parent individual and the fitness value of the offspring individual in the subspace k,i is the number of positive real numbers.

[0075] Preferably, the step S2 further includes:

[0076] When there are n subspaces, the advantage parameter distribution of each subspace is Different subspaces have different Gaussian distribution advantage parameter models, stored in V k ,The difference information of the parent and offspring in k∈{1,2,...,n} will be used to determine the contribution value w of the advantage parameters in different subspaces to the entire population in the current evolutionary generation;

[0077] The specific mathematical description is as follows:

[0078] w k =∑V k / (∑V1+∑V2+...+∑V n ),k∈{1,2,...,n} (16)

[0079] w k The numerical representation of the contribution of the dominance parameter in the kth subspace to the entire population;

[0080] V k , the sum of k∈{1,2,...,n} represents the sum of the fitness differences of individuals whose offspring perform better than their parents in the entire population;

[0081] By building a Gaussian mixture model of the dominant parameter model of the entire population, the mean and variance are generated using formulas (17) and (18):

[0082]

[0083]

[0084] In a second aspect, a multi-objective optimization system based on advantage information extraction is provided, the system comprising:

[0085] Module M1: Extract spatial advantage information and obtain spatial partitioning results;

[0086] Module M2: Extract parameter space advantage information based on the obtained spatial partitioning results and make full use of the parameter information contained in the dominant individuals at different evolutionary stages;

[0087] Module M3: Based on parameter information, select the best individuals distributed in different areas to guide the evolution process.

[0088] Preferably, the module M1 includes:

[0089] The calculated fitness value f is normalized to between 0 and 1, and the vector form is as follows:

[0090]

[0091]

[0092] in, Represents the fitness value after normalization operation;

[0093] x represents the decision variable, x i represents the i-th decision variable;

[0094] N means there are N decision variables;

[0095] m means there are m objective functions, where i and j represent the specified i-th decision variable and j-th objective function respectively;

[0096] f′(x i ) represents the i-th decision variable x i The set of fitness values ​​obtained on all objective functions;

[0097] [.] T Represents the transpose of a set;

[0098] The maximum and minimum values ​​of all objective functions in each dimension are composed of:

[0099] and

[0100]

[0101] t represents the selected tth dimension;

[0102] Rp max It consists of the maximum value of an objective function and the minimum value of the remaining functions;

[0103] Rp min It consists of the minimum values ​​of all objective functions;

[0104] Use formula (3) to calculate the adaptation value f′ and reference point Rp max The vector angle between:

[0105] θ=arccos(f′(x),Rp max ) (3)

[0106]

[0107] Among them, ||.|| represents the norm of the vector;

[0108] Calculate the vector angle β between the reference points:

[0109] β (t,j) =arccos(Rp max,t ,Rp max,j ),t∈{1,2,...,m},j∈{1,2,...,m},t≠j (5)

[0110] When the number of objective functions exceeds two, the reference points corresponding to the fitness values ​​of two objective functions are randomly selected to calculate the vector angle, and (t, j) is the selected t, jth objective function;

[0111] According to the calculated vector angles between reference points and the vector angles between fitness value and reference points, each individual participating in the evolution is given a 0-1 label of its own using formula (6):

[0112]

[0113] Where n is the number of subspaces; Sn i represents the label of the i-th decision variable, and the label set of all decision variables is represented by Sn;

[0114] Obtain the dominant individual P contained in the sub-solution set obtained in each generation during the evolution process best ;

[0115] By using formulas (1) to (6), the target space is divided into n subspaces, and the population X is also divided into several corresponding subpopulations;

[0116] Use formula (7) to calculate the center position of each subspace, the reference point Rp min The direction with respect to the center position is the optimal evolution direction of each subspace;

[0117]

[0118] Among them, T k Indicates the center position, z k Represents the kth th The number of individuals in a subspace.

[0119] Preferably, the module M1 further includes:

[0120] Calculate the kth th All individuals in the subspace and the reference point Rp in the optimal evolution direction min distance;

[0121] Among all the distances calculated, the individual with the shortest distance is defined as the optimal individual P in the subspace. best,k ;

[0122] kth th The number of all individuals in the subspace is z k express;

[0123] d i,k =||f′(x i,k )||cos(f′(x i,k ),T k ),k=1,2,...,n,i=1,2,...,z k (8)

[0124]

[0125] Among them, d i,k Indicates the reference point Rp between the i-th individual and the optimal evolutionary direction in the k-th subspace min the distance between them;

[0126] f′(x i,k ) represents the fitness value of the decision variable xi in the kth subspace;.

[0127] Preferably, the module M2 includes:

[0128] The result of spatial partitioning in step S1 is used to calculate the difference between the fitness value of the parent individual and the fitness value of the offspring individual through formula (10);

[0129]

[0130] Among them, k represents the kth th subspaces;

[0131] z k Represents the kth th The number of individuals in a subspace;

[0132] Δf k,i Represents the kth th The sum of the differences between the fitness values ​​of offspring individuals and parent individuals in the subspace;

[0133] At the same time, retain the Δf that is a positive real number k,i Stored in set V k ,k∈{1,2,...,n}, and its corresponding parameters are stored in the set R k ,k∈{1,2,...,n};

[0134] Build a Gaussian mixture model based on the data in the collection μ is the mean, σ 2 is the variance:

[0135]

[0136]

[0137]

[0138] Use formulas (14) and (15) to calculate the parameters required for Gaussian distribution:

[0139]

[0140]

[0141] in, Represents the mean of the dominant parameter information in the subspace;

[0142] Represents the kth th The mean of the dominant parameter information in the subspace;

[0143] R k,j Indicates that in the k-th subspace, the fitness value of the j-th offspring is better than that of the parent;

[0144] Represents the kth th The variance of the dominant parameter information in the subspace;

[0145] Represents the kth th The difference Δf between the fitness value of the parent individual and the fitness value of the offspring individual in the subspace k,i is the number of positive real numbers.

[0146] Preferably, the module M2 further includes:

[0147] When there are n subspaces, the advantage parameter distribution of each subspace is Different subspaces have different Gaussian distribution advantage parameter models, stored in V k ,The difference information of the parent and offspring in k∈{1,2,...,n} will be used to determine the contribution value w of the advantage parameters in different subspaces to the entire population in the current evolutionary generation;

[0148] The specific mathematical description is as follows:

[0149] w k =∑V k / (∑V1+∑V2+...+∑V n ),k∈{1,2,...,n} (16)

[0150] w k The numerical representation of the contribution of the dominance parameter in the kth subspace to the entire population;

[0151] V k , the sum of k∈{1,2,...,n} represents the sum of the fitness differences of individuals whose offspring perform better than their parents in the entire population;

[0152] By building a Gaussian mixture model of the dominant parameter model of the entire population, the mean and variance are generated using formulas (17) and (18):

[0153]

[0154]

[0155] Compared with the prior art, the present invention has the following beneficial effects:

[0156] 1. The spatial advantage information extraction method can effectively partition the target space so that the sub-population has its own search area. At the same time, the advantage information in different subspaces is extracted to guide the evolution of individuals and accelerate the convergence speed of the swarm intelligence algorithm.

[0157] 2. The spatial advantage information extraction method can effectively store and utilize the advantage parameter information contained in the advantage individuals at different evolutionary stages, provide the optimal control parameters for different stages of the swarm intelligence algorithm, and improve the performance of the algorithm;

[0158] 3. Establish a parameter space associated with the original population space to achieve information interaction between the two spaces and improve the autonomous adjustment capability of the algorithm control parameters. BRIEF DESCRIPTION OF THE DRAWINGS

[0159] Other features, objects and advantages of the present invention will become more apparent upon reading the detailed description of non-limiting embodiments with reference to the following drawings:

[0160] Figure 1 is the algorithm flow chart;

[0161] Figure 2 It is the process of extracting advantageous information. DETAILED DESCRIPTION

[0162] The present invention will be described in detail below with reference to specific embodiments. The following examples will help those skilled in the art to further understand the present invention, but are not intended to limit the present invention in any form. It should be noted that, for those skilled in the art, several changes and improvements can be made without departing from the scope of the present invention. These all fall within the scope of protection of the present invention.

[0163] The embodiment of the present invention provides a multi-objective optimization method based on advantage information extraction. The method can be applied to a variety of multi-objective swarm intelligence algorithms. The purpose is to improve the algorithm's ability to fully extract advantage information during the calculation process, guide evolution, and greatly improve the algorithm's search ability and multi-objective trade-off ability, so that the algorithm can efficiently optimize the actual industrial production process and improve economic benefits. The industrial production process contains at least ten or more control conditions, such as: temperature, raw material input, intermediate product content, etc.; and at least two optimization goals, such as: output, cost or profit, etc. Reference Figure 1 and Figure 2 As shown, the method specifically includes the following steps:

[0164] Step S1: extracting spatial advantage information and obtaining spatial partitioning results;

[0165] First, the calculated fitness value f is normalized to between 0 and 1, and the vector form is as follows:

[0166]

[0167]

[0168] in, Represents the fitness value after normalization operation;

[0169] x represents the decision variable, x i represents the i-th decision variable;

[0170] N means there are N decision variables;

[0171] m means there are m objective functions, where i and j represent the specified i-th decision variable and j-th objective function respectively;

[0172] f′(x i ) represents the i-th decision variable x i The set of fitness values ​​obtained on all objective functions;

[0173] [.] T Represents the transpose of a set;

[0174] The reference point is used as the boundary in the target space partitioning method, and the maximum and minimum values ​​of all objective functions in each dimension are composed of: and

[0175] t represents the selected tth dimension;

[0176] Rp max It consists of the maximum value of an objective function and the minimum value of the remaining functions;

[0177] Rp min It consists of the minimum values ​​of all objective functions;

[0178] Use formula (3) to calculate the adaptation value f′ and reference point Rp max The vector angle between:

[0179] θ=arccos(f′(x),Rp max ) (3)

[0180]

[0181] Among them, ||.|| represents the norm of the vector;

[0182] Calculate the vector angle β between the reference points:

[0183] β (t,j) =arccos(Rp max,t ,Rp max,j ),t∈{1,2,...,m},j∈{1,2,...,m},t≠j (5)

[0184] When the number of objective functions exceeds two, the reference points corresponding to the fitness values ​​of two objective functions are randomly selected to calculate the vector angle, and (t, j) is the selected t, jth objective function;

[0185] According to the calculated vector angles between reference points and the vector angles between fitness value and reference points, each individual participating in the evolution is given a 0-1 label of its own using formula (6):

[0186]

[0187] Where n is the number of subspaces; Sn i represents the label of the i-th decision variable, and the label set of all decision variables is represented by Sn;

[0188] Obtain the dominant individual P contained in the sub-solution set obtained in each generation during the evolution process best ;

[0189] By using formulas (1) to (6), the target space is divided into n subspaces, and the population X is also divided into several corresponding subpopulations;

[0190] Use formula (7) to calculate the center position of each subspace, the reference point Rp min The direction with respect to the center position is the optimal evolution direction of each subspace;

[0191]

[0192] Among them, T k Indicates the center position, z k Represents the kth th The number of individuals in a subspace.

[0193] Next, calculate the kth th All individuals in the subspace and the reference point Rp in the optimal evolution direction min distance;

[0194] Among all the distances calculated, the individual with the shortest distance is defined as the optimal individual P in the subspace. best,k ;

[0195] kth th The number of all individuals in the subspace is z k express;

[0196] d i,k =||f′(x i,k )||cos(f′(x i,k ),T k ),k=1,2,...,n,i=1,2,...,z k (8)

[0197]

[0198] Among them, d i,k Indicates the reference point Rp between the i-th individual and the optimal evolutionary direction in the k-th subspace min the distance between them;

[0199] f′(x i,k ) represents the fitness value of the decision variable xi in the kth subspace;

[0200] Step S2: extracting parameter space advantage information based on the obtained spatial partitioning results, and making full use of the parameter information contained in the dominant individuals at different evolutionary stages;

[0201] Assume that each individual participating in the evolution has its own parameters and a certain degree of intelligence. Use the results of the spatial partitioning in step 1 to calculate the difference between the fitness of the parent individual and the fitness of the offspring individual through formula (10);

[0202]

[0203] Among them, k represents the kth th subspaces;

[0204] z k Represents the kth th The number of individuals in a subspace;

[0205] Δf k,i Represents the kth th The sum of the differences between the fitness values ​​of offspring individuals and parent individuals in the subspace;

[0206] At the same time, retain the Δf that is a positive real number k,i Stored in set V k ,k∈{1,2,...,n}, and its corresponding parameters are stored in the set R k ,k∈{1,2,...,n};

[0207] Build a Gaussian mixture model based on the data in the collection μ is the mean, σ 2 is the variance:

[0208]

[0209]

[0210]

[0211] Use formulas (14) and (15) to calculate the parameters required for Gaussian distribution:

[0212]

[0213]

[0214] in, Represents the mean of the dominant parameter information in the subspace;

[0215] Represents the kth th The mean of the dominant parameter information in the subspace;

[0216] R k,j Indicates that in the k-th subspace, the fitness value of the j-th offspring is better than that of the parent;

[0217] Represents the kth th The variance of the dominant parameter information in the subspace;

[0218] Represents the kth th The difference Δf between the fitness value of the parent individual and the fitness value of the offspring individual in the subspace k,i is the number of positive real numbers.

[0219] When there are n subspaces, the advantage parameter distribution of each subspace is Different subspaces have different Gaussian distribution advantage parameter models, stored in V k ,The difference information of the parent and offspring in k∈{1,2,...,n} will be used to determine the contribution value w of the advantage parameters in different subspaces to the entire population in the current evolutionary generation;

[0220] The specific mathematical description is as follows:

[0221] w k =∑V k / (∑V1+∑V2+...+∑V n ),k∈{1,2,...,n} (16)

[0222] w k The numerical representation of the contribution of the dominance parameter in the kth subspace to the entire population;

[0223] V k , the sum of k∈{1,2,...,n} represents the sum of the fitness value differences of individuals in the entire population whose offspring perform better than their parents; different subspaces are linked together according to their contribution.

[0224] By building a Gaussian mixture model of the dominant parameter model of the entire population, the mean and variance are generated using formulas (17) and (18):

[0225]

[0226]

[0227] Step S3: Based on the parameter information, the optimal individuals distributed in different areas are selected to guide the evolution process.

[0228] The present invention also provides a multi-objective optimization system based on advantage information extraction, the system comprising:

[0229] Module M1: Extract spatial advantage information and obtain spatial partitioning results;

[0230] Module M2: Extract parameter space advantage information based on the obtained spatial partitioning results and make full use of the parameter information contained in the dominant individuals at different evolutionary stages;

[0231] Module M3: Based on parameter information, select the best individuals distributed in different areas to guide the evolution process.

[0232] Specifically, module M1 includes:

[0233] The calculated fitness value f is normalized to between 0 and 1, and the vector form is as follows:

[0234]

[0235]

[0236] in, Represents the fitness value after normalization operation;

[0237] x represents the decision variable, x i represents the i-th decision variable;

[0238] N means there are N decision variables;

[0239] m means there are m objective functions, where i and j represent the specified i-th decision variable and j-th objective function respectively;

[0240] f′(x i ) represents the i-th decision variable x i The set of fitness values ​​obtained on all objective functions;

[0241] [.] T Represents the transpose of a set;

[0242] The maximum and minimum values ​​of all objective functions in each dimension are composed of:

[0243] and

[0244]

[0245] t represents the selected tth dimension;

[0246] Rp max It consists of the maximum value of an objective function and the minimum value of the remaining functions;

[0247] Rp min It consists of the minimum values ​​of all objective functions;

[0248] Use formula (3) to calculate the adaptation value f′ and reference point Rp max The vector angle between:

[0249] θ=arccos(f′(x),Rp max ) (3)

[0250]

[0251] Among them, ||.|| represents the norm of the vector;

[0252] Calculate the vector angle β between the reference points:

[0253] β (t,j) =arccos(Rp max,t ,Rp max,j ),t∈{1,2,...,m},j∈{1,2,...,m},t≠j (5)

[0254] When the number of objective functions exceeds two, the reference points corresponding to the fitness values ​​of two objective functions are randomly selected to calculate the vector angle, and (t, j) is the selected t, jth objective function;

[0255] According to the calculated vector angles between reference points and the vector angles between fitness value and reference points, each individual participating in the evolution is given a 0-1 label of its own using formula (6):

[0256]

[0257] Where n is the number of subspaces; Sn i represents the label of the i-th decision variable, and the label set of all decision variables is represented by Sn;

[0258] Obtain the dominant individual P contained in the sub-solution set obtained in each generation during the evolution process best ;

[0259] By using formulas (1) to (6), the target space is divided into n subspaces, and the population X is also divided into several corresponding subpopulations;

[0260] Use formula (7) to calculate the center position of each subspace, the reference point Rp min The direction with respect to the center position is the optimal evolution direction of each subspace;

[0261]

[0262] Among them, T kIndicates the center position, z k Represents the kth th The number of individuals in a subspace.

[0263] Calculate the kth th All individuals in the subspace and the reference point Rp in the optimal evolution direction min distance;

[0264] Among all the distances calculated, the individual with the shortest distance is defined as the optimal individual P in the subspace. best,k ;

[0265] kth th The number of all individuals in the subspace is z k express;

[0266] d i,k =||f′(x i,k )||cos(f′(x i,k ),T k ),k=1,2,...,n,i=1,2,...,z k (8)

[0267] d min,k =min(d 1,k ,d 2,k ,d 3,k ,...,d zk,k ); (9)

[0268] Among them, d i,k Indicates the reference point Rp between the i-th individual and the optimal evolutionary direction in the k-th subspace min the distance between them;

[0269] f′(x i,k ) represents the fitness value of the decision variable xi in the kth subspace;

[0270] Module M2 includes:

[0271] The result of spatial partitioning in step 1 is used to calculate the difference between the fitness value of the parent individual and the fitness value of the offspring individual through formula (10);

[0272]

[0273] Among them, k represents the kth th subspaces;

[0274] z k Represents the kth th The number of individuals in a subspace;

[0275] Δf k,iRepresents the kth th The sum of the differences between the fitness values ​​of offspring individuals and parent individuals in the subspace;

[0276] At the same time, retain the Δf that is a positive real number k,i Stored in set V k ,k∈{1,2,...,n}, and its corresponding parameters are stored in the set R k ,k∈{1,2,...,n};

[0277] Build a Gaussian mixture model based on the data in the collection μ is the mean, σ 2 is the variance:

[0278]

[0279]

[0280]

[0281] Use formulas (14) and (15) to calculate the parameters required for Gaussian distribution:

[0282]

[0283]

[0284] in, Represents the mean of the dominant parameter information in the subspace;

[0285] Represents the kth th The mean of the dominant parameter information in the subspace;

[0286] R k,j Indicates that in the k-th subspace, the fitness value of the j-th offspring is better than that of the parent;

[0287] Represents the kth th The variance of the dominant parameter information in the subspace;

[0288] Represents the kth th The difference Δf between the fitness value of the parent individual and the fitness value of the offspring individual in the subspace k,i is the number of positive real numbers.

[0289] When there are n subspaces, the advantage parameter distribution of each subspace is Different subspaces have different Gaussian distribution advantage parameter models, stored in V k,The difference information of the parent and offspring in k∈{1,2,...,n} will be used to determine the contribution value w of the advantage parameters in different subspaces to the entire population in the current evolutionary generation;

[0290] The specific mathematical description is as follows:

[0291] w k =∑V k / (∑V1+∑V2+...+∑V n ),k∈{1,2,...,n} (16)

[0292] w k The numerical representation of the contribution of the dominance parameter in the kth subspace to the entire population;

[0293] V k , the sum of k∈{1,2,...,n} represents the sum of the fitness differences of individuals whose offspring perform better than their parents in the entire population;

[0294] By building a Gaussian mixture model of the dominant parameter model of the entire population, the mean and variance are generated using formulas (17) and (18):

[0295]

[0296]

[0297] Next, the present invention will be described in more detail.

[0298] The technical solution of the present invention is described clearly and completely below with reference to specific implementation examples. Here, the objective function of the multi-objective industrial process is set as cost and output. The applicable swarm intelligence algorithm is the differential evolution algorithm.

[0299] A multi-objective optimization method based on advantage information extraction, referring to Figure 1 and Figure 2 The specific steps are as follows:

[0300] 1. Determine the optimization goal of the control system:

[0301] A mathematical model is established based on the requirements of actual industrial control systems, with control conditions as independent variables and cost and output as objective functions. The mathematical formula is described as follows:

[0302] F(x)=[minf1(x),...,minf m (x)],x∈χ

[0303] x min ≤x≤x max (19)

[0304] Where x=(x1,x2,...,x n ) The decision variables are limited to the range of 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 target space. Usually, the objective function contains several constraints:

[0305]

[0306] Among them, g j (x) represents the jth inequality constraint;

[0307] h j (x) represents the jth equality constraint;

[0308] p and q represent the number of inequality and equality constraints contained in the multi-objective function, respectively.

[0309] 2. Control optimization process:

[0310] Taking the differential evolution algorithm as an example, using the present invention, the steps are as follows:

[0311] S1: Initialization

[0312] Randomly generate the original population S, the population size is set to N; the maximum evolutionary generation G max ; The current generation G in the evolution process; The number of subintervals n; The fitness value F(x) of the original population; The normalized fitness value

[0313] S2: Evolution of the population

[0314] The objective function value is calculated according to the optimization function in S1, and the advantage information is extracted using the method of the present invention. First, the fitness value f obtained by calculation is normalized to between 0 and 1, and the vector form is as follows:

[0315]

[0316]

[0317] The reference points, as the boundaries in the target space partitioning method, are not randomly generated, but are composed of the maximum and minimum values ​​of all objective functions in each dimension: and

[0318] Rp max It consists of the maximum value of an objective function and the minimum value of the remaining functions, Rp minIt consists of the minimum values ​​of all objective functions.

[0319] Use formula (23) to calculate the adaptation value f′ and reference point Rp max The vector angle between:

[0320] θ=arccos(f′(x),Rp max ) (twenty three)

[0321]

[0322] Calculate the vector angle β between the reference points:

[0323] β (t,j) =arccos(Rp max,t ,Rp max,j ),t∈{1,2,...,m},j∈{1,2,...,m},t≠j (25)

[0324] When the number of objective functions exceeds two, the reference points corresponding to the fitness values ​​of the two objective functions are randomly selected to calculate the vector angle. (t, j) is the t, jth objective function selected. Based on the calculated vector angle between the reference points and the vector angle between the fitness value and the reference point, each individual participating in the evolution is assigned a 0-1 label using formula (26):

[0325]

[0326] Here n is the number of subspaces.

[0327] Through S1 and S2, the target space is divided into n subspaces, and the population X is also divided into several corresponding subpopulations. The center position of each subspace is calculated using formula (27), and the reference point Rp is defined as min The direction of the center position is the optimal evolution direction of each subspace, T k Indicates the center position.

[0328]

[0329] Calculate the kth th All individuals in the subspace and the reference point Rp in the optimal evolution direction min The distance of the subspace. Define the individual with the shortest distance among all the distances calculated as the optimal individual P in the subspace best,k .kth th The number of all individuals in the subspace is z k express.

[0330] d i,k =||f′(x i,k)||cos(f′(x i,k ),T k ),k=1,2,...,n,i=1,2,...,z k (28)

[0331]

[0332] At the same time, select the dominant individual x in each subinterval best,k ;

[0333] Mutation strategy:

[0334] Select DE / best / 2:

[0335] Calculate the fitness value of the individual objective function after the mutation operation and perform selection operations on the population.

[0336] Select an action:

[0337] if Dominate So Will be retained in population S G .if Dominate So Will replace Save in population S G If and Do not dominate each other, then and Will be stored in population S G In. Use non-dominated solution sorting and crowding distance sorting to select N individuals to maintain the population size and generate the next generation population S G+1 .

[0338] S3: Parameter space advantage information extraction method

[0339] The parameters of the swarm intelligence algorithm play an important role in the calculation effect of the algorithm. The difference between the fitness value of the parent individual and the fitness value of the offspring individual is calculated by formula (31).

[0340]

[0341] Among them, k represents the kth th subspace; z k Represents the kth th The number of individuals in the subspace; Δf k,i Represents the kth th The sum of the differences between the fitness values ​​of the offspring individuals and the parent individuals in the subspace. At the same time, retain the result Δf which is a positive real number k,iStored in set V k ,k∈{1,2,…,n}, and its corresponding parameters are stored in the set R k ,k∈{1,2,...,n}. Build a mixed Gaussian model based on the data in the set μ is the mean, σ 2 is the variance:

[0342]

[0343]

[0344]

[0345] Use formulas (35) to (36) to calculate the parameters required for Gaussian distribution:

[0346]

[0347]

[0348] in, Represents the kth th The mean of the dominant parameter information in the subspace; Represents the kth th The variance of the dominant parameter information in the subspace; Represents the kth th The difference Δf between the fitness value of the parent individual and the fitness value of the offspring individual in the subspace k,i is the number of positive real numbers.

[0349] When there are n subspaces, the advantage parameter distribution of each subspace is Different subspaces have different Gaussian distribution advantage parameter models, stored in V k The difference information between the parent and child generations in k∈{1,2,...,n} will be used to determine the contribution value w of the advantage parameters in different subspaces to the entire population in the current evolutionary generation. The specific mathematical description is as follows:

[0350] w k =∑V k / (∑V1+∑V2+...+∑V n ),k∈{1,2,...,n} (37)

[0351] V k ,k∈{1,2,...,n} represents the sum of the fitness differences of individuals whose offspring perform better than their parents in the entire population. Different subspaces are linked together based on their contribution. The dominant parameter model of the entire population is a mixed Gaussian model, and the mean and variance are generated using formulas (38) and (39):

[0352]

[0353]

[0354] S4: Evolutionary algebraic update, if G = G max , the whole evolution process ends, if G does not reach G max , then repeat S2 to S4.

[0355] The embodiment of the present invention provides a multi-objective optimization method and system based on advantage information extraction. In view of the fact that multi-objective problems have multiple dimensions and non-unique solutions, a method for extracting spatial advantage information is proposed to improve the utilization rate of effective information in the target space.

[0356] Aiming at the problem that swarm intelligence algorithms have different requirements for parameters at different evolutionary stages, a method for extracting advantage information from parameter space is proposed, so that the parameter information contained in the advantage individuals at different evolutionary stages can be fully utilized, thereby improving the performance of the algorithm.

[0357] To address the problem of a large number of non-dominated solutions when solving multi-objective problems, the optimal individuals distributed in different regions are selected to guide the evolutionary process, thereby reducing the computational complexity of the swarm intelligence algorithm and accelerating the convergence speed.

[0358] Those skilled in the art will appreciate that, in addition to implementing the system and its various devices, modules, and units provided by the present invention in purely computer-readable program code, it is entirely possible to implement the same functions of the system and its various devices, modules, and units provided by the present invention in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers by logically programming the method steps. Therefore, the system and its various devices, modules, and units provided by the present invention can be considered a hardware component, and the devices, modules, and units included therein for implementing various functions can also be considered as structures within the hardware component; the devices, modules, and units for implementing various functions can also be considered as both software modules implementing the method and structures within the hardware component.

[0359] The above describes specific embodiments of the present invention. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art may make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. The embodiments of this application and the features in the embodiments may be combined with each other in any manner unless there is a conflict.

Claims

1. A multi-objective optimization method based on advantage information extraction, characterized in that: include: Step S1: extracting spatial advantage information and obtaining spatial partitioning results; Step S2: extracting parameter space advantage information based on the obtained spatial partitioning results, and making full use of the parameter information contained in the dominant individuals at different evolutionary stages; Step S3: Based on the parameter information, the optimal individuals distributed in different areas are selected to guide the evolution process; The step S1 comprises: The calculated fitness value f is normalized to between 0 and 1, and the vector form is as follows: in, Represents the fitness value after normalization operation; x represents the decision variable, x i represents the i-th decision variable; N means there are N decision variables; m means there are m objective functions, where i and j represent the specified i-th decision variable and j-th objective function respectively; f′(x i ) represents the i-th decision variable x i The set of fitness values ​​obtained on all objective functions; [.] T Represents the transpose of a set; The maximum and minimum values ​​of all objective functions in each dimension are composed of: 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 tth dimension; Rp max It consists of the maximum value of an objective function and the minimum value of the remaining functions; Rp min It consists of the minimum values ​​of all objective functions; Use formula (3) to calculate the adaptation value f′ and reference point Rp max The vector angle between: θ=arccos(f′(x),Rp max ) (3) Among them, ||.|| represents the norm of the vector; Calculate the vector angle β between the 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 objective functions exceeds two, the reference points corresponding to the fitness values ​​of two objective functions are randomly selected to calculate the vector angle, and (t, j) is the selected t, jth objective function; According to the calculated vector angles between reference points and the vector angles between fitness value and reference points, each individual participating in the evolution is given a 0-1 label of its own using formula (6): Where n is the number of subspaces; Sn i represents the label of the i-th decision variable, and the label set of all decision variables is represented by Sn; Obtain the dominant individual P contained in the sub-solution set obtained in each generation during the evolution process best ; By using formulas (1) to (6), the target space is divided into n subspaces, and the population X is also divided into several corresponding subpopulations; Use formula (7) to calculate the center position of each subspace, the reference point Rp min The direction with respect to the center position is the optimal evolution direction of each subspace; Among them, T k Indicates the center position, z k Represents the kth th The number of individuals in a subspace.

2. The multi-objective optimization method based on advantage information extraction according to claim 1, characterized in that: The step S1 further includes: Calculate the kth th All individuals in the subspace and the reference point Rp in the optimal evolution direction min distance; Among all the distances calculated, the individual with the shortest distance is defined as the optimal individual P in the subspace. best,k ; kth th The number of all individuals in the subspace is z k express; 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) Among them, d i,k Indicates the reference point Rp between the i-th individual and the optimal evolutionary direction in the k-th subspace min The distance between them; f′(x i,k ) represents the fitness value of the decision variable xi in the kth subspace.

3. The multi-objective optimization method based on advantage information extraction according to claim 2, characterized in that: The step S2 comprises: The result of spatial partitioning in step S1 is used to calculate the difference between the fitness value of the parent individual and the fitness value of the offspring individual through formula (10); Among them, k represents the kth th subspaces; z k Represents the kth th The number of individuals in a subspace; Δf k,i Represents the kth th The sum of the differences between the fitness values ​​of offspring individuals and parent individuals in the subspace; At the same time, retain the Δf that is a positive real number k,i Stored in set V k ,k∈{1,2,K,n}, and its corresponding parameters are stored in the set R k ,k∈{1,2,K,n}; Build a Gaussian mixture model based on the data in the collection μ is the mean, σ 2 is the variance: Use formulas (14) and (15) to calculate the parameters required for Gaussian distribution: in, Represents the mean of the dominant parameter information in the subspace; Represents the kth th The mean of the dominant parameter information in the subspace; R k,j Indicates that in the k-th subspace, the fitness value of the j-th offspring is better than that of the parent; Represents the kth th The variance of the dominant parameter information in the subspace; Represents the kth th The difference Δf between the fitness value of the parent individual and the fitness value of the offspring individual in the subspace k,i is the number of positive real numbers.

4. The multi-objective optimization method based on advantage information extraction according to claim 3 is characterized in that: The step S2 further includes: When there are n subspaces, the advantage parameter distribution of each subspace is Different subspaces have different Gaussian distribution advantage parameter models, stored in V k ,The difference information between the parent and offspring in k∈{1,2,K,n} will be used to determine the contribution w of the dominant parameters in different subspaces to the entire population in the current evolutionary generation; The specific mathematical description is as follows: w k =∑V k / (∑V1+∑V2+K+∑V n ),k∈{1,2,K,n} (16) w k The numerical representation of the contribution of the dominance parameter in the kth subspace to the entire population; V k , the sum of k∈{1,2,K,n} represents the sum of the fitness differences of individuals in the entire population whose offspring perform better than their parents; By building a Gaussian mixture model of the dominant parameter model of the entire population, the mean and variance are generated using formulas (17) and (18):

5. A multi-objective optimization system based on advantage information extraction, characterized in that: include: Module M1: Extract spatial advantage information and obtain spatial partitioning results; Module M2: Extract parameter space advantage information based on the obtained spatial partitioning results and make full use of the parameter information contained in the dominant individuals at different evolutionary stages; Module M3: Based on parameter information, select the best individuals distributed in different areas to guide the evolution process; The module M1 includes: The calculated fitness value f is normalized to between 0 and 1, and the vector form is as follows: in, Represents the fitness value after normalization operation; x represents the decision variable, x i represents the i-th decision variable; N means there are N decision variables; m means there are m objective functions, where i and j represent the specified i-th decision variable and j-th objective function respectively; f′(x i ) represents the i-th decision variable x i The set of fitness values ​​obtained on all objective functions; [.] T Represents the transpose of a set; The maximum and minimum values ​​of all objective functions in each dimension are composed of: 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 tth dimension; Rp max It consists of the maximum value of an objective function and the minimum value of the remaining functions; Rp min It consists of the minimum values ​​of all objective functions; Use formula (3) to calculate the adaptation value f′ and reference point Rp max The vector angle between: θ=arccos(f′(x),Rp max ) (3) Among them, ||.|| represents the norm of the vector; Calculate the vector angle β between the 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 objective functions exceeds two, the reference points corresponding to the fitness values ​​of two objective functions are randomly selected to calculate the vector angle, and (t, j) is the selected t, jth objective function; According to the calculated vector angles between reference points and the vector angles between fitness value and reference points, each individual participating in the evolution is given a 0-1 label of its own using formula (6): Where n is the number of subspaces; Sn i represents the label of the i-th decision variable, and the label set of all decision variables is represented by Sn; Obtain the dominant individual P contained in the sub-solution set obtained in each generation during the evolution process best ; By using formulas (1) to (6), the target space is divided into n subspaces, and the population X is also divided into several corresponding subpopulations; Use formula (7) to calculate the center position of each subspace, the reference point Rp min The direction with respect to the center position is the optimal evolution direction of each subspace; Among them, T k Indicates the center position, z k Represents the kth th The number of individuals in a subspace.

6. The multi-objective optimization system based on advantage information extraction according to claim 5, characterized in that: The module M1 further comprises: Calculate the kth th All individuals in the subspace and the reference point Rp in the optimal evolution direction min distance; Among all the distances calculated, the individual with the shortest distance is defined as the optimal individual P in the subspace. best,k ; kth th The number of all individuals in the subspace is z k express; 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) Among them, d i,k Indicates the reference point Rp between the i-th individual and the optimal evolutionary direction in the k-th subspace min the distance between them; f′(x i,k ) represents the fitness value of the decision variable xi in the kth subspace.

7. The multi-objective optimization system based on advantage information extraction according to claim 6, characterized in that: The module M2 includes: The result of spatial partitioning in step S1 is used to calculate the difference between the fitness value of the parent individual and the fitness value of the offspring individual through formula (10); Among them, k represents the kth th subspaces; z k Represents the kth th The number of individuals in a subspace; Δf k,i Represents the kth th The sum of the differences between the fitness values ​​of offspring individuals and parent individuals in the subspace; At the same time, retain the Δf that is a positive real number k,i Stored in set V k ,k∈{1,2,K,n}, and its corresponding parameters are stored in the set R k ,k∈{1,2,K,n}; Build a Gaussian mixture model based on the data in the collection μ is the mean, σ 2 is the variance: Use formulas (14) and (15) to calculate the parameters required for Gaussian distribution: in, Represents the mean of the dominant parameter information in the subspace; Represents the kth th The mean of the dominant parameter information in the subspace; R k,j Indicates that in the k-th subspace, the fitness value of the j-th offspring is better than that of the parent; Represents the kth th The variance of the dominant parameter information in the subspace; Represents the kth th The difference Δf between the fitness value of the parent individual and the fitness value of the offspring individual in the subspace k,i is the number of positive real numbers.

8. The multi-objective optimization system based on advantage information extraction according to claim 7, characterized in that: The module M2 further comprises: When there are n subspaces, the advantage parameter distribution of each subspace is Different subspaces have different Gaussian distribution advantage parameter models, stored in V k ,The difference information between the parent and offspring in k∈{1,2,K,n} will be used to determine the contribution w of the dominant parameters in different subspaces to the entire population in the current evolutionary generation; The specific mathematical description is as follows: w k =∑V k / (∑V1+∑V2+K+∑V n ),k∈{1,2,K,n} (16) w k The numerical representation of the contribution of the dominance parameter in the kth subspace to the entire population; V k , the sum of k∈{1,2,K,n} represents the sum of the fitness differences of individuals in the entire population whose offspring perform better than their parents; By building a Gaussian mixture model of the dominant parameter model of the entire population, the mean and variance are generated using formulas (17) and (18):

Images