CN107067121A - A kind of improvement grey wolf optimized algorithm based on multiple target - Google Patents

Abstract

The embodiment of the present invention discloses an improved gray wolf optimization algorithm based on multi-objective, which is used to solve the problems of slow convergence speed and easy to fall into local optimal value in the standard gray wolf algorithm in the prior art when dealing with multi-objective optimization problems. Defective technical issues. The method of the embodiment of the present invention includes: S1, setting the wolf group initialization parameters and direction correction probability, and randomly initializing the position of the wolf individual; S2, calculating the fitness value of each wolf individual according to the solution target, and selecting the top three wolves Individual; S3. Optimizing the position of wolves in the wolf pack, generating moderate wolves, and updating the position of the wolf pack; S4. Performing the direction correction operation on the updated wolf pack and controlling the scale of the updated wolf pack participating in the correction dimension according to the direction correction probability , to obtain the corrected wolf pack position; S5, determine whether the number of iterations reaches the preset maximum number of iterations, if so, output the corrected wolf pack position as the final optimization result, otherwise, go to S3 to continue iterative search.

Description

An Improved Gray Wolf Optimization Algorithm Based on Multi-objective

technical field

The invention relates to the technical field of multi-objective optimization algorithms, in particular to an improved gray wolf optimization algorithm based on multi-objectives.

Background technique

With the development and application of modern computer technology in the field of multi-objective optimization, various new methods and technologies emerge in an endless stream as the research on system engineering theory matures day by day. Common methods are mainly divided into two categories: one is to transform multi-objective into single-objective methods, mainly including weight coefficient method and membership function method. However, the rationality and effectiveness of the weight coefficient setting is a difficult problem for the weight coefficient method, and it cannot effectively deal with the target with a non-convex frontier; the membership function method has the defect of constructing rationality. The other is to use heuristic algorithms to directly solve multi-objective problems, such as fast non-dominated sorting genetic algorithm (NSGAⅡ), enhanced Pareto evolutionary algorithm (strength pareto evolutionary algorithm 2, SPEA2), etc. .

The rationality and effectiveness of the weight coefficient setting is a difficult problem for the weight coefficient method, and it cannot effectively deal with the target with non-convex frontier; the membership function rule has the defect of constructing rationality. The other is to use heuristic algorithms to directly solve multi-objective problems, such as fast non-dominated sorting genetic algorithm (NSGA II), enhanced Pareto evolution algorithm (strength pareto evolutionary algorithm2, SPEA2) and so on. Based on strategies such as fast non-dominated sorting, external archiving, and selection of male parents based on crowding distance, NSGA II ensures the diversity of the population and improves computational efficiency to a certain extent. The defect of premature convergence. The SPEA2 algorithm has the opportunity to find multiple Pareto optimal solutions in a single run, so it is widely used in various multi-objective optimization problems. It has the disadvantages of slow convergence speed and low accuracy of solution set. Especially when faced with a multimodal optimization problem with a large number of local optimum points, the problem of not converging to the global optimum is particularly prominent.

Gray Wolf Optimizer (GWO) is a new swarm intelligence optimization algorithm proposed by Mirjalili et al. in 2014. This algorithm has the characteristics of simple structure, few control parameters, easy operation, and strong search ability. In the field of optimization, it has been proved that it is superior to the particle swarm optimization algorithm in terms of computational efficiency and solution accuracy. However, the algorithm still has the defect that it is easy to fall into local optimum in the optimization process. In addition, the current domestic and foreign research on the gray wolf algorithm for solving multi-objective optimization problems is still not in-depth. Only Mao Senmao et al. used the multi-objective gray wolf algorithm to solve the optimal scheduling problem of carbon-energy composite flow in the power grid, and obtained a relatively good Pareto front. However, this algorithm did not target the dominant wolf in the external archive during the actual iteration process. Some of its dimensions are easy to fall into local optimal problems for improvement.

In the existing technology, the standard gray wolf algorithm still has inherent defects such as slow convergence speed and easy to fall into local optimum when dealing with multi-objective optimization problems.

Contents of the invention

The embodiment of the present invention provides an improved gray wolf optimization algorithm based on multi-objective, which solves the shortcomings of the standard gray wolf algorithm in the prior art, such as slow convergence speed and easy to fall into local optimum when dealing with multi-objective optimization problems. technical problems.

A kind of improved gray wolf optimization algorithm based on multi-objective that the embodiment of the present invention provides, comprises:

S1. Set the initialization parameters and direction correction probability of the wolf group, and randomly initialize the position of each wolf individual in the solution space;

S2. Calculate the fitness value of each wolf individual according to the solution goal, and select the top three wolf individuals to assign X _α , X _β , and X _δ in turn;

S3. According to X _α , X _β , and X _δ , optimize the position of each individual wolf in the wolf pack, generate moderate wolves, and calculate the fitness value of moderate wolves and update the position of the wolf pack;

S4. Perform the direction correction operation on the updated wolves and control the size of the updated wolves participating in the correction dimension according to the direction correction probability, generate new moderate wolves, and calculate the fitness value of the new moderate wolves to obtain the corrected pack position;

S5. Determine whether the number of iterations reaches the preset maximum number of iterations. If yes, output the corrected wolf pack position as the final optimization result; otherwise, go to S3 to continue the iterative search.

Optionally, S1 specifically includes:

Set the size M of the wolf pack, the maximum number of iterations max gen and the direction correction probability p _v , and randomly initialize the position of each wolf individual in the solution space.

Optionally, S2 specifically includes:

Calculate the fitness value of each wolf individual according to the solution goal, and select the top three wolf individuals according to the fast non-inferior solution sorting operation, crowding distance calculation, and elite retention strategy to assign X _α , X _β , and X _δ in turn.

Optionally, the fast non-inferior solution sorting operation specifically includes:

Find the non-dominated solution set in the wolf pack, mark the non-dominated solution set as the first non-dominated layer F1 and assign the first non-dominated sequence value to all wolves in the non-dominated solution set, and remove all wolves;

Find the next layer of non-dominated solution sets in the eliminated wolves and perform marking, non-dominated sequence value assignment operations and elimination operations;

Continue to perform non-dominated disassembly stratification, marking, non-dominated sequence value assignment and elimination operations on the wolf pack in sequence until the entire wolf pack is completely stratified and the wolves in the same non-dominated layer have the same non-dominated sequence. value.

Optionally, the calculation of the crowding distance specifically includes:

Initialize the distance of wolf individuals in the same non-dominated layer, so that the crowding distance L[i] _d of wolf individual i is 0;

Wolf individuals in the same non-dominant layer are sorted incrementally according to the mth target value;

A large number Inf is given to the two wolves on the given edge, so that the two wolves have an absolute selection advantage;

For the wolf individuals in the middle of the sorting, the crowding distance of the wolf individuals in the middle of the sorting is calculated according to formula 8. Formula 8 is specifically:

Among them, N _obj is the target number, are the mth fitness value of the i+1th and i-1th wolf individuals respectively, are the maximum and minimum values of the mth fitness value in the non-inferior solution set, respectively.

Optionally, S3 specifically includes:

According to X _α , X _β , X _δ , the position of each wolf individual in the wolf pack is optimized through the steps of wolf pack encirclement and wolf pack hunting, and a moderate wolf is generated, and the fitness value of the moderate wolf is calculated and sorted according to the fast non-inferior solution , Calculation of crowding distance, selective updating of wolves' positions by elite retention strategy.

Optionally, between S3 and S4 also includes:

Perform a normalization operation on each dimension of all wolf individuals in the updated wolf pack through Formula 9, and Formula 9 is specifically:

Among them, D is the dimension, for the wolf The d-th dimension variable of , for The corresponding scalars after normalization, max(d) and min(d) are respectively the upper and lower limits of the d-th dimension variable in the wolf pack.

Optionally, S4 specifically includes:

Perform the direction correction operation on the updated wolves and control the size of the updated wolves participating in the correction dimension according to the direction correction probability, generate new moderate wolves, and calculate the fitness value of the new moderate wolves, sort according to the fast non-inferior solution Operation, crowding distance calculation, and elite retention strategy select the optimal position of wolf individuals, and divide the wolf pack into X _α , X _β , X _δ , X _ω according to the ranking of wolf individuals in the wolf pack, and obtain the corrected wolf pack positions.

Optionally, performing a direction correction operation on the updated wolf pack specifically includes:

Perform the direction correction operation on the updated wolves through Formula 10. Formula 10 is specifically:

Among them, d ₁ , d ₂ ∈ (1, D), r is a random number from 0 to 1, is the mean wolf individual scalar The _d1th dimension of ;

For each dimension of the generated moderate wolf individual scalar, the denormalization operation is performed through formula 11. Formula 11 is specifically:

in, mean wolf The d-th dimension of .

Optionally, S5 specifically includes:

Judging whether the number of iterations reaches the preset maximum number of iterations, if so, output the corrected wolf pack position as the final optimization result, and combine the fuzzy decision-making method to select the optimal compromise solution, otherwise, go to S3 to continue iterative search.

It can be seen from the above technical solutions that the embodiments of the present invention have the following advantages:

The embodiment of the present invention provides an improved gray wolf optimization algorithm based on multi-objective, including: S1, setting the initialization parameters and direction correction probability of wolves, and randomly initializing the position of each wolf individual in the solution space; S2, according to the solution The goal is to calculate the fitness value of each wolf individual, and select the top three wolf individuals to assign X _α , X _β , X _δ in turn; S3, optimize each wolf individual in the wolf pack according to X _α , X _β , X _δ , generate moderate wolves, and calculate the fitness value of moderate wolves and update the position of wolves; S4, perform direction correction operation on the updated wolves and control the scale of the updated wolves participating in the correction dimension according to the direction correction probability, Generate a new moderate wolf, and calculate the fitness value of the new moderate wolf, and obtain the corrected wolf pack position; S5, judge whether the number of iterations reaches the preset maximum number of iterations, if so, output the corrected wolf pack position as the final Optimize the result, otherwise, go to S3 to continue the iterative search. In the embodiment of the present invention, by using the unique advantage of the vertical cross operation in the vertical cross algorithm to deal with some dimensions that are easy to fall into the local optimum problem, on the basis of the standard gray wolf algorithm, the direction correction operation (vertical cross operation) is integrated to provide a new The method for updating the position of wolves in order to help some of the dimensions trapped in the local optimum get rid of the current predicament, correct the direction of the wolves, enhance the global convergence of the algorithm, and solve the problem of the standard gray wolf algorithm in the prior art when dealing with multi-objectives. There are technical problems such as slow convergence speed and easy to fall into local optimum when optimizing problems.

Description of drawings

In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings that need to be used in the description of the embodiments or the prior art. Obviously, the accompanying drawings in the following description are only These are some embodiments of the present invention. For those skilled in the art, other drawings can also be obtained according to these drawings on the premise of not paying creative efforts.

Fig. 1 is a schematic diagram of the social level and main responsibilities of specific wolves in the gray wolf algorithm provided by the embodiment of the present invention;

Fig. 2 is a schematic diagram of the wolf group position update process of the gray wolf algorithm provided by the embodiment of the present invention;

Fig. 3 is a schematic flow chart of an embodiment of an improved gray wolf optimization algorithm based on multi-objective provided by the embodiment of the present invention;

Fig. 4 is a schematic flow chart of another embodiment of a multi-objective-based improved gray wolf optimization algorithm provided by an embodiment of the present invention;

Fig. 5 is a comparison diagram of a thermal power plant consumption characteristic curve considering and ignoring the valve point effect provided by the embodiment of the present invention;

Fig. 6 is a schematic diagram of the thermoelectric coupling relationship of the cogeneration unit provided by the embodiment of the present invention;

Fig. 7 is a schematic diagram of comparison of optimal Pareto optimal frontiers of various algorithms provided by the embodiment of the present invention.

detailed description

The embodiment of the present invention provides an improved gray wolf optimization algorithm based on multi-objective, which is used to solve the problems of slow convergence speed and easy to fall into local optimal value in the standard gray wolf algorithm in the prior art when dealing with multi-objective optimization problems. Defective technical issues.

In order to make the purpose, features and advantages of the present invention more obvious and understandable, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the following The described embodiments are only some, not all, embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by persons of ordinary skill in the art without making creative efforts belong to the protection scope of the present invention.

For ease of understanding, the basic principles of the gray wolf algorithm will be briefly introduced below.

As a canine animal, the gray wolf is at the top of the food chain in nature and is often regarded as the top predator. Most of their lifestyles like to live in groups, and each wolf pack usually has an average of 5 to 12 wolves. In daily life, especially when they go hunting, they follow an extremely strict social hierarchy and task division system, such as in the gray wolf algorithm. , the highest level is called the alpha wolf and is recorded as α, which is mainly responsible for leading the entire wolf pack and making decisions during the hunting process. The third level of the wolf pack is mainly responsible for tasks such as investigation, vigilance, besieging, and guarding. The remaining wolf pack is ω, which is located at the bottom of the entire wolf pack. It obeys the orders of other high-level wolves and carries out related group hunting operations according to the instructions. . The specific social levels and main responsibilities of the wolves are shown in Figure 1.

In each iteration, the individual with the best fitness is assigned to X _α , the second-best individual is assigned to X _β , the third individual is defined as X _δ , and the rest of the individuals are assigned to X _ω . The GWO algorithm bionic wolf pack hunting process is mainly divided into three steps, namely encirclement, hunting and attack, and the specific steps are as follows.

1. Surrounded

When wolves perform hunting tasks, they first surround the prey. The mathematical model of this process can be expressed as:

In the formula, t is the current wolf group algebra, is the distance vector between the wolf and the prey; with is the swing factor vector, is the current position of the prey (the global optimal solution vector), is the position of the wolf (potential solution vector). with The value of is calculated by formulas (3) and (4):

In the formula, Characterizes a random vector with a value range of [0,1], The value a of the vector decreases linearly from 2 to 0 with the number of iterations.

2. Hunting

After encircling the prey, the wolves will execute the hunting action. In order to search for the location of the prey in a more directional way, this action is usually guided by α, β, δ, and other ω wolves follow the instructions of α, β, δ to update their respective positions. The specific update expression is:

In the formula, are the distance vectors between ω wolf and α, β, δ respectively, For the updated wolf position, the position update process is shown in Figure 2.

3. Attack

At the end of the wolf pack hunting, it will enter the attack stage. The main task of the wolf pack at this stage is to complete the goal of catching prey, that is, the gray wolf algorithm obtains the global optimal solution. The implementation of this process is mainly as follows: with the formula (3) The value of is linearly decreased from 2 to 0, correspondingly, The value of will also take any number between [-2a,2a]. when When , the wolves are in the state of concentrating on attacking prey, and when At this time, the wolf pack will gradually disperse from the location of the prey, causing the gray wolf algorithm to lose the optimal solution position, and then turn to the process of finding other local optimal solutions, which is why the gray wolf algorithm is easy to fall into the local optimal solution. The problem is that the solution is optimal and the convergence time is long.

The above is a brief description of the basic principle of the gray wolf algorithm, and an embodiment of an improved gray wolf optimization algorithm based on multi-objective provided by the embodiment of the present invention will be described in detail below.

Please refer to Fig. 3, a kind of improved gray wolf optimization algorithm based on multi-objective provided by the embodiment of the present invention, comprises:

S1. Set the initialization parameters and direction correction probability of the wolf group, and randomly initialize the position of each wolf individual in the solution space;

First, set the initialization parameters of the wolf pack (such as the size of the wolf pack, the maximum number of iterations of the algorithm, etc.) and the direction correction probability, and randomly initialize the position of each wolf individual in the solution space of the solution target.

S2. Calculate the fitness value of each wolf individual according to the solution goal, and select the top three wolf individuals to assign X _α , X _β , and X _δ in turn;

After setting the initialization parameters and direction correction probability of the wolf group, and randomly initializing the position of each wolf individual in the solution space, calculate the fitness value of each wolf individual according to the solution goal, and select the top three wolves Individuals assign X _α , X _β , and X _δ sequentially.

S3. According to X _α , X _β , and X _δ , optimize the position of each individual wolf in the wolf pack, generate moderate wolves, and calculate the fitness value of moderate wolves and update the position of the wolf pack;

After obtaining the top three wolves, according to X _α , X _β , and X _δ , optimize the position of each wolf individual in the wolf pack through the above formula (1-7), generate a moderate wolf, and calculate the fitness of the moderate wolf The degree value and update the position of the wolves, that is, to execute the siege and hunting behavior of the wolves.

S4. Perform the direction correction operation on the updated wolves and control the size of the updated wolves participating in the correction dimension according to the direction correction probability, generate new moderate wolves, and calculate the fitness value of the new moderate wolves to obtain the corrected pack position;

After generating the moderate wolves and updating the position of the wolves, perform the direction correction operation on the updated wolves and control the scale of the updated wolves participating in the correction dimension according to the direction correction probability, generate new moderate wolves, and calculate the new moderate The fitness value of wolves to obtain the corrected wolf pack position.

S5. Determine whether the number of iterations reaches the preset maximum number of iterations. If yes, output the corrected wolf pack position as the final optimization result; otherwise, go to S3 to continue the iterative search.

Finally, it is judged whether the number of iterations of the improved gray wolf algorithm reaches the preset maximum number of iterations, and if so, output the corrected wolf pack position as the final optimization result, otherwise, go to S3 to continue iterative search.

The embodiment of the present invention provides an improved gray wolf optimization algorithm based on multi-objective, including: S1, setting the initialization parameters and direction correction probability of wolves, and randomly initializing the position of each wolf individual in the solution space; S2, according to the solution The goal is to calculate the fitness value of each wolf individual, and select the top three wolf individuals to assign X _α , X _β , X _δ in turn; S3, optimize each wolf individual in the wolf pack according to X _α , X _β , X _δ , generate moderate wolves, and calculate the fitness value of moderate wolves and update the position of wolves; S4, perform direction correction operation on the updated wolves and control the scale of the updated wolves participating in the correction dimension according to the direction correction probability, Generate a new moderate wolf, and calculate the fitness value of the new moderate wolf, and obtain the corrected wolf pack position; S5, judge whether the number of iterations reaches the preset maximum number of iterations, if so, output the corrected wolf pack position as the final Optimize the result, otherwise, go to S3 to continue the iterative search. In the embodiment of the present invention, by using the unique advantage of the vertical cross operation in the vertical cross algorithm to deal with some dimensions that are easy to fall into the local optimum problem, on the basis of the standard gray wolf algorithm, the direction correction operation (vertical cross operation) is integrated to provide a new The method for updating the position of wolves in order to help some of the dimensions trapped in the local optimum get rid of the current predicament, correct the direction of the wolves, enhance the global convergence of the algorithm, and solve the problem of the standard gray wolf algorithm in the prior art when dealing with multi-objectives. There are technical problems such as slow convergence speed and easy to fall into local optimum when optimizing problems.

The above is a detailed description of an embodiment of an improved gray wolf optimization algorithm based on multi-objective provided by the embodiment of the present invention, and another implementation of the improved gray wolf optimization algorithm based on multi-objective provided by the embodiment of the present invention will be described below Examples are described in detail.

Referring to Fig. 4, another embodiment of a multi-objective-based improved gray wolf optimization algorithm provided by an embodiment of the present invention includes:

201. Set the size M of the wolf pack, the maximum number of iterations max gen and the direction correction probability p _v , and randomly initialize the position of each wolf individual in the solution space;

First, set the initialization parameters of the wolf pack (such as the size M of the wolf pack, and the maximum number of iterations max gen of the algorithm, etc.) and the direction correction probability p _v , and randomly initialize the position of each wolf individual in the solution space of the solution target.

202. Calculate the fitness value of each wolf individual according to the solution goal, and select the top three wolf individuals according to the fast non-inferior solution sorting operation, crowding distance calculation, and elite retention strategy to assign X _α , X _β , and X _δ in turn ;

After setting the initialization parameters and direction correction probability of the wolf group, and randomly initializing the position of each wolf individual in the solution space, the fitness value of each wolf individual is calculated according to the solution target, and the sorting operation is performed according to the fast non-inferior solution, Crowding distance calculation, elite retention strategy selection of the top three wolf individuals are given X _α , X _β , X _δ in turn.

Specifically, the fast non-inferior solution sorting operation, congestion distance calculation, and elite retention strategy will be described in detail below.

Fast non-dominated sorting operation: In order to guide the position update of the wolves towards the Pareto optimal solution set, a fast non-dominated sorting operation must be performed on the wolves. This operation is a cyclic fitness stratification process. Specifically: first find out the non-dominated solution set in the wolf group, which is recorded as the first non-dominated layer F1, and secondly, assign non-dominated ranks to all wolf individuals in the solution set (where i _rank represents the non-dominated rank of individual i Value), and removed from the entire wolf group; then continue to find the next level of non-dominated solution set from the remaining wolves, similarly recorded as the second non-dominated layer F2, wolf individuals are given non-dominated rank i _rank =2 , and removed from the wolf group; and so on, until the whole wolf group is stratified, and the wolf individuals in the same layer have the same non-dominant rank i _rank . It can be divided into the following steps: find the non-dominated solution set in the wolf group, mark the non-dominated solution set as the first non-dominated layer F1 and assign the first non-dominated sequence value to all wolves in the non-dominated solution set, and set Eliminate all wolves; find the next level of non-dominated disassembly in the eliminated wolf group and perform marking, non-dominated order value assignment and elimination operations; continue to carry out non-dominated disassembly layering and marking on the wolf group in sequence , Non-dominated order value assignment operation and elimination operation, until the whole wolf group is completely stratified and the wolves in the same non-dominated layer have the same non-dominated order value.

Calculation of individual crowding distance: Aiming at the problem that the fast non-dominated sorting operation cannot perform selective sorting on non-dominated solution sets of the same layer, an individual crowded distance calculation operation is introduced. The wolf individual crowding distance refers to the distance between two wolf individuals i-1 and i+1 adjacent to individual i in the target space, and the specific steps are as follows:

①Initialize the distance of wolf individuals in the same layer, that is, the crowding distance L[i] _d of wolf individual i is 0;

②Wolf individuals in the same layer are sorted incrementally according to the m-th target value;

③The two wolf individuals on the given edge are given a large number Inf, so that they have an absolute selection advantage;

④ Calculate the crowding distance of wolf individuals in the middle according to formula (8):

In the formula: N _obj is the target number, are the mth fitness value of the i+1th and i-1th wolf individuals respectively, are the maximum and minimum values of the mth fitness value in the non-inferior solution set, respectively.

⑤Similarly, for different objective functions, repeat steps ②～④ to get the crowding distance of wolf individual i in the non-inferior solution set.

Elite retention strategy: In the hunting stage, in order to give individual wolves a certain degree of autonomy, when the position of wolves is updated, according to the evolution law of "survival of the fittest, survival of the fittest", only wolves with better positions, that is, the top M The wolf individuals can be retained, become the dominant wolf DS, and participate in the next iteration.

It can be seen that the position of the ω wolf is not only based on the guidance of the α, β, and δ wolves, but also retains a part of the wolf's own greed and selectively updates its own position. While approaching, the position of the entire wolf pack will always be kept optimal, which further speeds up the search speed of the wolf pack.

203. According to X _α , X _β , and X _δ , optimize the position of each individual wolf in the wolf pack through the steps of wolf pack encirclement and wolf pack hunting, generate moderate wolves, and calculate the fitness value of moderate wolves and based on the fast non-inferior solution Sorting operation, calculation of crowding distance, selective updating of wolves' position by elite retention strategy;

After obtaining the top three wolves, according to X _α , X _β , and X _δ , optimize the position of each individual wolf in the wolf pack through the steps of wolf pack encirclement and wolf pack hunting, generate a mean wolf, and calculate the mean wolf The fitness value of , and the location of wolves are selectively updated according to the fast non-inferior solution sorting operation, crowding distance calculation, and elite retention strategy.

204. Perform a normalization operation on each dimension of all wolf individuals in the updated wolf pack through Formula 9;

In order to solve the problem that direct arithmetic crossover cannot be directly performed on different dimension variables with different dimensions and different upper and lower limits, it is necessary to uniformly perform normalization on each dimension of all wolf individuals in the updated wolf pack before performing the direction correction operation. Operation:

Among them, D is the dimension, for the wolf The d-th dimension variable of , for The corresponding scalars after normalization, max(d) and min(d) are respectively the upper and lower limits of the d-th dimension variable in the wolf pack.

205. Perform the direction correction operation on the updated wolf pack and control the scale of the updated wolf pack participating in the correction dimension according to the direction correction probability, generate new moderate wolves, and calculate the fitness value of the new moderate wolf, according to the fast non-inferiority Solve the sorting operation, calculation of crowding distance, and elite retention strategy to select and retain the wolf individual position, and divide the wolf pack into X _α , X _β , X _δ , X _ω according to the ranking of wolf individuals in the wolf pack, and obtain the corrected wolf pack Location;

In view of the phenomenon that some dimensions may fall into local optimum in the wolf pack, the direction correction operation adopts a direction correction probability p _v to control the size of the modified dimension in the current wolf pack, and each correction only produces one-dimensional offspring, which has It is beneficial to assist some dimensions to get rid of the local optimum of the dimension while avoiding destroying the normal dimension, and effectively correct the direction of the wolf pack. The model construction of this process is as follows:

A scalar of wolves in a hypothetical wolf pack The d ₁ , d ₂ dimensions are respectively with Then perform the direction correction operation on them to produce the d ₁ dimension of the mean wolf can be expressed as:

In the formula: d ₁ , d ₂ ∈ (1, D), r is a random number from 0 to 1, is the mean wolf individual scalar The _d1th dimension of .

After performing the direction correction operation, the denormalization operation must be performed on each dimension of the generated mean wolf individual scalar:

In the formula, mean wolf The d-th dimension of .

In addition, in order to facilitate effective sorting of the dominant wolf pack DS and the generated moderate wolf pack X ^t+1 /MS, they must be merged to generate a merged wolf pack CM with 2M individuals.

206. Determine whether the number of iterations reaches the preset maximum number of iterations. If yes, output the corrected wolf pack position as the final optimization result, and select the optimal compromise solution in combination with the fuzzy decision-making method; otherwise, go to 203 to continue iterative search.

Finally, it is judged whether the number of iterations reaches the preset maximum number of iterations. If so, the corrected wolf pack position is output as the final optimization result, and the optimal compromise solution is selected in combination with the fuzzy decision-making method. Otherwise, go to S3 to continue the iterative search.

In actual operation, generally there is only one final implementation scheme. Therefore, in order to assist decision makers to select an optimal compromise solution from the Pareto optimal frontier, it can be determined according to fuzzy set theory. Among them, the degree of satisfaction corresponding to each target value of each Pareto solution can be expressed by a fuzzy membership function, which is specifically defined as follows:

In the formula: m∈(1,N _obj ), i∈(1,M)f _m ( _xi ) is the mth objective function value of the non-inferior solution i.

Therefore, the standardized satisfaction degree of each non-inferior solution in the Pareto front can be obtained by formula (13):

Finally, through comparison, the solution with the greatest satisfaction in the Pareto front is selected as the optimal compromise solution.

The above is a detailed description of another embodiment of a multi-objective-based improved gray wolf optimization algorithm provided by the embodiment of the present invention. The following will combine a specific example to verify that the improved gray wolf algorithm has multiple constraints, nonlinearity, and impossible Effectiveness in micro and multi-objective optimization problems involving a large number of local optima.

In order to verify the effectiveness of the improved gray wolf algorithm in dealing with multi-objective optimization problems with multi-constraints, nonlinearity, non-differentiability and a large number of local optimum points, the improved gray wolf algorithm and the gray wolf algorithm were respectively applied to The simulation analysis is carried out on the combined heat and power power system of the unit, two cogeneration units and one pure heating unit. , heat load demand are 700MW and 150MWth respectively. The calculation example uses MATLAB R2010b for programming language; the computer operating environment is Inter(R) CPU G5400, 2.49GHz, the memory is 3.40GB, and the operating system is Windows XP Professional. At the same time, in order to ensure the rationality of the test results and effectively verify the influence of the direction correction operation on the standard gray wolf algorithm, therefore, except that the unique correction probability p _v of the improved gray wolf algorithm is set to 0.4, both the improved gray wolf algorithm and the gray wolf algorithm are The same population size of 50, the maximum number of iterations of 500, and the same initialization population were used in 100 trials, and the respective optimal solutions were selected as the final Pareto optimal frontier.

For ease of understanding, the following will explain the optimization problem model of cogeneration economic and environmental protection in detail.

The core of the economic and environmental scheduling optimization problem of combined heat and power generation is to simultaneously optimize the two objectives of fuel cost and environmental protection under the satisfaction of heat and power production load balance and various constraints, so as to obtain a more satisfactory optimal compromise scheduling scheme. Its mathematical model can be expressed as follows.

Objective function:

(1) Fuel cost function

This system includes ordinary thermal power pure generating units, cogeneration units and pure heating units. Therefore, its total fuel cost is expressed as formula (14)

In the formula: C _total is the total fuel cost; N _p , N _c , and N _h are the numbers of thermal power pure generating units, combined heat and power units, and pure heating units respectively; C _pi (P _i ) is the i-th thermal power pure generating set Fuel cost; C _ci (O _i ,H _i ) is the fuel cost of the i-th cogeneration unit; C _hi (T _i ) is the fuel cost of the i-th pure heat generation unit; P _i is the fuel cost of the i-th thermal power pure generator set Output, O _i , H _i are the power generation and calorific value of the i-th cogeneration unit respectively; T _i is the calorific value of the i-th pure heating unit;

In the actual cogeneration economic and environmental protection scheduling problem, it is usually necessary to consider the sudden opening of the steam turbine inlet valve in the thermal power pure generating set as shown in Figure 5 (comparison of the consumption characteristic curve of the thermal power plant with and without the valve point effect) The wire-drawing phenomenon that occurs when the valve point effect occurs, this phenomenon superimposes a sinusoidal pulsation function on the secondary consumption characteristic curve of the original thermal power pure generator set, so while solving the problem more accurately, it also makes the problem suddenly A large number of local optimal points have been added, which increases the difficulty of solving the problem. Its specific expression is as formula (15).

In the formula: a _i , b _i , and c _i are the fuel cost coefficients of the i-th pure thermal power generator set; e _i , f _i are the valve point effect coefficients of the thermal power pure generator set i; Contribute to the minimum technology of thermal power pure generator set i. Secondly, the fuel cost functions of combined heat and power and pure heating units are shown in equation (16) and equation (17) respectively.

In the formula: α _i , β _i , γ _i , δ _i , ε _i , ξ _i are the fuel cost coefficients of cogeneration unit i; ψ _i , η _i , λ _i are the fuel cost coefficients of pure heating unit i.

(2) Pollutant gas emission function

The pollutant gases produced by pure thermal power generating units, combined heat and power units and pure heating units during operation are mainly SO2, NOx and CO2, etc., and their emissions mainly depend on the power generation and calorific value of the units. The specific mathematical model is:

In the formula: E _total is the total pollutant emission; E _pi (P _i ) is the emission of pure thermal power generating unit i; E _ci (O _i ) is the emission of cogeneration unit i;

E _hi (T _i ) is the emission of pure heating unit i; μ _i , _ki , π _i , σ _i , θ _i are the emission coefficients of pure generating unit i; τ _i is the emission coefficient of cogeneration unit i; ρi is the emission coefficient of pure heat generation unit _i ;

Restrictions:

(1) System thermal and electrical load balance constraints

Large-scale storage of electric energy and heat energy is not easy, requiring simultaneous heat and electricity production and consumption in the system, so it is necessary to ensure that the heat and electricity production in the system meets the load demand balance, as shown below.

In the formula: P _D , _PL are the electrical load demand and network loss of the system respectively; _HD is the heat load demand of the system.

Pure generating unit output constraints

In the formula: It is the upper limit of output of pure generating set.

Cogeneration Unit Operational Constraints

Figure 6 shows the thermoelectric coupling relationship of the cogeneration unit. The closed area surrounded by the fixed point ABCDEF is the safe operation area of the cogeneration unit. Along the boundary line segment BC of the region, the output of the unit gradually decreases with the increase of the calorific value, while along the line segment CD, the calorific value of the unit decreases gradually.

In the formula: Respectively, the upper and lower limits of the power generation output of cogeneration unit i; are the upper and lower limits of the calorific value of cogeneration unit i, respectively.

Pure Heater Constraint

In the formula: are the upper and lower limits of the calorific value of the pure heating unit, respectively.

The above is a detailed introduction to the optimization problem model of cogeneration economic and environmental protection scheduling. The optimization results of the two algorithms will be analyzed below.

Analysis of optimization results:

Fig. 7 shows the best Pareto optimal front obtained by NSGAII algorithm, SPEA2 algorithm, gray wolf algorithm and improved gray wolf algorithm proposed in the present invention for 100 independent runs. Table 1 lists the minimum fuel cost and emission for single-objective optimization of the RCGA algorithm, and lists the objective function values at the Pareto optimal frontier endpoints of the gray wolf algorithm and the improved gray wolf algorithm. In order to verify the validity of the solution, Table 2 gives the optimal compromise solution of each algorithm and its corresponding scheduling scheme.

From Table 1-2, the comparison of the single-objective extreme values and compromise solutions of each algorithm shows that all dispatching schemes, whether it is the output of pure thermal power generating units, the power generation and calorific value of combined heat and power units, or the calorific value of pure heating units, all strictly meet the various requirements. Complicated constraints, and heat and electricity can better meet the load balance requirements, this optimization result shows the correctness of the optimal solution set obtained by the gray wolf algorithm and the improved gray wolf algorithm. At the same time, it can be found from Table 1 that although the improved gray wolf algorithm introduces the direction correction operation to increase the CPU running time by 18.54% compared with the gray wolf algorithm, the extreme value of the Pareto economic target obtained by the improved gray wolf algorithm is 10069.38$, which is higher than that of the gray wolf algorithm. The algorithm reduces the cost by 8.85%, and reduces the cost by 6.01% compared with the RCGA algorithm, and the extreme value of its environmental protection target is 14.0443kg, which reduces the emission by 16.03% compared with gray wolf, and even reduces the emission by 17% compared with NSGAⅡ. Therefore, the improved gray wolf algorithm can obtain a wider range of Pareto optimal frontiers in a relatively reasonable calculation time when solving the multi-constraint, nonlinear, non-differentiable cogeneration economic and environmental dispatch optimization problem, which also shows that the algorithm has Stronger global search capability. Secondly, from Table 2 combined with the relevant parameters of each unit, it is not difficult to find that the compromise solution obtained by the improved gray wolf algorithm is correct and reasonable, and both the fuel cost and the emission value are smaller than other algorithms, which further illustrates the improved gray wolf algorithm superiority in scheduling decisions. Finally, compared with the Pareto optimal front obtained by the NSGAⅡ algorithm, SPEA2 algorithm, and gray wolf algorithm, the Pareto optimal front obtained by the improved gray wolf algorithm is evenly distributed in the solution space and has a wider range, which is closer to the global optimal solution. This is because the improved gray wolf algorithm not only expands the multi-objective optimization of the gray wolf algorithm, but also introduces the fast non-inferior solution sorting and congestion distance calculation of NSGA II to deal with the multi-objective sorting problem, which effectively maintains the particle diversity and improves the algorithm. computing efficiency. It also combines the unique advantages of the direction correction operation in dealing with the problem of partial dimensions falling into local optimum, effectively avoiding premature convergence. This series shows that the improved multi-objective gray wolf optimization algorithm has better global convergence and adaptability.

Table 1 Comparison of extreme values and scheduling schemes of each algorithm

Table 2 Comparison of optimal compromise solutions of each algorithm

The significant advantages of the improved gray wolf optimization algorithm based on multi-objective provided by the embodiment of the present invention are:

1) Integrating the vertical cross operation in the vertical and horizontal cross algorithm into the gray wolf algorithm to help some dimensions trapped in local optimum get rid of the current predicament, correct the direction of the wolf pack, and enhance the global convergence of the algorithm.

2) Introduce the fast non-inferior solution sorting and crowding distance calculation strategy of NSGA II to assist in sorting wolf individuals and maintain the diversity of particles to a certain extent.

3) When the position of the wolf pack is updated, the elite retention strategy is adopted to give the wolf pack a certain degree of autonomy. This kind of wolf pack always maintains the overall optimal position of the wolf pack, which effectively speeds up the convergence speed of the entire algorithm.

4) The calculation example of the combined heat and power power system including 4 thermal power pure generating units, 2 combined heat and power units and 1 pure heating unit verifies the improved gray wolf algorithm proposed in the embodiment of the present invention, and the results show that the improved The gray wolf algorithm has strong global convergence and adaptability.

Those skilled in the art can clearly understand that for the convenience and brevity of the description, the specific working process of the above-described system, device and unit can refer to the corresponding process in the foregoing method embodiment, which will not be repeated here.

In the several embodiments provided in this application, it should be understood that the disclosed system, device and method can be implemented in other ways. For example, the device embodiments described above are only illustrative. For example, the division of the units is only a logical function division. In actual implementation, there may be other division methods. For example, multiple units or components can be combined or May be integrated into another system, or some features may be ignored, or not implemented. In another point, the mutual coupling or direct coupling or communication connection shown or discussed may be through some interfaces, and the indirect coupling or communication connection of devices or units may be in electrical, mechanical or other forms.

The units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, that is, they may be located in one place, or may be distributed to multiple network units. Part or all of the units can be selected according to actual needs to achieve the purpose of the solution of this embodiment.

In addition, each functional unit in each embodiment of the present invention may be integrated into one processing unit, each unit may exist separately physically, or two or more units may be integrated into one unit. The above-mentioned integrated units can be implemented in the form of hardware or in the form of software functional units.

If the integrated unit is realized in the form of a software function unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on such an understanding, the essence of the technical solution of the present invention or the part that contributes to the prior art or all or part of the technical solution can be embodied in the form of a software product, and the computer software product is stored in a storage medium , including several instructions to make a computer device (which may be a personal computer, a server, or a network device, etc.) execute all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM, Read-OnlyMemory), random access memory (RAM, Random Access Memory), magnetic disk or optical disk and other media that can store program codes.

As mentioned above, the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: it can still understand the foregoing The technical solutions recorded in each embodiment are modified, or some of the technical features are replaced equivalently; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the various embodiments of the present invention.

Claims (10)

1. A kind of improved gray wolf optimization algorithm based on multi-objective, it is characterized in that, comprises: S1. Set the initialization parameters and direction correction probability of the wolf group, and randomly initialize the position of each wolf individual in the solution space; S2. Calculate the fitness value of each wolf individual according to the solution target, and select the top three wolf individuals and assign them to X _α , X _β , and X _δ in turn; S3. Optimizing the position of each wolf individual in the wolf pack according to the X _α , the X _β , and the X _δ to generate a moderate wolf, and calculate the fitness value of the moderate wolf and update the position of the wolf pack; S4. Perform a direction correction operation on the updated wolf pack and control the scale of the updated wolf pack participating in the correction dimension according to the direction correction probability, generate a new moderate wolf, and calculate the fitness of the new moderate wolf value, to obtain the corrected wolf pack position; S5. Determine whether the number of iterations reaches the preset maximum number of iterations. If yes, output the corrected wolf pack position as the final optimization result; otherwise, go to S3 to continue the iterative search. 2. the improved gray wolf optimization algorithm based on multi-objective according to claim 1, is characterized in that, described S1 specifically comprises: Set the size M of the wolf pack, the maximum number of iterations maxgen and the direction correction probability p _v , and randomly initialize the position of each wolf individual in the solution space. 3. the improved gray wolf optimization algorithm based on multi-objective according to claim 1, is characterized in that, described S2 specifically comprises: Calculate the fitness value of each wolf individual according to the solution goal, and select the top three wolf individuals according to the fast non-inferior solution sorting operation, crowding distance calculation, and elite retention strategy to assign X _α , X _β , and X _δ in turn . 4. the improved gray wolf optimization algorithm based on multi-objective according to claim 3, is characterized in that, described fast non-inferior solution ordering operation specifically comprises: Find the non-dominated solution set in the wolf group, mark the non-dominated solution set as the first non-dominated layer F1 and assign the first non-dominated sequence value to all wolves in the non-dominated solution set, and set all the wolves in the non-dominated solution set Wolf individual culling; Find the next layer of non-dominated solution sets in the eliminated wolves and perform marking, non-dominated sequence value assignment operations and elimination operations; Continue to perform non-dominated disassembly stratification, marking, non-dominated sequence value assignment and elimination operations on the wolf pack in sequence until the entire wolf pack is completely stratified and the wolves in the same non-dominated layer have the same non-dominated sequence. value. 5. the improved gray wolf optimization algorithm based on multi-objective according to claim 4, is characterized in that, described congestion distance calculation specifically comprises: Initialize the distance of wolf individuals in the same non-dominated layer, so that the crowding distance L[i] _d of wolf individual i is 0; Wolf individuals in the same non-dominated layer are sorted incrementally according to the mth target value; Two wolf individuals on the given edge are assigned a large number Inf, so that the two wolf individuals have an absolute selection advantage; The wolf individual in the middle of the sorting is calculated according to the formula eight for the crowding distance of the wolf individual in the middle of the sorting, and the formula eight is specifically: <mrow> <mi>L</mi> <msub> <mrow> <mo>&amp;lsqb;</mo> <mi>i</mi> <mo>&amp;rsqb;</mo> </mrow> <mi>d</mi> </msub> <mo>=</mo> <mi>L</mi> <msub> <mrow> <mo>&amp;lsqb;</mo> <mi>i</mi> <mo>&amp;rsqb;</mo> </mrow> <mi>d</mi> </msub> <mo>+</mo> <mrow> <mo>(</mo> <msubsup> <mi>f</mi> <mi>m</mi> <mrow> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> </msubsup> <mo>-</mo> <msubsup> <mi>f</mi> <mi>m</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mo>)</mo> </mrow> <mo>/</mo> <mrow> <mo>(</mo> <msubsup> <mi>f</mi> <mi>m</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msubsup> <mo>-</mo> <msubsup> <mi>f</mi> <mi>m</mi> <mrow> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> </msubsup> <mo>)</mo> </mrow> <mo>,</mo> <mi>m</mi> <mo>&amp;Element;</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>,</mo> <msub> <mi>N</mi> <mrow> <mi>o</mi> <mi>b</mi> <mi>j</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>;</mo> </mrow> Among them, N _obj is the target number, are the mth fitness value of the i+1th and i-1th wolf individuals respectively, are the maximum and minimum values of the mth fitness value in the non-inferior solution set, respectively. 6. the improved gray wolf optimization algorithm based on multi-objective according to claim 3, is characterized in that, described S3 specifically comprises: According to the X _α , the X _β , and the X _δ , optimize the position of each wolf individual in the wolf pack through the steps of wolf pack encirclement and wolf pack hunting, generate a moderate wolf, and calculate the fitness of the moderate wolf The degree value and selective updating of wolf pack positions are based on fast non-inferior solution sorting operations, congestion distance calculation, and elite retention strategy. 7. the improved gray wolf optimization algorithm based on multi-objective according to claim 6, is characterized in that, also comprises between described S3 and S4: Perform a normalization operation on each dimension of all wolf individuals of the updated wolf group by formula nine, and the formula nine is specifically: <mrow> <mover> <mi>N</mi> <mo>&amp;RightArrow;</mo> </mover> <mrow> <mo>(</mo> <mi>d</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <msup> <mover> <mi>X</mi> <mo>&amp;RightArrow;</mo> </mover> <mi>t</mi> </msup> <mrow> <mo>(</mo> <mi>d</mi> <mo>)</mo> </mrow> <mo>-</mo> <mi>m</mi> <mi>i</mi> <mi>n</mi> <mrow> <mo>(</mo> <mi>d</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mi>max</mi> <mrow> <mo>(</mo> <mi>d</mi> <mo>)</mo> </mrow> <mo>-</mo> <mi>m</mi> <mi>i</mi> <mi>n</mi> <mrow> <mo>(</mo> <mi>d</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>,</mo> <mi>d</mi> <mo>&amp;Element;</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>,</mo> <mi>D</mi> <mo>)</mo> </mrow> <mo>;</mo> </mrow> Among them, D is the dimension, for the wolf The d-th dimension variable of , for The corresponding scalars after normalization, max(d) and min(d) are respectively the upper and lower limits of the d-th dimension variable in the wolf pack. 8. the improved gray wolf optimization algorithm based on multi-objective according to claim 7, is characterized in that, described S4 specifically comprises: Performing a direction correction operation on the updated wolf pack and controlling the size of the updated wolf pack participating in the correction dimension according to the direction correction probability, generating a new moderate wolf, and calculating the fitness value of the new moderate wolf, According to the fast non-inferior solution sorting operation, the calculation of crowding distance, and the elite retention strategy, the positions of individual wolves are selected and reserved, and according to the ranking of individual wolves in the wolf pack, the wolf pack is divided into X _α , X _β , X _δ , X _ω , and the correction is obtained The position of the wolf pack behind. 9. the improved gray wolf optimization algorithm based on multi-objective according to claim 8, is characterized in that, described carrying out direction correction operation to the wolves after updating specifically comprises: Perform the direction correction operation on the updated wolves through formula ten, which is specifically: <mrow> <mover> <mi>M</mi> <mo>&amp;RightArrow;</mo> </mover> <mi>N</mi> <mrow> <mo>(</mo> <msub> <mi>d</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mi>r</mi> <mo>&amp;CenterDot;</mo> <mover> <mi>N</mi> <mo>&amp;RightArrow;</mo> </mover> <mrow> <mo>(</mo> <msub> <mi>d</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mo>+</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <mi>r</mi> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <mover> <mi>N</mi> <mo>&amp;RightArrow;</mo> </mover> <mrow> <mo>(</mo> <msub> <mi>d</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> <mo>;</mo> </mrow> Among them, d ₁ , d ₂ ∈ (1, D), r is a random number from 0 to 1, is the mean wolf individual scalar The _d1th dimension of ; Each dimension of the generated mediocre wolf individual scalar is denormalized by formula 11, and the formula 11 is specifically: in, mean wolf The d-th dimension of . 10. the improved gray wolf optimization algorithm based on multi-objective according to claim 9, is characterized in that, described S5 specifically comprises: Judging whether the number of iterations reaches the preset maximum number of iterations, if so, output the corrected wolf pack position as the final optimization result, and combine the fuzzy decision-making method to select the optimal compromise solution, otherwise, go to S3 to continue iterative search.