CN111027666A - Function optimization method, device and system - Google Patents
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Abstract
The invention provides a method, a device and a system for optimizing a function, wherein the method comprises the steps of determining a target function and a decision variable corresponding to an actual application scene; constructing a system model of a matched bacterial chemotaxis function optimization algorithm based on a target function and a decision variable corresponding to an actual application scene; performing function optimization operation on a system model of the bacterial chemotaxis function optimization algorithm to obtain a decision variable optimal solution for optimizing the objective function; the moving step length of the decision variable in the function optimization operation is in a decreasing trend along with the increase of the iteration times; and outputting the optimal solution of the decision variables for the actual application scene. The invention provides a scheme for realizing the trend of moving step length from large to small in the function optimization process of the bacterial chemotaxis function optimization algorithm, thereby improving the convergence and the optimization rate of the bacterial chemotaxis function optimization algorithm. In addition, a directional variation strategy is also provided in the system model aiming at the multi-target bacterial population chemotaxis algorithm to improve the distribution of the bacterial population.
Description
Technical Field
The invention relates to the technical field of automatic decision making, in particular to a function optimization method, a device and a system.
Background
Among many function optimization algorithms, there are many heuristics derived from natural biological processes, such as bacterial chemotaxis function optimization algorithms derived from the movement behavior of bacteria towards attractants. The bacterial chemotaxis function optimization algorithm can be divided into the following steps according to the number of objective functions and the number of bacteria in a decision space:
the method comprises the steps of performing function optimization on a single objective function by adopting a single bacterium, performing function optimization on the single objective function by adopting a bacterium group, and performing function optimization on a plurality of objective functions by adopting a multi-objective bacterium group. The rate of optimization of the bacterial population is greater than the rate of optimization of a single bacterium.
The bacterial chemotaxis function optimization algorithm is based on the movement behavior of the bacterial chemotaxis attractant, and the approximate execution process is as follows: setting a single decision variable or a plurality of decision variables (corresponding to a single bacterium or a bacterium group), a single objective function or a multi-objective function (corresponding to one or more attractants) in a decision space, and setting a position adjustment rule of the decision variables.
In one iteration, the moving direction and the moving step length of the decision variable (namely the distance variation between the new position of the decision variable and the original position in the moving direction) are adjusted based on the position adjusting rule, and the new position can be determined based on the moving direction and the moving step length; if the objective function value corresponding to the new position is better (equivalent to the concentration rise of the attractant), moving to the new position; conversely, if the objective function value corresponding to the new position is worse (equivalent to the decrease of the concentration of the attractant), the original position is maintained, so that one iteration is completed; the optimal position of the decision variables is obtained in successive iterations.
To represent the random mobility of the new positions of the decision variables, the moving step is determined using a probability distribution function. The movement steps used in the function optimization process to determine the new position are therefore randomly variable, increasing in time and decreasing in time.
However, as the number of iterations in the bacterial chemotaxis function optimization algorithm increases, the current position of the decision variable will be closer to the optimal position (which is equivalent to the bacteria tending to attractants more and more). In the case that the moving step size is randomly changed, the moving step size may be moved from a home position closer to the attractant to a new position farther from the attractant, which results in poor convergence and low optimization rate of the function optimization process.
Disclosure of Invention
During the research process of the inventor, the following results are found: in general, the system model parameters of the bacterial chemotaxis function optimization algorithm are invariable in the function optimization process, and the function optimization is carried out through a fixed system model.
In a certain paper, a system model of a bacterial chemotaxis function optimization algorithm can be continuously optimized in a function optimization process, for example, parameters of the system model are optimized by adopting a whole parameter adaptive updating strategy to obtain an optimized system model, and function optimization is performed on the basis of the optimized system model to achieve better effects.
And setting optimization precision in the optimization process of the system model, and after adopting the self-adaptive updating of all parameters, providing that the moving step length can be adjusted based on the optimization precision. Setting the moving step length to be larger when the optimization precision is lower; when the optimization precision is higher, the bacteria is determined to reach the vicinity of the optimal position range, and the set moving step length is reduced.
However, this paper is only applicable to the case with optimized precision, and is no longer applicable to the case without optimized precision. That is, the present invention is not applicable to the case where there is no optimization accuracy in the process of performing function optimization using a fixed system model. In addition, under the condition of optimizing a system model of the bacterial chemotaxis function optimization algorithm, the moving step length cannot be adjusted by other modes except the optimization precision.
In view of this, the invention provides a function optimization method, device and system, which implement a trend scheme of moving step length from large to small in the function optimization process of the bacterial chemotaxis function optimization algorithm, thereby improving the convergence and optimization rate of the bacterial chemotaxis function optimization algorithm.
In order to achieve the above object, the present application provides the following technical features:
a method of function optimization, comprising:
determining a target function and a decision variable corresponding to an actual application scene;
constructing a system model of a matched bacterial chemotaxis function optimization algorithm based on a target function and a decision variable corresponding to the actual application scene;
performing function optimization operation on the system model of the bacterial chemotaxis function optimization algorithm to obtain a decision variable optimal solution for optimizing the objective function; wherein the moving step length of the decision variable in the function optimization operation is in a decreasing trend along with the increase of the iteration number;
and outputting the optimal solution of the decision variables for the actual application scene.
Optionally, the step size of the decision variable in the function optimization operation decreases with the increase of the number of iterations includes:
the moving step length is reduced along with the increase of the iteration times; or the like, or, alternatively,
in the case of a decision variable with constant speed, the duration decreases as the number of iterations increases.
Optionally, the decreasing the moving step with the increase of the number of iterations includes:
the moving step length of a decision variable in the function optimization operation is linearly decreased along with the increase of the iteration times; or the like, or, alternatively,
the moving step length of a decision variable in the function optimization operation is exponentially decreased along with the increase of the iteration times; or the like, or, alternatively,
the step size of the movement of the decision variable in the function optimization operation is randomly decreased along with the increase of the iteration number.
Optionally, the decreasing duration with the increasing number of iterations includes:
the duration of a decision variable in the function optimization operation is linearly decreased along with the increase of the iteration times; or the like, or, alternatively,
the duration of a decision variable in the function optimization operation is exponentially decreased along with the increase of the iteration number; or the like, or, alternatively,
the duration of the decision variable in the function optimization operation is randomly decreased along with the increase of the iteration number.
Optionally, the constructing a system model of a matched bacterial chemotaxis function optimization algorithm based on the objective function and the decision variables corresponding to the actual application scenario includes:
under the condition that the actual application scene corresponds to a single objective function and a decision variable of the single objective function, constructing a system model of a bacterial chemotaxis algorithm or a system model of a bacterial population chemotaxis algorithm;
and constructing a system model of the multi-target bacteria population chemotaxis algorithm under the condition that the actual application scene corresponds to a plurality of objective functions and decision variables of the objective functions.
Optionally, in the case of constructing the system model of the multi-objective bacterial population chemotaxis algorithm, the performing a function optimization operation on the system model of the bacterial chemotaxis function optimization algorithm to obtain an optimal solution of a decision variable for optimizing the objective function includes:
individual optimization is performed for each decision variable in the decision space: executing individual optimization according to a multi-target bacteria group drug-trending algorithm to obtain the position of a decision variable, if the function value corresponding to the position is superior to the function value corresponding to the original position, moving the decision variable to the position, and if not, maintaining the original position; wherein, in the individual optimization executed by the bacterial chemotaxis algorithm, the moving step length of the decision variable is in a decreasing trend along with the increase of the iteration times;
determining decision variables meeting group optimization conditions after performing individual optimization on each decision variable in a decision space;
performing group optimization for each decision variable in the decision space that satisfies the group optimization condition: executing group optimization according to a multi-target bacteria group drug-trending algorithm to obtain the position of a decision variable, if the function value corresponding to the position is superior to the function value corresponding to the original position, moving the decision variable to the position, and if not, maintaining the original position;
judging whether an iteration end condition is reached;
if not, re-entering the step of performing individual optimization aiming at each decision variable in the decision space;
if so, determining the position corresponding to each decision variable in the bacterial population as each solution to be determined;
respectively calculating the comprehensive satisfaction corresponding to each solution to be determined based on the fuzzy membership function;
and determining the solution to be determined with the maximum comprehensive satisfaction degree in all the solutions to be determined as the optimal solution of the decision variables for optimizing the objective function.
Optionally, before the re-entering performs the individual optimization step for each decision variable in the decision space, the method further includes:
and (3) improving the distribution of the bacterial population by adopting a bacterial population directed mutation strategy.
Optionally, the improving the distribution of the bacterial population by using the bacterial population directed variation strategy comprises:
calculating the crowding distance of each decision variable in the bacterial population in the space of the objective function value;
sequencing each decision variable according to the size of the crowding distance, and dividing the bacterial population into two halves: a half decision variable set with a smaller congestion distance and a half decision variable set with a larger congestion distance;
for each decision variable in the half of the decision variable set with the smaller congestion distance:
calculating a new position of a decision variable according to a directional variation formula, wherein the new position is positioned in a half decision variable set with a larger crowding distance; and if the target function value corresponding to the new position is not worse than the target function value corresponding to the original position, the decision variable is moved to the new position, otherwise, the original position is maintained.
A function optimization device, comprising:
the determining unit is used for determining an objective function and a decision variable corresponding to an actual application scene;
the construction unit is used for constructing a system model of a matched bacterial chemotaxis function optimization algorithm based on a target function and a decision variable corresponding to the actual application scene;
the optimization unit is used for executing function optimization operation on the system model of the bacterial chemotaxis function optimization algorithm to obtain a decision variable optimal solution for optimizing the objective function; wherein the moving step length of the decision variable in the function optimization operation is in a decreasing trend along with the increase of the iteration number;
and the output unit is used for outputting the optimal solution of the decision variables to be used in the actual application scene.
A function optimization system, comprising:
the automatic application unit is used for operating according to an actual application scene;
the processing equipment is used for determining a target function and a decision variable corresponding to an actual application scene in the automatic application unit; constructing a system model of a matched bacterial chemotaxis function optimization algorithm based on a target function and a decision variable corresponding to the actual application scene; performing function optimization operation on the system model of the bacterial chemotaxis function optimization algorithm to obtain a decision variable optimal solution for optimizing the objective function; wherein the moving step length of the decision variable in the function optimization operation is in a decreasing trend along with the increase of the iteration number; and outputting the optimal solution of the decision variables for the actual application scene.
Through the technical means, the following beneficial effects can be realized:
the invention provides a function optimization method, which is characterized in that when a system model based on a bacterial chemotaxis function optimization algorithm executes function optimization operation to determine a new position, a random distribution function is not used for determining the moving step length, but a scheme that the moving step length is in a decreasing trend according to the increase of iteration times is provided.
The moving step length is adjusted according to the iteration times, so that the function optimization early stage has a relatively large moving step length, and the function optimization later stage has a relatively small moving step length. Therefore, excessive time consumption in a local range can be avoided in the early stage of function optimization, and optimization efficiency is improved; and in the later stage of function optimization, the optimal position can be gradually approached by a relatively small moving step length, so that the convergence of the bacterial chemotaxis function optimization algorithm is improved.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a flowchart of a first embodiment of a method for optimizing a function according to the present invention;
FIG. 2 is a flowchart of a second embodiment of a method for optimizing a function according to the present invention;
FIG. 3 is a flow chart of function optimization in a second embodiment of the method for function optimization according to the present invention;
FIG. 4 is a schematic structural diagram of a function optimization apparatus according to an embodiment of the present invention;
fig. 5 is a schematic structural diagram of a function optimization system according to an embodiment of the present invention.
Detailed Description
In many technical fields such as the technical field of electric power systems, the technical field of automation, the technical field of industrial control, the technical field of smart homes and the like, a bacterial chemotaxis function optimization algorithm can be used for performing function optimization, and the optimal solution based on the function optimization is used for guiding production or use in an actual application scene.
Taking the technical field of industrial control as an example, in the application scene of coal-fired power generation, when the coal consumption cost is high, the corresponding carbon emission is small, and when the coal consumption cost is low, the corresponding carbon emission is large; therefore, the minimum coal consumption cost function and the minimum carbon emission function are subjected to function optimization by adopting a bacterial chemotaxis function optimization algorithm, so that an optimal solution with low coal consumption cost and low carbon emission is obtained.
Taking the technical field of intelligent home as an example, in the application scene of electric heating, when the power consumption is large, the temperature is high, the user comfort level is good, and when the power consumption is small, the coal consumption cost is low, and the user comfort level is not good; therefore, the minimum heating cost function and the maximum comfort level function are subjected to function optimization by adopting a bacterial chemotaxis function optimization algorithm so as to obtain an optimal solution with lower heating cost and better comfort level.
Of course, the bacterial chemotaxis function optimization algorithm can also be applied to many practical application scenarios, which are not listed here. The actual application scenario may be determined according to specific situations, which are not limited.
When the function optimization process is executed by using the bacterial chemotaxis function optimization algorithm, the problems of convergence and optimization speed deviation caused by the random change of the moving step length of the bacteria can be faced. Therefore, the invention provides a scheme that the moving step length in the process of executing the function optimization by the bacterial chemotaxis function optimization algorithm is in a trend from large to small, thereby improving the convergence and the optimization rate of the bacterial chemotaxis function optimization algorithm.
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Referring to fig. 1, a first embodiment of the method for optimizing a function provided by the present invention is applied to a processing device, and the method includes:
step S101: and determining an objective function and a decision variable corresponding to the actual application scene.
And determining an objective function based on the actual application scene, and determining a decision variable in the objective function. It can be understood that the objective functions corresponding to different practical application scenarios are different, and the decision variables used in the objective functions are also different.
Continuing the application scenario of electric heating, the objective function may be: a minimum heating cost function and a maximum comfort function; the decision variables may be: the temperature of the circulating water in the radiator and the indoor temperature; of course, the objective function may also be other functions, and the decision variable may also be other variables, and the specific situation is determined according to the actual situation, which is not limited in the present invention.
After determining the objective function and the decision variables, the user may input the objective function and the decision variables to the processing device, or the processing device may obtain the objective function and the decision variables from other devices. The specific implementation manner of determining the objective function and the decision variable corresponding to the actual application scenario by the processing device is not limited.
Step S102: and constructing a system model of a matched bacterial chemotaxis function optimization algorithm based on the objective function and the decision variables corresponding to the actual application scene.
This step can be made in two cases:
in the first case: and under the condition that the actual application scene corresponds to a single objective function and the decision variables of the single objective function, constructing a system model of the bacterial chemotaxis algorithm or a system model of the bacterial population chemotaxis algorithm.
It will be appreciated that the bacterial population use in the bacterial population chemotaxis algorithm for the functional optimization operation has a greater rate of optimization than the rate of optimization of the functional optimization using a single bacterium in the bacterial chemotaxis algorithm.
The system model of the bacterial chemotaxis algorithm or the system model of the bacterial population chemotaxis algorithm is specifically adopted and can be determined according to the actual application scene. Under the condition of not considering the optimization rate, a system model of a bacterial chemotaxis algorithm can be adopted, so that the method is simple and convenient; under the condition of considering the optimization rate, the optimization rate of the system model which can adopt the bacterial population chemotaxis algorithm is better.
Of course, the choice of the system model depends on the actual situation, which is not limited by the present invention.
In the second case: and constructing a system model of the multi-target bacteria population chemotaxis algorithm under the condition that the actual application scene corresponds to a plurality of objective functions and decision variables of the objective functions.
When at least two or more objective functions are provided, a system model of a multi-objective bacterial population chemotaxis algorithm is adopted, and the model is mainly applied to the condition of the multi-objective functions.
After the specific system model is determined, initialization parameters of the specific system model are set. Different initialization parameters may be set depending on different system models.
Step S103: performing function optimization operation on the system model of the bacterial chemotaxis function optimization algorithm to obtain a decision variable optimal solution for optimizing the objective function; wherein the step size of the decision variable in the function optimization operation is reduced along with the increase of the iteration number.
In performing a function optimization operation on the system model of the bacterial chemotaxis function optimization algorithm, a decision variable (i.e. bacteria) needs to be moved from an original position to a new position in a moving step size and a moving direction. In order to improve the convergence of function optimization and the optimization speed, the moving step length of the decision variable is proposed to be in a decreasing trend along with the increase of the iteration number.
This example provides two scenarios:
the first scheme reduces the moving step length along with the increase of the iteration times; i.e. directly on the step of moving, and directly decreasing the step of moving as the number of iterations increases.
The second scheme reduces the duration with increasing number of iterations, with a constant speed of the decision variable; i.e. indirectly on the step of moving, the duration is reduced at constant speed with increasing number of iterations, thereby reducing the step of moving.
Three implementations provided by the first scheme are described below.
It will be appreciated that other implementations may be used, as long as the step size of the move decreases as the number of iterations increases.
The first implementation mode comprises the following steps: the step size of the movement of the decision variable in the function optimization operation is linearly decreased along with the increase of the iteration number.
The moving step length is linearly decreased, so that the moving step length in each iteration is linearly decreased, the decreasing degree in each iteration is consistent, the decreasing of the moving step length is regular, and the optimization speed and the convergence are better.
The second implementation mode comprises the following steps: the step size of the movement of the decision variable in the function optimization operation decreases exponentially with the increase of the number of iterations.
The moving step size decreases exponentially, so that the moving step size decreases exponentially in each iteration. The descending speed is high in the early stage of function optimization, the local range can be quickly jumped out through a relatively large moving step length, and the optimization efficiency is improved; and the descending speed is low in the later stage of function optimization, the optimal position can be gradually approached through a relatively small moving step length, and the convergence of the bacterial chemotaxis function optimization algorithm is further improved.
The third implementation mode comprises the following steps: the step size of the movement of the decision variable in the function optimization operation is randomly decreased along with the increase of the iteration number. The step size of the movement at each iteration in this implementation is in a decreasing trend, but the degree of each decrease is randomly determined. This step can also improve the optimization speed and convergence of the function optimization to some extent.
The effects of the first implementation and the second implementation may be superior to the third implementation.
Three implementation modes provided by the second scheme are described below, and the three implementation modes have the same principle as the three implementation modes of the first scheme. It will be appreciated that other implementations may be used, as long as the step size of the move decreases as the number of iterations increases.
The first implementation mode comprises the following steps: the duration of the decision variables in the function optimization operation decreases linearly with the number of iterations.
The constant speed of the decision variable is preset, and under the condition that the duration time is linearly decreased, the moving step length in each iteration is linearly decreased, the decrease degree in each iteration is consistent, the decrease of the moving step length is enabled to be regular, and therefore the optimization speed and the convergence are better.
The second implementation mode comprises the following steps: the duration of the decision variables in the function optimization operation decreases exponentially as the number of iterations increases.
The constant speed of the decision variable is preset, and under the condition that the duration is exponentially decreased, the moving step length in each iteration is exponentially decreased. The descending speed is high in the early stage of function optimization, the local range can be quickly jumped out through a relatively large moving step length, and the optimization efficiency is improved; and the descending speed is low in the later stage of function optimization, the optimal position can be gradually approached through a relatively small moving step length, and the convergence of the bacterial chemotaxis function optimization algorithm is further improved.
The third implementation mode comprises the following steps: the duration of the decision variable in the function optimization operation is randomly decreased along with the increase of the iteration number.
The constant speed of the decision variable is preset, and the duration of each iteration in the implementation mode is in a descending trend, but the descending degree of each iteration is randomly determined. This step can also improve the optimization speed and convergence of the function optimization to some extent.
The effects of the first implementation and the second implementation may be superior to the third implementation.
Under the condition of a system model adopting a bacterial chemotaxis algorithm, a single decision variable (namely a single bacterium) exists in the system model, so that the function optimization operation is executed on the single decision variable, and the optimal position obtained after the iteration ending condition is finally reached is the optimal solution.
Under the condition of adopting a system model of a bacterial population chemotaxis algorithm or a system model of a multi-target bacterial population chemotaxis algorithm, the system model is provided with a plurality of decision variables (namely a plurality of bacteria exist in a bacterial population), so that the function optimization operation is executed on each decision variable to obtain the solution to be determined of each decision variable. Subsequently, each undetermined solution is screened, and one undetermined solution which can optimize the objective function is determined as an optimal solution.
Step S104: and outputting the optimal solution of the decision variables for the actual application scene.
After obtaining the decision variable optimal solution for optimizing the objective function in step S103, the processing device may output the decision variable optimal solution.
In particular, the decision variable optimal solution may be displayed for viewing by a technician, output to a database for storage of the decision variable optimal solution, or output to other devices for subsequent use or processing operations by other devices. The specific implementation of this step is not limited.
When the decision variable optimal solution meets the requirements of the actual application scene, the decision variable optimal solution can be applied to the actual production of the actual application scene.
When the decision variable optimal solution does not meet the requirements of the actual application scenario, the system model of the bacterial chemotaxis function optimization algorithm can be adjusted, or the objective function and the decision variable are adjusted to re-execute the function optimization method shown in fig. 1, so that the decision variable optimal solution meeting the requirements is obtained.
Optionally, the first implementation manner (the moving step size decreases linearly) in step S103 may be implemented as follows:
and calculating the moving step length of the decision variable in each iteration according to the following linear decreasing formula:
where t is the number of iterations, ltStep size of the move of this iteration, lmaxFor the maximum step size in the decision space, lminIs the minimum step size in the decision space, tmaxIs the total number of iterations.
Initially, the move step is equal to the maximum step l in the decision spacemaxAfter iteration, the number of iterations t is increased by 1. The formula (1) is used to recalculate the moving step length in each iteration process, and the number of times of each iteration t is increased continuously, so that the obtained moving step length ltAre continuously decreasing.
Optionally, in the first implementation manner (with the duration decreasing linearly) in step S103, the moving step may be implemented as follows:
and calculating the moving step length of the decision variable in each iteration according to the following linear decreasing formula:
wherein, taumaxAnd τminThe maximum time and the minimum time, which may be preset according to the decision space, are preferably,
so that the bacteria can move within the maximum range of the decision space, τminIs 0, so thatThe later iteration stage can use the smallest moving step size.
Optionally, the second implementation manner (the moving step size decreases exponentially) in step S103 may be implemented as follows:
and calculating the moving step length of the decision variable in each iteration according to the following exponential decreasing formula:
lt＝lmax·at-1,t＝1,2,...,tmax，0＜a<1…………(3)
optionally, in the second implementation manner (the duration is exponentially decreased) in step S103, the moving step may be implemented as follows:
and calculating the moving step length of the decision variable in each iteration according to the following exponential decreasing formula:
lt＝ν*τt＝ν*[τmax·at-1,],t＝1,2,...,tmax，0＜a<1…………(4)
wherein, taumaxAnd τminThe maximum time and the minimum time, which may be preset according to the decision space, are preferably,
so that bacteria can move within the maximum range of the decision space.
Optionally, the third implementation manner (the moving step size decreases randomly) in step S103 may be implemented as follows:
s11: the step size of the movement of the decision variable in each iteration is calculated by the following steps.
S12: determining the current moving step length of a decision variable and the minimum step length in a decision space; wherein the current move step size for the first iteration is the largest step size in the decision space.
S13: and outputting a random step size between the current moving step size and the minimum step size by using a random function.
S14: and determining the difference value of the current moving step length and the random step length as the moving step length of the decision variable in the iteration.
Optionally, in the third implementation manner (with the duration decreasing randomly) in step S103, the moving step may be implemented as follows:
s21: the duration of the decision variables in each iteration is calculated by the following steps.
S22: determining a current movement time of a decision variable and a minimum time in a decision space; wherein the current move time in the case of the first iteration is the maximum time in the decision space.
S23: and outputting a random time between the current moving time and the minimum time by using a random function.
S24: and determining the difference value between the current moving time and the random time as the duration of the decision variable in the iteration.
S25: the product of the constant speed and the duration is determined as the step of movement.
The foregoing is some specific implementations of the moving step, and of course, other specific implementations may also be adopted, which is not limited in the present invention.
According to the first embodiment, the invention has the following beneficial effects:
when the new position is determined in the process of executing the function optimization operation by the system model based on the bacterial chemotaxis function optimization algorithm, the moving step length is not determined by adopting a random distribution function, but a scheme that the moving step length is in a decreasing trend according to the increase of the iteration times is provided.
The moving step length is adjusted according to the iteration times, so that the function optimization early stage has a relatively large moving step length, and the function optimization later stage has a relatively small moving step length. Therefore, excessive time consumption in a local range can be avoided in the early stage of function optimization, and optimization efficiency is improved; and in the later stage of function optimization, the optimal position can be gradually approached by a relatively small moving step length, so that the convergence of the bacterial chemotaxis function optimization algorithm is improved.
Referring to fig. 2, the second embodiment of the function optimization method provided by the present invention is applied to a processing device. In the second embodiment, a specific implementation of the system model of the multi-target bacterial population chemotaxis algorithm is described, and the method includes:
step S201: and determining a multi-objective function and a decision variable corresponding to the actual application scene.
The specific implementation of the multi-objective function is related to the actual application scenario, and is not limited to this.
Decision variables in a multi-objective function generally include a plurality of variables, one variable corresponding to one dimension, and a plurality of variables corresponding to a plurality of dimensions. Assuming that the decision variables include n variables, the decision variables have n dimensions. Spherical coordinates may be used to represent each of the decision variables.
The decision variables are moved from the original position to the new position, namely, each variable in the decision variables is moved from the original position to the new position according to the moving direction and the moving step length. The implementation is based on the fact that the moving step sizes of the variables are the same in the same iteration.
Step S202: and constructing a system model of the multi-target bacterial chemotaxis function optimization algorithm.
Initializing system model parameters, and performing a system model of a multi-target bacterial chemotaxis function optimization algorithm, wherein a spherical coordinate system is usually adopted. The system model parameters include: diameter d of decision space calculated by using decision variable space parametersmaxThe number of bacteria in the bacterial population, i.e. the number of decision variables P, the total number of iterations tmax。
And building a system model of the multi-target bacterial chemotaxis function optimization algorithm according to the initialization parameters.
Step S203: performing function optimization operation on the system model of the bacterial chemotaxis function optimization algorithm to obtain a decision variable optimal solution for optimizing the objective function; wherein the step size of the decision variable in the function optimization operation is reduced along with the increase of the iteration number.
Alternatively, referring to fig. 3, the step may include the following steps:
s0: the plurality of decision variables are randomly distributed at different locations in the decision space.
There are multiple bacteria in the bacterial population, i.e. multiple decision variables, and the multiple decision variables are randomly distributed at different positions in a decision space, where one position represents one solution of the decision variables and an optimal position, i.e. an optimal solution, needs to be found in the decision space.
S1: individual optimization is performed for each decision variable in the decision space: executing individual optimization according to the multi-target bacteria group drug-trending algorithm to obtain a new position of the decision variable, if the function value corresponding to the new position is superior to the function value corresponding to the original position, moving the decision variable to the new position, otherwise, maintaining the original position; wherein, in the individual optimization executed by the bacterial chemotaxis algorithm, the moving step length of the decision variable is in a decreasing trend along with the increase of the iteration times.
This step will be described in detail by taking as an example that the step size of the decision variable in the function optimization operation decreases linearly as the number of iterations increases. It will be appreciated that other ways of determining the step size of the movement of the decision variable may be used.
And calculating the moving step length of the decision variable in each iteration according to the following linear decreasing formula:
wherein the content of the first and second substances,
lmin0; t is the number of iterations,. ltStep size of the t-th iteration, lmaxAs the largest step size in the decision space, dmaxAs the maximum of the vector in the decision space,/minIs the minimum step size in the decision space, tmaxIs the total number of iterations.
Determining the moving direction after determining the moving step length, wherein the included angle between the new direction and the original direction follows Gaussian distribution, and the included angle can be determined by a Gaussian distribution function
For example, a random number is generated between 0 and 180 °, or between 0 and 360 °. Determining an included angle
Are not described in detail herein for the mature technology.
Under the condition that the decision variables comprise n variables, namely the decision variables have n dimensions, in the spherical coordinate system, the variables corresponding to each dimension need to be included according to the included angle
Moving step length lt. The moving step length of each dimension corresponding variable in the spherical vector space is as follows:
wherein the content of the first and second substances,
and
representing the moving step length of the 1 st dimensional variable, the ith dimensional variable and the nth dimensional variable in a coordinate system; ltIs the moving step of the t-th iteration calculated in formula (1).
The new position of the decision variables is equal to the original position superimposed by the step size of the movement of the corresponding dimension, and then the new position of each decision variable is represented by the following formula:
Xj k＝Xj k+lt k,j＝1,2,...,P,k＝1,2,...,n……………………………(8)
wherein the position of a decision variable is Xj kIndicates (the same symbol is used for both the new position and the original position), j is 1,2,.. the P, k is 1,2,. the n,Xj kthe position of the jth decision variable (i.e., the jth bacterium in the bacterial population) in k dimensions is represented.
After each decision variable executes individual optimization operation, obtaining a new position of each decision variable; if the multi-objective function values corresponding to the new position are all better (equivalent to the concentration rise of the attractant), the decision variable moves to the new position; conversely, the new position is maintained if the at least one objective function value for the new position does not change well (corresponding to a constant or decreasing concentration of attractant).
S2: after individual optimization is performed for each decision variable in the decision space, the decision variables that satisfy the population optimization condition are determined.
The default bacterial individual in the bacterial population optimization has global perception capability, namely, the position information of other bacterial individuals in the bacterial population can be perceived. For a bacterial individual in a bacterial population, if at least one other bacterial individual in the bacterial population is better located than the bacterial individual, then it is determined that the bacterial individual requires population optimization in order to move the bacterial individual to the center of the other bacterial individual whose location is better than the bacterial individual, resulting in a population-optimized location.
S3: performing group optimization for each decision variable in the decision space that satisfies the group optimization condition: and executing group optimization according to the multi-target bacteria group drug-trending algorithm to obtain a new position of the decision variable, if the function value corresponding to the new position is superior to the function value corresponding to the original position, moving the decision variable to the new position, and if not, maintaining the original position. The group optimization operation is a mature technique and is not described herein again.
If the multi-objective function values corresponding to the new position are all better (equivalent to the concentration rise of the attractant), the decision variable moves to the new position; conversely, the new position maintains the home position if the at least one objective function value for the new position is not better than the home position (which corresponds to an unchanged or decreased attractant concentration).
S4: and judging whether an iteration end condition is reached.
Maximum number of iterations tmaxIf the current iteration number t is equal to tmaxThen it means that an overlap is reachedThe flow proceeds to step S6 in place of the end condition; if the current iteration times t is less than tmaxIf the iteration end condition is not met, the process proceeds to step S5.
When the iteration end condition is not met, the process may directly proceed to S1, and optionally, step S5 may be performed before step S1, and then the process may proceed to step S1.
S5: if not, the distribution of the bacterial population is improved by adopting a bacterial population directed mutation strategy, and the process is entered into S1.
After individual optimization operation and group optimization operation, local optimization is easy to fall into. In order to expand the distribution of the bacterial population, a bacterial population directed variation strategy can be adopted, and the aim of the bacterial population directed variation is to improve the distribution of the bacterial population in the space of the objective function value.
Alternatively, the following steps may be employed to improve the distribution of the bacterial population:
s51: and calculating the crowding distance of each decision variable in the bacterial population in the space of the objective function value.
And calculating objective function values corresponding to the positions of the decision variables, wherein a space formed by the objective function values is called an objective function value space. Based on the objective function value space, a crowding distance between the respective objective function values can be calculated.
The crowding distance may reflect the density of the objective function value space of each decision variable in the bacterial population, with a greater crowding distance giving a lower density and a smaller crowding distance giving a higher density. The objective of the directed variation of the bacterial population is to improve the distribution of the bacterial population in the space of the objective function value.
S52: sequencing each decision variable according to the size of the crowding distance, and dividing the bacterial population into two halves: the decision variable set for the smaller congestion distance is half, and the decision variable set for the larger congestion distance is half.
In order to improve the distribution of the bacterial population in the objective function value space, sequencing operation is carried out on each decision variable according to the size of the crowding distance, and the bacterial population is divided into two parts: half the set of decision variables with smaller congestion distance, and half the set of decision variables with larger congestion distance.
This is done to shift the smaller half of the crowding distance to the larger half of the crowding distance, thereby improving the distribution of the bacterial population.
S53: and carrying out directional mutation on the decision variable of the half with the smaller crowding distance to the decision variable of the half with the larger crowding distance.
For each decision variable in the half of the set of decision variables for which the crowding distance is small:
a) calculating a new position of a decision variable according to a directional mutation formula, wherein the new position is positioned in a half of the decision variable set with larger crowding distance. Optionally, the present invention provides a calculation formula of directional variation, which calculates a directional variation position of each decision variable:
b) and if the objective function value corresponding to the new position of the directional variation is not worse than the objective function value corresponding to the original position, moving to the new position determined by the directional variation operation, and otherwise, maintaining the original position unchanged.
S6: and if so, determining the position corresponding to each decision variable in the bacterial population as each solution to be determined.
After the iteration ending condition is reached, the positions corresponding to the decision variables in the bacterial population can be obtained, and the positions corresponding to the decision variables are determined as the solutions to be determined for the convenience of the description of the subsequent steps. Taking the example that the bacterial population has P decision variables, P pending solutions can be obtained.
S7: and respectively calculating the comprehensive satisfaction corresponding to each solution to be determined based on the fuzzy membership function.
Continuing with the above example, the step is to determine the comprehensive satisfaction degrees corresponding to the P pending solutions, so as to subsequently determine the optimal solution from the respective pending solutions.
Taking the multi-objective function as two objective functions as an example, the step is explained:
wherein, muiIs the satisfaction of the ith objective function, where i is 1,2, indicating that there are two objective functions. f. ofi maxAnd fi minRespectively the maximum value and the minimum value of the ith objective function in all the obtained solutions to be determined.
On the basis of the satisfaction degree of the objective function of a single objective, calculating the comprehensive satisfaction degree of a plurality of objective functions, and defining the comprehensive satisfaction degree as S, wherein the calculation formula can participate in the following formula:
wherein, ciIs a weight of the satisfaction of the ith objective function on the overall satisfaction influence, an
S8: and determining the solution to be determined with the maximum comprehensive satisfaction degree in all the solutions to be determined as the optimal solution of the decision variables for optimizing the objective function.
And sequencing the comprehensive satisfaction degrees of all the solutions to be determined, selecting the solution to be determined with the maximum comprehensive satisfaction degree, and determining the solution to be determined as the optimal solution of the decision variable for optimizing the multi-objective function.
Step S203 then proceeds to step S204: and outputting the optimal solution of the decision variables for the actual application scene.
This step is the same as the execution process of step S104 in fig. 1, and is not described herein again.
The second embodiment shows that the invention has the following beneficial effects:
in the individual optimization operation of the second function optimization of this embodiment, the moving step is no longer determined by using the random distribution function, but is set to decrease as the iteration number increases. Therefore, the function optimization early stage has a relatively large moving step length, and the function optimization later stage has a relatively small moving step length; the method avoids excessive time consumption in a local range in the early stage of function optimization, improves optimization efficiency, and can gradually approach to an optimal position through a relatively small moving step length in the later stage of function optimization, so that the convergence of a bacterial chemotaxis function optimization algorithm is improved.
In addition, in each iteration process of performing function optimization in step S203, the second embodiment additionally adopts a bacteria population directed mutation strategy to improve the distributivity of the bacteria population, so that the local optimal solution can be avoided from being trapped in the function optimization process.
Referring to fig. 4, the present invention provides a function optimization apparatus, including:
a determining unit 41, configured to determine an objective function and a decision variable corresponding to an actual application scenario;
a construction unit 42, configured to construct a system model of a matched bacterial chemotaxis function optimization algorithm based on the objective function and the decision variable corresponding to the actual application scenario;
an optimizing unit 43, configured to perform function optimization operation on the system model of the bacterial chemotaxis function optimization algorithm to obtain an optimal solution of a decision variable for optimizing the objective function; wherein the moving step length of the decision variable in the function optimization operation is in a decreasing trend along with the increase of the iteration number;
and the output unit 44 is configured to output the optimal solution of the decision variables for the actual application scenario.
For specific implementation of the function optimization device, reference may be made to the embodiments shown in fig. 1 and fig. 2, which are not described herein again.
Referring to fig. 5, the present invention provides a function optimization system, comprising:
the automatic application unit 100 is used for operating according to actual application scenes;
the processing device 200 is configured to determine a target function and a decision variable corresponding to an actual application scenario in the automation application unit; constructing a system model of a matched bacterial chemotaxis function optimization algorithm based on a target function and a decision variable corresponding to the actual application scene; performing function optimization operation on the system model of the bacterial chemotaxis function optimization algorithm to obtain a decision variable optimal solution for optimizing the objective function; wherein the moving step length of the decision variable in the function optimization operation is in a decreasing trend along with the increase of the iteration number; and outputting the optimal solution of the decision variables for the actual application scene.
For specific implementation of the processing device in the function optimization system, reference may be made to the embodiments shown in fig. 1 and fig. 2, which are not described herein again.
The automation application unit can comprise automation equipment corresponding to an actual application scene; the processing device may include a server, a server cluster, a cloud platform, a local controller, and the like, and the specific implementation of the automation application group and the processing device is not limited.
The functions described in the method of the present embodiment, if implemented in the form of software functional units and sold or used as independent products, may be stored in a storage medium readable by a computing device. Based on such understanding, part of the contribution of the embodiments of the present invention to the prior art or part of the technical solution may be embodied in the form of a software product stored in a storage medium and including instructions for causing a computing device (which may be a personal computer, a server, a mobile computing device, a network device, or the like) to execute all or part of the steps of the method described in the embodiments of the present invention. And the aforementioned storage medium includes: a U-disk, a removable hard disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), a magnetic disk or an optical disk, and other various media capable of storing program codes.
The embodiments are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same or similar parts among the embodiments are referred to each other.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
Claims (10)
1. A method of function optimization, comprising:
determining a target function and a decision variable corresponding to an actual application scene;
constructing a system model of a matched bacterial chemotaxis function optimization algorithm based on a target function and a decision variable corresponding to the actual application scene;
performing function optimization operation on the system model of the bacterial chemotaxis function optimization algorithm to obtain a decision variable optimal solution for optimizing the objective function; wherein the moving step length of the decision variable in the function optimization operation is in a decreasing trend along with the increase of the iteration number;
and outputting the optimal solution of the decision variables for the actual application scene.
2. The method of claim 1, wherein the step size of the movement of the decision variable in the function optimization operation decreases as the number of iterations increases comprises:
the moving step length is reduced along with the increase of the iteration times; or the like, or, alternatively,
in the case of a decision variable with constant speed, the duration decreases as the number of iterations increases.
3. The method of claim 2, wherein the decreasing the step size as the number of iterations increases comprises:
the moving step length of a decision variable in the function optimization operation is linearly decreased along with the increase of the iteration times; or the like, or, alternatively,
the moving step length of a decision variable in the function optimization operation is exponentially decreased along with the increase of the iteration times; or the like, or, alternatively,
the step size of the movement of the decision variable in the function optimization operation is randomly decreased along with the increase of the iteration number.
4. The method of claim 2, wherein the decreasing duration as the number of iterations increases comprises:
the duration of a decision variable in the function optimization operation is linearly decreased along with the increase of the iteration times; or the like, or, alternatively,
the duration of a decision variable in the function optimization operation is exponentially decreased along with the increase of the iteration number; or the like, or, alternatively,
the duration of the decision variable in the function optimization operation is randomly decreased along with the increase of the iteration number.
5. The method of claim 1, wherein constructing a system model of a matched bacterial chemotaxis function optimization algorithm based on objective functions and decision variables corresponding to the actual application scenario comprises:
under the condition that the actual application scene corresponds to a single objective function and a decision variable of the single objective function, constructing a system model of a bacterial chemotaxis algorithm or a system model of a bacterial population chemotaxis algorithm;
and constructing a system model of the multi-target bacteria population chemotaxis algorithm under the condition that the actual application scene corresponds to a plurality of objective functions and decision variables of the objective functions.
6. The method of claim 5, wherein, in the case of the constructing the system model of multi-objective bacterial population chemotaxis algorithms, the performing a function optimization operation on the system model of bacterial chemotaxis function optimization algorithms to obtain a decision variable optimal solution that optimizes the objective function comprises:
individual optimization is performed for each decision variable in the decision space: executing individual optimization according to the multi-target bacteria group drug-trending algorithm to obtain a new position of the decision variable, if the function value corresponding to the new position is superior to the function value corresponding to the original position, moving the decision variable to the new position, otherwise, maintaining the original position; wherein, in the individual optimization executed by the bacterial chemotaxis algorithm, the moving step length of the decision variable is in a decreasing trend along with the increase of the iteration times;
determining decision variables meeting group optimization conditions after performing individual optimization on each decision variable in a decision space;
performing group optimization for each decision variable in the decision space that satisfies the group optimization condition: executing group optimization according to a multi-target bacteria group drug-trending algorithm to obtain a new position of a decision variable, if a function value corresponding to the new position is superior to a function value corresponding to an original position, moving the decision variable to the new position, and if not, maintaining the original position;
judging whether an iteration end condition is reached;
if not, re-entering the step of performing individual optimization aiming at each decision variable in the decision space;
if so, determining the position corresponding to each decision variable in the bacterial population as each solution to be determined;
respectively calculating the comprehensive satisfaction corresponding to each solution to be determined based on the fuzzy membership function;
and determining the solution to be determined with the maximum comprehensive satisfaction degree in all the solutions to be determined as the optimal solution of the decision variables for optimizing the objective function.
7. The method of claim 6, wherein prior to said re-entering performing individual optimization steps for each decision variable in a decision space, further comprising:
and (3) improving the distribution of the bacterial population by adopting a bacterial population directed mutation strategy.
8. The method of claim 7, wherein the improvement of the distribution of the bacterial population using a bacterial population directed variation strategy comprises:
calculating the crowding distance of each decision variable in the bacterial population in the space of the objective function value;
sequencing each decision variable according to the size of the crowding distance, and dividing the bacterial population into two halves: a half decision variable set with a smaller congestion distance and a half decision variable set with a larger congestion distance;
for each decision variable in the half of the decision variable set with the smaller congestion distance:
calculating a new position of a decision variable according to a directional variation formula, wherein the new position is positioned in a half decision variable set with a larger crowding distance; and if the target function value corresponding to the new position is not worse than the target function value corresponding to the original position, the decision variable is moved to the new position, otherwise, the original position is maintained.
9. A function optimization device, comprising:
the determining unit is used for determining an objective function and a decision variable corresponding to an actual application scene;
the construction unit is used for constructing a system model of a matched bacterial chemotaxis function optimization algorithm based on a target function and a decision variable corresponding to the actual application scene;
the optimization unit is used for executing function optimization operation on the system model of the bacterial chemotaxis function optimization algorithm to obtain a decision variable optimal solution for optimizing the objective function; wherein the moving step length of the decision variable in the function optimization operation is in a decreasing trend along with the increase of the iteration number;
and the output unit is used for outputting the optimal solution of the decision variables to be used in the actual application scene.
10. A function optimization system, comprising:
the automatic application unit is used for operating according to an actual application scene;
the processing equipment is used for determining a target function and a decision variable corresponding to an actual application scene in the automatic application unit; constructing a system model of a matched bacterial chemotaxis function optimization algorithm based on a target function and a decision variable corresponding to the actual application scene; performing function optimization operation on the system model of the bacterial chemotaxis function optimization algorithm to obtain a decision variable optimal solution for optimizing the objective function; wherein the moving step length of the decision variable in the function optimization operation is in a decreasing trend along with the increase of the iteration number; and outputting the optimal solution of the decision variables for the actual application scene.
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