CN113033755A - Bacterial foraging optimization method with Weber-Ficna emotional mutation operation - Google Patents
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Abstract
The invention relates to a bacterial foraging optimization method with Weber-Fibona emotional mutation operation. The classic bacterial foraging algorithm mainly comprises the following steps: according to the method, on the basis of basic operation of a classical bacterial foraging algorithm, Weber-Fiknar emotional mutation operation is introduced, and emotion of a bacterial individual is regulated by using a hormone regulation mechanism, so that the running mode of the bacterial individual is changed, self-adaptive updating of the running speed of the bacterial individual is realized, the defect that the classical bacterial foraging algorithm is easy to fall into local optimum is overcome, and the convergence of the algorithm is improved while the quality of the optimal solution is ensured.
Description
Technical Field
The invention belongs to the field of intelligent optimization algorithms, and particularly relates to a bacterial foraging optimization method with Weber-Fibona emotional mutation operation.
Background
The heuristic algorithms are all biological intelligent algorithms, such as: frog leaping algorithm, whale algorithm, imperial butterfly algorithm, ant colony algorithm, particle swarm algorithm and the like. The heuristic search is to evaluate each individual in the state space dimension and imitate certain characteristics of biological activities to realize the search of the optimal position in the state space dimension, so that the search path can be shortened and the arithmetic efficiency of the algorithm can be improved.
The development of heuristic algorithms is promoted by the demand of production development of the actual society, as a heuristic intelligent optimization algorithm, a bacterial foraging algorithm is proposed in 2002 by Passino and introduced into China in 2007, but some relevant theories of the classical bacterial foraging algorithm are still not mature, such as: the self-adaptive adjustment of the running speed of the bacteria individual can not be realized, so that the algorithm is easy to fall into local optimum and low in optimization precision, and therefore the classical bacterial foraging algorithm needs to be further improved.
According to the invention, a Weber-Fiknar emotional mutation operation with a hormone regulation mechanism is introduced into a classical bacterial foraging algorithm, the emotion of a bacterial individual is controlled by utilizing hormone, the emotional state of the bacterial individual is judged through an emotion perception factor, so that the self-adaptive adjustment of the running speed of the bacterial individual is realized according to the emotional state of the bacterial individual, the running speed of the bacterial individual is updated, the convergence of the algorithm is improved, and the quality of the optimal solution is ensured.
Disclosure of Invention
The step length of the bacteria individual in the classical bacteria foraging algorithm is uncertain, so that the running speed of the bacteria individual cannot be self-adaptively adjusted according to the actual environment.
In order to achieve the purpose, the invention adopts the following technical scheme: a bacterial foraging optimization method with weber-fickeran emotional mutation operation, the algorithm comprising the following sequential steps:
(1) determining an optimization variable X ═ { X) of an object to be studied1,x2,x3,...,xs};
(2) Converting the searching merit value, namely the fitness of the object to be researched into a fitness function with the optimal state of 0: j. the design is a squarefitness(X) the optimum value is Jmin=0;
(3) Initializing relevant parameters of a bacterial foraging optimization method with Weber-Ficner emotional mutation operation;
(4) and (3) optimizing by using a bacterial foraging optimizing method with a Weber-Ficner emotional mutation operation.
Initializing relevant parameters of the bacterial foraging optimization method with the Weber-Fibona emotional mutation operation in the step (3), wherein the parameters comprise:
(3a) initializing bacterial foraging-related parameters
Number of cycles N is stipulated in chemotaxis stepcThe propagation step appoints the cycle number NreContract number of cycles N for elimination-diffusion stepedProbability of elimination-diffusion PedStep length N of the runsTotal number of bacteria N, and depth measurement coefficient d of attractant factorattractAttraction factor width measurement coefficient wattractAversion height measurement coefficient hrepellentEvasion width measurement coefficient wrepellent;
(3b) Initializing other relevant parameters
(3b-1) initialization of hormone regulatory parameters
The hormone regulation mechanism conforms to the Hill function, and the parameters include: maximum value w of inertia factormaxMinimum value of inertia factor wminInitial value w of inertia factor0Threshold T, Hill factor n;
(3b-2) initializing Emotion mutation-related parameters
Stimulation threshold S0A stimulation function S and an emotional constant factor k;
the step (4) comprises the following steps:
(4a) chemotaxis operation: when in useThen the individual will step by stepGradually towardsAnd thetagb(j, k, l) that would otherwise be gradually shifted toward the same step size and patternAnd thetagb(j, k, l) to update the position of the bacteria in the above manner;
wherein: i denotes the individual bacteria, j denotes the chemotaxis step, k denotes the propagation step, l denotes the elimination-diffusion step, [ theta ] bpbRepresenting local maximaGood position, θgbRepresenting a global optimal position;
(4b) clustering operation: the interplay between individual bacteria within the population was calculated at this stage:
wherein: j. the design is a squarecc(, P (j, k, l)) represents the function value of the relationship between individual bacteria, and s represents a node in the dimension;
(4c) Weber-Fickner emotional mutation operation based on hormone regulation mechanism: in the process, defining a global perception factor and a historical perception factor of the bacteria individual according to the Weber-Fickner law, calculating an emotion perception factor according to the global perception factor and the historical perception factor, and taking the magnitude relation between the emotion perception factor and a random function as a judgment standard of an emotional running speed updating mode of the bacteria individual;
defining the global perception factor r of bacteria according to Weber-Fickner's lawgAnd a historical perception factor rh;
the best location of the bacteria away from the global environment will have a strong response to stimuli which will dynamically change their speed compared to the historical perceptions experienced by the bacteria, both happy and sad, and the individual bacteria affected by the global, historical and emotional perception factors will operate as follows:
happy individual running speed of bacteria:
v(i+1,j,k,l)=w(k0)×v(i,j,k,l)+c×rg×rh×rand×[f(θg)-f(θ(i,j,k,l))] (10)
the running speed of the sadness bacteria individual is as follows:
the hormone is adopted to adjust the inertia factor of the bacteria in the updating process of the running speed of the bacteria, and the hormone adjusting process is in accordance with the change rule of a Hill function, so that the hormone adjusting process is realized by the Hill function, and the Hill function is a rising functionAnd a decreasing functionThe Hill function is a concave function and has a descending trend in a positive number region, and has monotonicity and nonnegativity, the characteristics show that the Hill function has better convergence, the quality of the optimization solution can be ensured, the tightness between individuals in the updating process of the running speed of the bacteria individual can be well controlled by applying the Hill function on the inertia factor, the quality of the optimization solution can be ensured while the convergence of the algorithm is improved, and the inertia factor w (k) of the bacteria individual is adjusted by the Hill function0) The calculation formula is as follows:
the emotional updating mode of the running speed of the bacteria individual after the improvement of the hormone regulation mechanism is as follows:
happy individual running speed of bacteria:
the running speed of the sadness bacteria individual is as follows:
when the random function rand is smaller than es, the bacteria serve as happy individuals to update the running speed of the bacteria; otherwise, updating the running speed of the user as a sad individual;
wherein: s represents a stimulation function, S0Representing the stimulation threshold, f (θ (i, j, k, l)) representing the location where the individual is far from the global optimum, k0Representing the current number of iterations, c the acceleration coefficient, rand 0,1]A random value of; w represents an inertia factor, wmaxRepresenting the maximum value of the inertia factor, wminRepresents the minimum value of the inertia factor, w0Denotes an initial value of an inertia factor, T denotes a threshold value, n0Represents the Hill coefficient;
(4d) and (3) propagation operation: calculating the health fitness value J of the individual bacteriahealthSorting from small to large, screening out bacteria individuals with smaller health fitness value to execute breeding operation, and eliminating the bacteria individuals with larger health fitness value, wherein the offspring formed after breeding inherits the step length and the running direction of the parents;
(4e) elimination-diffusion operation: individual bacteria with a given probability of elimination-diffusion PedPerforming the operation and randomly assigning to an arbitrary position;
(4f) and (4) judging whether the optimization of the algorithm is completed or not according to whether each bacteria individual is completed or not, jumping to the step (4a) if the optimization is not completed, and outputting an optimization result if the optimization is completed.
Advantageous effects
The invention has the beneficial effects that: Weber-Fickner emotional mutation operation is introduced into a classical bacterial foraging algorithm, the emotion of a bacterial individual is controlled by hormone, the emotional state of the bacterial individual is judged by an emotion perception factor, and therefore self-adaptive adjustment of the running speed of the bacterial individual is achieved according to the current emotional state, updating of the running speed of the bacterial individual is achieved, convergence and precision of the algorithm are improved, and the algorithm is effectively prevented from falling into local optimum.
Drawings
FIG. 1 is a block diagram of the algorithm of the present invention;
FIG. 2 is a flow chart of the algorithm of the present invention.
Detailed Description
The optimization performance of the Algorithm is compared and analyzed by using 23 reference functions including single mode, multi-mode and fixed mode, and the optimization results of the Algorithm are compared with the optimization results of Bacterial Foraging Algorithm (BFAQB) with Quantum Behavior, IBFABDE (advanced Bacterial Foraging Algorithm Based on Differential Evolution) and BFABGD (Bacterial Foraging Algorithm Based on Gaussian Distribution).
Step 1: determining an optimization variable X ═ { X) of an object to be studied1,x2,x3,...,xsAs shown in table 1:
TABLE 1 reference function-related information
Step 2: converting the searching merit value, namely the fitness of the object to be researched into a fitness function with the optimal state of 0: j. the design is a squarefitness(X) the optimum value is Jmin=0;
Step 3: initializing relevant parameters of a bacterial foraging optimization method with Weber-Ficner emotional mutation operation;
step 4: optimizing by using a bacterial foraging optimization method with Weber-Ficnaccideration mutation operation;
step 5: and outputting the optimizing result.
Initializing relevant parameters of the bacterial foraging optimization method with the Weber-Fibona emotional mutation operation in Step3, wherein the relevant parameters comprise:
(3a) initializing relevant parameters of bacterial foraging algorithm
Number of cycles N is stipulated in chemotaxis stepcThe propagation step appoints the cycle number NreContract number of cycles N for elimination-diffusion stepedProbability of elimination-diffusion PedStep length N of the runsTotal number of bacteria N, and depth measurement coefficient d of attractant factorattractAttraction factor width measurement coefficient wattractAversion height measurement coefficient hrepellentEvasion width measurement coefficient wrepellentWherein: n is a radical ofc=50,Nre=5,Ned=4,Ped=0.25,Ns=125,N=500。
(3b) Initializing other relevant parameters
(3b-1) initialization of hormone regulatory parameters
The hormone regulation mechanism conforms to the Hill function, and the parameters include: maximum value w of inertia factormaxMinimum value of inertia factor wminInitial value w of inertia factor0Threshold T, Hill factor n, wherein: w is amax=0.9,wmin=0.4,w0=0.4,T=12,n=2。
(3b-2) initializing Emotion mutation-related parameters
Stimulation threshold S0A stimulus function S, a mood constant factor k, wherein: s0=10,S=2,k=0.5。
Step4 comprises the following steps:
(4a) chemotaxis operation: when in useThen the individual will step by stepGradually towardsAnd thetagb(j, k, l) that would otherwise be gradually shifted toward the same step size and patternAnd thetagb(j, k, l) the central position of the bacteria is moved, in this way the updating of the individual positions of the bacteria is achieved;
wherein: i denotes the individual bacterium, j denotes the chemotactic stepStep, k denotes the propagation step, l denotes the elimination-diffusion step, θpbIndicating the local optimum position, thetagbRepresenting a global optimal position;
(4b) clustering operation: the interplay between individual bacteria within the population was calculated at this stage:
(4c) Weber-Fickner emotional mutation operation based on hormone regulation mechanism: in the process, defining a global perception factor and a historical perception factor of the bacteria individual according to the Weber-Fickner law, calculating an emotion perception factor according to the global perception factor and the historical perception factor, and taking the magnitude relation between the emotion perception factor and a random function as a judgment standard of an emotional running speed updating mode of the bacteria individual;
defining the global perception factor r of bacteria according to Weber-Fickner's lawgAnd a historical perception factor rh;
the best location of the bacteria away from the global environment will have a strong response to stimuli which will dynamically change their speed compared to the historical perceptions experienced by the bacteria, both happy and sad, and the individual bacteria affected by the global, historical and emotional perception factors will operate as follows:
happy individual running speed of bacteria:
v(i+1,j,k,l)=w(k0)×v(i,j,k,l)+c×rg×rh×rand×[f(θg)-f(θ(i,j,k,l))] (17)
the running speed of the sadness bacteria individual is as follows:
the hormone is adopted to adjust the inertia factor of the bacteria in the updating process of the running speed of the bacteria, and the hormone adjusting process is in accordance with the change rule of a Hill function, so that the hormone adjusting process is realized by the Hill function, and the Hill function is a rising functionAnd a decreasing functionThe Hill function is a concave function and has a descending trend in a positive number region, and has monotonicity and nonnegativity, the characteristics show that the Hill function has better convergence, the quality of the optimization solution can be ensured, the tightness between individuals in the updating process of the running speed of the bacteria individual can be well controlled by applying the Hill function on the inertia factor, the quality of the optimization solution can be ensured while the convergence of the algorithm is improved, and the inertia factor w (k) of the bacteria individual is adjusted by the Hill function0) The calculation formula is as follows:
the emotional updating mode of the running speed of the bacteria individual after the improvement of the hormone regulation mechanism is as follows:
happy individual running speed of bacteria:
the running speed of the sadness bacteria individual is as follows:
when the random function rand is smaller than es, the bacteria serve as happy individuals to update the running speed of the bacteria; otherwise, updating the running speed of the user as a sad individual;
wherein: s represents a stimulation function, S0Representing the stimulation threshold, f (θ (i, j, k, l)) representing the location where the individual is far from the global optimum, k0Representing the current number of iterations, c the acceleration coefficient, rand 0,1]A random value of; w represents an inertia factor, wmaxRepresenting the maximum value of the inertia factor, wminRepresents the minimum value of the inertia factor, w0Denotes an initial value of an inertia factor, T denotes a threshold value, n0Represents the Hill coefficient;
(4d) and (3) propagation operation: calculating the health fitness value J of the individual bacteriahealthSorting from small to large, screening out bacteria individuals with smaller health fitness value to execute breeding operation, and eliminating the bacteria individuals with larger health fitness value, wherein the offspring formed after breeding inherits the step length and the running direction of the parents;
(4e) elimination-diffusion operation: individual bacteria with a given probability of elimination-diffusion PedExecuting the operation, and randomly distributing the operation to any position, wherein the iteration number is 1000;
(4f) and (4) judging whether the algorithm optimizing is finished according to whether the set iteration times are reached, jumping to the step (4a) if the algorithm optimizing is not finished, and outputting an optimizing result if the algorithm optimizing is finished.
Step5 comprises the following steps:
the result of the optimization operation of each comparison algorithm on the basis function is shown in table 2:
TABLE 2 results of the operations
The operation results in table 2 show intuitively: compared with the other three comparison algorithms, the algorithm of the invention has good superiority in the aspect of optimizing performance.
The above embodiments are preferred embodiments of the present invention, but the present invention is not limited thereto, and any other changes, modifications, substitutions, combinations, and simplifications which do not depart from the spirit and principle of the present invention are all equivalent substitutions and are intended to be included within the scope of the present invention.
Claims (3)
1. A bacterial foraging optimization method with Weber-Ficnacclimatization mutation operation is characterized in that: comprises the following steps in sequence:
(1) determining an optimization variable X ═ { X) of an object to be studied1,x2,x3,...,xs};
(2) Converting the searching merit value, namely the fitness of the object to be researched into a fitness function with the optimal state of 0: j ═ fitness (x), with the most preferred value of Jmin=0;
(3) Initializing relevant parameters of a bacterial foraging optimization method based on Weber-Fibona emotional mutation operation;
(4) and (3) optimizing by using a bacterial foraging method with a Weber-Ficner emotional mutation operation.
2. The bacterial foraging optimization method with weber-fickeran emotional mutation manipulation of claim 1, wherein: the step (3) specifically comprises the following steps:
initializing relevant parameters of the bacterial foraging optimization method with the Weber-Ficner emotional mutation operation, wherein the relevant parameters comprise:
(3a) initializing bacterial foraging-related parameters
Number of cycles N is stipulated in chemotaxis stepcThe propagation step appoints the cycle number NreContract number of cycles N for elimination-diffusion stepedProbability of elimination-diffusion PedStep length N of the runsTotal number of bacteria N, and depth measurement coefficient d of attractant factorattractBreadth of attractant factorMeasurement coefficient wattractAversion height measurement coefficient hrepellentEvasion width measurement coefficient wrepellent;
(3b) Initializing other relevant parameters
(3b-1) initialization of hormone regulatory parameters
The hormone regulation process conforms to the change rule of the Hill function, and the parameters comprise: maximum value w of inertia factormaxMinimum value of inertia factor wminInitial value w of inertia factor0Threshold T, Hill factor n;
(3b-2) initializing Emotion mutation-related parameters
Stimulation threshold S0A stimulus function S, an emotional constant factor k.
3. The hormone regulatory mechanism-based emotive bacterial foraging optimization algorithm of claim 1, wherein: the step (4) specifically comprises the following steps:
(4a) chemotaxis operation: when in useThen the individual will step by stepGradually towardsAnd thetagb(j, k, l) that would otherwise be gradually shifted toward the same step size and patternAnd thetagb(j, k, l) to update the position of the bacteria in the above manner;
wherein: i denotes the individual bacteria, j denotes the chemotaxis step, k denotes the propagation step, l denotes the elimination-diffusion step, [ theta ] bpbIndicating the local optimum position, thetagbRepresenting a global optimal position;
(4b) clustering operation: the interplay between individual bacteria within the population was calculated at this stage:
wherein: j. the design is a squarecc(θ, P (j, k, l)) represents a relationship function value between individual bacteria, and s represents a dimension;
(4c) Weber-Fickner emotional mutation operation based on hormone regulation mechanism: in the process, defining a global perception factor and a historical perception factor of the bacteria individual according to the Weber-Fickner law, calculating an emotion perception factor according to the global perception factor and the historical perception factor, and taking the magnitude relation between the emotion perception factor and a random function as a judgment standard of an emotional running speed updating mode of the bacteria individual;
defining the global perception factor r of bacteria according to Weber-Fickner's lawgAnd a historical perception factor rh;
the best location of the bacteria away from the global environment will have a strong response to stimuli which will dynamically change their speed compared to the historical perceptions experienced by the bacteria, both happy and sad, and the individual bacteria affected by the global, historical and emotional perception factors will operate as follows:
happy individual running speed of bacteria:
v(i+1,j,k,l)=w(k0)×v(i,j,k,l)+c×rg×rh×rand×[f(θg)-f(θ(i,j,k,l))] (3)
the running speed of the sadness bacteria individual is as follows:
the hormone is adopted to adjust the inertia factor of the bacteria in the updating process of the running speed of the bacteria, and the hormone adjusting process is in accordance with the change rule of a Hill function, so that the hormone adjusting process is realized by the Hill function, and the Hill function is a rising functionAnd a decreasing functionThe Hill function is a concave function and has a descending trend in a positive number region, and has monotonicity and nonnegativity, the characteristics show that the Hill function has better convergence, the quality of the optimization solution can be ensured, the tightness between individuals in the updating process of the running speed of the bacteria individual can be well controlled by applying the Hill function on the inertia factor, the quality of the optimization solution can be ensured while the convergence of the algorithm is improved, and the inertia factor w (k) of the bacteria individual is adjusted by the Hill function0) The calculation formula is as follows:
the emotional updating mode of the running speed of the bacteria individual after the improvement of the hormone regulation mechanism is as follows:
happy individual running speed of bacteria:
the running speed of the sadness bacteria individual is as follows:
when the random function rand is smaller than es, the bacteria serve as happy individuals to update the running speed of the bacteria; otherwise, updating the running speed of the user as a sad individual;
wherein: s represents a stimulation function, S0Representing the stimulation threshold, f (θ (i, j, k, l)) representing the location where the individual is far from the global optimum, k0Representing the current number of iterations, c the acceleration coefficient, rand 0,1]A random value of; w represents an inertia factor, wmaxRepresenting the maximum value of the inertia factor, wminRepresents the minimum value of the inertia factor, w0Denotes an initial value of an inertia factor, T denotes a threshold value, n0Represents the Hill coefficient;
(4d) and (3) propagation operation: calculating the health fitness value J of the individual bacteriahealth(X), sequencing from small to large, screening out bacteria individuals with small health fitness value to perform breeding operation, and eliminating bacteria individuals with large health fitness value, wherein the filial generations formed after breeding inherit the step length and the running direction of the parents;
(4e) elimination-diffusion operation: individual bacteria with a given probability of elimination-diffusion PedPerforming the operation and randomly assigning to an arbitrary position;
(4f) and (4) judging whether the optimization of the algorithm is completed or not according to whether each bacteria individual is completed or not, jumping to the step (4a) if the optimization is not completed, and outputting an optimization result if the optimization is completed.
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