CN111126547A - Penicillium propagation algorithm based on colony intelligent optimization algorithm - Google Patents

Penicillium propagation algorithm based on colony intelligent optimization algorithm Download PDF

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CN111126547A
CN111126547A CN201911224540.7A CN201911224540A CN111126547A CN 111126547 A CN111126547 A CN 111126547A CN 201911224540 A CN201911224540 A CN 201911224540A CN 111126547 A CN111126547 A CN 111126547A
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赵亮
赵伟莨
林娜
拱长青
石峻岭
郦铸辉
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Shenyang Aerospace University
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Abstract

The invention belongs to the field of optimization algorithms, and provides a novel colony intelligent optimization algorithm with excellent optimizing capability, namely a penicillium breeding algorithm. The penicillium breeding algorithm can be divided into a local search process of spores, a global search process of the spores, a selection strategy of the spores and a negative feedback regulation process. The local search of the spores can lead the algorithm to be fast converged, the global search process can effectively avoid the occurrence of local optimal solutions, and the selection strategy can select the solution with the optimal fitness value, thus being a preferred process. The negative feedback regulation process regulates the whole search process according to the change of the fitness value of the past generation, and can effectively jump out of the local optimum condition when the local optimum occurs. The method uses the propagation process of penicillium for reference, has easy understanding of the algorithm, has excellent optimizing capability and can be applied by combining with specific scenes.

Description

Penicillium propagation algorithm based on colony intelligent optimization algorithm
Technical Field
The invention relates to the field of intelligent optimization algorithms, in particular to a novel group intelligent optimization algorithm penicillium breeding algorithm.
Background
Natural heuristic computation is a type of meta-heuristic algorithm, the inspiration of which derives from some natural phenomena, including biological phenomena, physical phenomena, chemical phenomena, and the like. They are widely used in the fields of scientific research and engineering to solve some complex optimization problems. In natural heuristic computation, group intelligence is a very important branch, which means that individuals in a group can search solutions of complex optimization problems without centralized control and a global model through cooperation, competition, learning and other behaviors. The Particle Swarm Optimization (PSO) classic swarm intelligence algorithm, the basic concept of which is derived from the research of the foraging behavior of birds. PSO uses an information sharing mechanism that enables each individual to learn from each other's experience, thereby promoting overall development. In addition, the ant colony optimization Algorithm (ACO) and the artificial bee colony Algorithm (ABC) are also representatives of the classical colony intelligent algorithm, and are respectively inspired by the foraging behavior of the ant colony and the honey collection behavior of the bee colony.
The group intelligent algorithm has wide application in various fields. For example, in a network, swarm intelligence algorithms may be used for specific problems of load balancing, computation offloading, routing, and so on. In the known technology, the "optimizing the power using real-based evaluating devices for optimizing the cluster construction using the fireworks algorithm to reduce the energy consumption in the internet of things network. An Application of New hybrid Jaya Grey Wolf Optimizer to Antenna Design for 5G Communications Systems proposes a group intelligent algorithm based on a gray Wolf Optimizer, which is applied to the Design of two different antennas in 5G mobile communication. Multi-objective auto-regenerative wireless optimization for traffic-aware routing in the routing process of VANET using whale optimization algorithm, a traffic-aware routing protocol is provided.
The swarm intelligence algorithm can effectively solve the optimization of complex problems. The currently proposed group intelligent algorithms are large in quantity and various in variety, but the parameters which are usually adjusted by the algorithms are many, so that the algorithms are inconvenient to understand, and for non-professionals, the algorithms are greatly limited when used.
Disclosure of Invention
The invention originally provides a penicillium breeding algorithm with a colony intelligent optimization algorithm, which comprises the following steps: the Penicillium propagation algorithm (PRA) is used for the continuous function optimization problem.
After the penicillium strain matures, a part of the spores will fall around the strain and another part will fall with the wind in a more distant area, and PRA can classify conidia into two types according to this phenomenon: local search spores (LES) and global search spores (GES). In the searching process, the PRA can adjust the searching range of the spores according to the current fitness value, the local searching process aims to enable the algorithm to be quickly converged to obtain the optimal solution, the global searching process searches the solution in a larger searching space, and the global information is effectively utilized to avoid the local optimal solution. The negative feedback process is used for adjusting the distribution of LES and GES in the whole searching process, and the local optimal solution can be timely jumped out when the local optimal solution occurs.
The penicillium breeding algorithm specifically comprises the following steps,
step 1: initializing parameters of the PRA;
the total iteration number of the algorithm is set as TiterIn each iteration, the number of individuals in the population is set to be N, the dimension of the problem to be optimized is M, the upper and lower bounds of the search space are UL and LL respectively, and the initial value of the negative feedback factor FD is 0. The maximum and minimum fraction of the LES are 0.9 and 0.4, respectively. In the initialization process of the penicillium breeding algorithm, the value of each dimension of an individual is a random number between an upper limit and a lower limit, N spores are generated in total, and the position of the individual with the best fitness value is reserved as the reference of the next iteration process.
Step 2, local search process of spores;
number of LES NLES_tDetermined by the formulas (1), (2), (3). t represents the current number of iterations, Rs(t) is the propagation radius of the locally searched spore LES in the tth iteration.
Figure BDA0002301781310000031
Figure BDA0002301781310000032
Figure BDA0002301781310000033
Propagation radius R of LES in the t-th iterations(t) is calculated according to equation (4).
Figure BDA0002301781310000034
Where δ and γ are greedy and shrinkage factors, respectively, δ is set to 1.1, γ is set to 0.9, fsporeAnd (t) is the fitness value of t rounds of iteration. When the fitness value of the spores is smaller than that of the previous generation, a better solution is found, the conidia have greedy behaviors at the moment, the search of a propagation area is enlarged, and when the fitness value of the spores is larger than or equal to that of the previous generation, the spores do not find a more suitable propagation area. The local search process for spores is as follows [01]-[06]The steps of (a) are described.
[01] Calculating the number of local search spore LES according to the formulas (1), (2) and (3);
[02] calculating the search radius of locally searching spore LES according to the formula (4);
[03]from N equal to 1 to N equal to NLES_tExecute [03]To [06]]The step length of n change is 1;
[04] performing a process of [04] to [06] from m equal to 1 to m equal to the length of S (n), m varying by a step size of 1;
[05]S(n)mis set to PosmAnd (-R)s(t),Rs(t)) the sum of random values between;
[06]if S (n)mExceed from top to bottomConstrained by the constraints, then randomly selected (LL)m,ULm) Value of between S (n)mThe value of (c).
Wherein S (n) is the position information of the nth spore, the total dimension of the coordinates of the position is len (S (n)), and m is the mth dimension of the position.
Step 3, a global search process of spores is carried out;
the number of global search spore GES was calculated according to equation (5).
NGES_t＝N-NLES_tFormula (5)
In the global search process, an algorithm randomly selects one dimension of the position of the spore, and then the value of the dimension is adjusted through random numbers generated by Gaussian distribution. The random number is generated by a global heuristic variable (GEV), which follows a gaussian distribution as follows.
GEV～N(S(n)-Rs(t),SD2) GEV≤S(n)-Rs(t) formula (6)
GEV～N(S(n)+Rs(t),SD2) GEV≤S(n)+Rs(t) formula (7)
S (n) is information on the location of a spore, S (n). + -. RsThe sign of the operation symbol (t) depends on the direction of the flight of the spores, and the probability of the sign is the same. During local search, spores will fall on (-R)s(t),Rs(t)) interval, and during the global search, the GES avoids the local search area. The position is calculated according to formula (8) or formula (9).
S(n)ρ＝Posρ-Rs(t)-|N(0,SD2) Equation (8)
S(n)ρ＝Posρ+Rs(t)+|N(0,SD2) I formula (9)
The standard deviation of the gaussian distribution to which the GEV conforms is calculated according to equation (10). Changes in SD can affect the search range of GES.
Figure BDA0002301781310000051
The global search process for spores is described by the steps [01] - [08 ].
[01] Obtaining the number of global search spores GES according to a formula (5);
[02] calculating SD according to equation (10);
[03]from n to n equals
Figure BDA0002301781310000052
Until N equals N, execute [03]]To [08]]The step length of n change is 1;
[04] randomly selecting a dimensionality rho;
Figure BDA0002301781310000053
[06]if the random number between (0,1) generated randomly is less than or equal to PT, executing S (n)ρ＝Posρ-Rs(t)-|N(0,SD2)|；
[07]If not, [06]]If so, executing S (n)ρ＝Posρ+Rs(t)+|N(0,SD2)|；
[08]If S (n)ρExceeding the upper and lower limits of the constraint, then S (n)ρIs equal to (LL)ρ,ULρ) A random value in between;
step 4, selecting a strategy of spores;
after step 2 and step 3, the algorithm will evaluate the fitness values of all the positions of the spores, the position of the spore with the best fitness value will be retained, and at the beginning of the next iteration, all the positions of the spores will be set as the position worth the best fitness value in the previous iteration. The specific fitness calculation method is related to the problem to be optimized.
Step 5 is a negative feedback process;
the negative feedback process adjusts the assignment of LES and GES to jump out of the locally optimal solution by recording the value of the fitness value changes during the iterative process. When the fitness value is not changed for multiple consecutive generations, the LES needs to be sharply reduced, the number of GES needs to be increased, and the FD can be set according to a specific optimization problem.
The termination condition of the algorithm needs to be set according to the requirements of the user, for example, the maximum iteration number is set, and the required accuracy is set.
The method uses the penicillium breeding process and the adaptability to the environment for reference, has few control parameters, has excellent searching capability, can quickly converge and has high convergence precision, and has extremely strong optimizing capability no matter solving the unimodal optimization problem or the multimodal optimization problem.
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FIG. 1 is a flow chart of the present algorithm;
FIG. 2 is a simplified schematic of the present algorithm;
FIG. 3 is a graph of a comparative experiment with various algorithms;
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
Penicillium is a fungus, the mycelium of which consists of multiple hyphae with transverse septa. Typically, they propagate by producing conidia. In the production of spores, the top portion of the mycelium produces a multicellular conidiophor. The top of the stem branches two to three times, with the terminal cells of each branch dividing into spore forming clusters. Conidia are dispersed in the wind after maturation and germinate into strains when it encounters suitable environments. The penicillium breeding algorithm references the breeding process of penicillium and the adaptive regulation to the environment. The algorithm can be divided into a local search process of spores, a global search process of spores, a selection strategy of spores and a negative feedback regulation process.
The penicillium breeding algorithm takes the search space of the problem to be optimized as a breeding area of the penicillium, and conidia of the penicillium select a suitable breeding area to germinate strains so as to form colonies; wherein, one part of conidia can fall on the area where the colony is located, and the other part of conidia can fall at a farther place along with wind to search for a new propagation area, which respectively corresponds to the local search process and the global search process of the spores; the algorithm uses part of intelligent behaviors in the penicillium breeding process as a reference, adds a selection strategy and a negative feedback regulation process,
as shown in FIG. 1, the invention provides a new colony intelligent optimization algorithm, i.e. a Penicillium propagation algorithm, comprising the following steps:
step 1: initializing parameters of the penicillium breeding algorithm. Spores will randomly scatter throughout the search space and the spore with the best fitness value (best position) will be retained for subsequent iterations.
The total iteration number of the algorithm is set as TiterIn each iteration, the number of individuals in the population is set to be N, the dimension of the problem to be optimized is M, the upper and lower bounds of the search space are UL and LL respectively, and the initial value of the negative feedback factor FD is 0. The maximum and minimum fraction of the LES are 0.9 and 0.4, respectively. In the initialization process of the penicillium breeding algorithm, the value of each dimension of an individual is a random number between an upper limit and a lower limit, N spores are generated in total, and the position of the individual with the best fitness value is reserved as the reference of the next iteration process.
Step 2: local search process of spore. This process allows the algorithm to converge quickly, with the LES scattered in the vicinity of the strain, for determining a more precise location.
Number of LES NLES_tDetermined by the formulas (1), (2), (3). t represents the current number of iterations, Rs(t) is the propagation radius of the locally searched spore LES in the tth iteration.
Figure BDA0002301781310000081
Figure BDA0002301781310000082
Figure BDA0002301781310000083
Propagation radius of LES in t-th iterationRs(t) is calculated according to equation (4).
Figure BDA0002301781310000084
Where δ and γ are greedy and shrinkage factors, respectively, δ is set to 1.1, γ is set to 0.9, fsporeAnd (t) is the fitness value of t rounds of iteration. When the fitness value of the spores is smaller than that of the previous generation, a better solution is found, the conidia have greedy behaviors at the moment, the search of a propagation area is enlarged, and when the fitness value of the spores is larger than or equal to that of the previous generation, the spores do not find a more suitable propagation area. The local search process for spores is as follows [01]-[06]The steps of (a) are described.
[01] Calculating the number of local search spore LES according to the formulas (1), (2) and (3);
[02] calculating the search radius of locally searching spore LES according to the formula (4);
[03]from N equal to 1 to N equal to NLES_tExecute [03]To [06]]The step length of n change is 1;
[04] performing a process of [04] to [06] from m equal to 1 to m equal to the length of S (n), m varying by a step size of 1;
[05]S(n)mis set to PosmAnd (-R)s(t),Rs(t)) the sum of random values between;
[06]if S (n)mIf the upper and lower limits are exceeded, then random selection (LL)m,ULm) Value of between S (n)mThe value of (c).
Wherein S (n) is the position information of the nth spore, the total dimension of the coordinates of the position is len (S (n)), and m is the mth dimension of the position.
And step 3: a global search process for spores. This process can avoid local optimality, with GES scattered in more distant areas, and when GES explores a more suitable breeding area, penicillium will replace the breeding area.
The number of global search spore GES was calculated according to equation (5).
NGES_t＝N-NLES_tFormula (5)
In the global search process, an algorithm randomly selects one dimension of the position of the spore, and then the value of the dimension is adjusted through random numbers generated by Gaussian distribution. The random number is generated by a global heuristic variable (GEV), which follows a gaussian distribution as follows.
GEV～N(S(n)-Rs(t),SD2) GEV≤S(n)-Rs(t) formula (6)
GEV～N(S(n)+Rs(t),SD2) GEV≤S(n)+Rs(t) formula (7)
S (n) is information on the location of a spore, S (n). + -. RsThe sign of the operation symbol (t) depends on the direction of the flight of the spores, and the probability of the sign is the same. During local search, spores will fall on (-R)s(t),Rs(t)) interval, and during the global search, the GES avoids the local search area. The position is calculated according to formula (8) or formula (9).
S(n)ρ＝Posρ-Rs(t)-|N(0,SD2) Equation (8)
S(n)ρ＝Posρ+Rs(t)+|N(0,SD2) I formula (9)
The standard deviation of the gaussian distribution to which the GEV conforms is calculated according to equation (10). Changes in SD can affect the search range of GES.
Figure BDA0002301781310000091
The global search process for spores is described by the steps [01] - [08 ].
[01] Obtaining the number of global search spores GES according to a formula (5);
[02] calculating SD according to equation (10);
[03]from n to n equals
Figure BDA0002301781310000101
Until N equals N, execute [03]]To [08]]The step length of n change is 1;
[04] randomly selecting a dimensionality rho;
Figure BDA0002301781310000102
[06]if the random number between (0,1) generated randomly is less than or equal to PT, executing S (n)ρ＝Posρ-Rs(t)-|N(0,SD2)|；
[07]If not, [06]]If so, executing S (n)ρ＝Posρ+Rs(t)+|N(0,SD2)|；
[08]If S (n)ρExceeding the upper and lower limits of the constraint, then S (n)ρIs equal to (LL)ρ,ULρ) A random value in between;
and 4, step 4: breeding areas were selected (selection strategy). This process allows the fitness values of all spore positions to be evaluated, and the position with the best fitness value is retained for the next iteration.
After step 2 and step 3, the algorithm will evaluate the fitness values of all the positions of the spores, the position of the spore with the best fitness value will be retained, and at the beginning of the next iteration, all the positions of the spores will be set as the position worth the best fitness value in the previous iteration. The specific fitness calculation method is related to the problem to be optimized.
And 5: a negative feedback process. This process adjusts the assignment of LES and GES of the algorithm by recording the change in fitness value, which can effectively jump out of a locally optimal solution.
The negative feedback process adjusts the assignment of LES and GES to jump out of the locally optimal solution by recording the value of the fitness value changes during the iterative process. When the fitness value is not changed for multiple consecutive generations, the LES needs to be sharply reduced, the number of GES needs to be increased, and the FD can be set according to a specific optimization problem.
The termination condition of the algorithm needs to be set according to the requirements of the user, for example, the maximum iteration number is set, and the required accuracy is set.
In summary, the overall process of the Penicillium propagation algorithm is described by the steps [01] - [11 ].
[01] Let the initial value of the negative feedback factor FD be 0
[02]Fitnesslist [ T ] fitness value listiter]Are all set to Null (empty)
[03] If the termination condition is not satisfied, repeatedly executing the processes from [03] to [10]
[04] Local search algorithm for spores in execution algorithm (1)
[05] Global search algorithm for spores in execution algorithm (2)
[06] Measuring the fitness value of each spore region
[07]Selecting the spore with the best fitness value as (BF)Pos)
[08]Determine the best fitness value BFPosWrite Fitnesslist [ t ]]
[09] If t is greater than 1, then execute [10]
[10] If Fitnesslist [ t ] is equal to Fitnesslist [ t-1], FD +1, otherwise FD 1
[11] Returning Pos and the fitness value of the Pos after the whole process is finished
Fig. 2 is a simple schematic diagram of the PRA algorithm, spores generated by penicillium strains randomly scatter in the whole search space in the initial stage, positions with the best fitness value are screened out, then according to the content described in the specification, the local search and global search processes of the spores are carried out, and the local search range and the global search range dynamically change according to the change of the fitness value.
In order to verify the performance of the PRA algorithm, 9 industry-recognized benchmark test functions are selected for testing, and compared with the classical algorithm and the efficient group intelligence algorithm proposed in recent years. Table 1 shows 9 benchmark functions for testing PRA performance, including the dimensions of the benchmark functions and the variation range of each dimension. Wherein f1-f4 are unimodal functions, and the functions have only one global optimal solution and can be used for testing the searching capability and the convergence rate of the algorithm. f5-f9 are multi-peak test functions with multiple locally optimal solutions. The multi-peak function may be used to test the ability of the algorithm to search for a global optimal solution and jump out of a local optimal solution.
Figure BDA0002301781310000121
TABLE 1
In the testing process, the benchmark test function is used as an adaptability value evaluation function, the positions S (n) of the spores are brought into the benchmark test function to obtain the adaptability value, and various intelligent optimization algorithms can adjust the selection of the positions in the next iteration according to the change of the adaptability value.
Fig. 3 shows a comparison between the PRA algorithm and the particle swarm algorithm (PSO), the Gravity Search Algorithm (GSA), the pollination algorithm (FPA), the wolf optimization algorithm (GWO), and the whale algorithm (WOA), where PSO and GSA are both classic intelligent optimization algorithms, FPA, GWO, and WOA are intelligent optimization algorithms proposed in recent years, and have very high cognition, and parameters in the comparison experiment are set according to the original text when each algorithm is proposed.
In each sub-graph of fig. 3, the abscissa is the number of iterations and the ordinate represents the optimum value. From the comparison it can be found that PRA has excellent optimization capability for both unimodal and multimodal functions. The PRA has high convergence rate and high precision. In the tests of (e) and (f), the PRA curve is smooth in part, followed by a rapid drop, indicating that the PRA is able to quickly jump out of the locally optimal solution in producing the locally optimal interpretation.
In each sub-graph of fig. 3, the area of the PRA algorithm is smooth, and in order to theoretically prove the convergence of the PRA algorithm, this section gives a proof of the convergence of the PRA.
The convergence of the algorithm means that a stable solution can be obtained through a limited number of iterations, and all that is necessary is to prove the convergence of the algorithm. Assuming a stochastic model of PRA employing basic infimum, i.e.
τ. inf (t: v [ n. S | f (n) < t ]) formula (11)
Definition 1:
Figure BDA0002301781310000131
represents a markov process and represents a process of,
Figure BDA0002301781310000132
is a space of optimization β (t) ═ P { α (t) ∈ Y' } denotes the probability of the random state reaching the optimum at time t
Figure BDA0002301781310000133
Then
Figure BDA0002301781310000134
Convergence
Introduction 1: the stochastic process of PRA is an absorption markov stochastic process.
Proof of lemma 1: in PRA, the scattering events for the next generation of spores are based on the optimal solution for the current spore location. By using
Figure BDA0002301781310000135
Representing a random process of PRA, α (t +1) then depends on α (t).
Figure BDA0002301781310000136
Is a markov random process.
If it is not
Figure BDA0002301781310000137
In the optimal solution space, α (t) belongs to the optimal solution space state Y '. according to the idea of PRA, α (t +1) cannot be worse than α (t). therefore, state α (t +1) also belongs to Y'. since equation (12) is valid, the stochastic process of PRA
Figure BDA0002301781310000138
Is an absorption markov process.
Figure BDA0002301781310000139
Theorem 1: assuming that the absorption Markov process of the PRA is
Figure BDA00023017813100001310
And the optimal state space is
Figure BDA00023017813100001311
For t, if equation (13) and equation (14) remain unchanged, then P { α (t) ∈ Y' } ≧ 1- (1-k)t。
Figure BDA0002301781310000141
Figure BDA0002301781310000142
Proof of theorem 1: if t is 1, then
Figure BDA0002301781310000143
Figure BDA0002301781310000144
Since (1-k) >0, k + (1-k). P { α (0) ∈ Y' } ≧ k
Suppose P { α (t) ∈ Y' } ≧ 1- (1-k)tFor the
Figure BDA0002301781310000145
If true, then for t ═ n, there are
Figure BDA0002301781310000146
Figure BDA0002301781310000147
According to the induction method, P { α (t) ∈ Y' } ≧ 1- (1-k)tFor the
Figure BDA0002301781310000148
Is established
Theorem 2: given an absorption Markov process
Figure BDA0002301781310000149
And an optimal state space
Figure BDA00023017813100001410
The probability that the PRA random state reaches the optimal state is 1.
Proof of theorem 2: we use Pop(t) to represent the probability of GES going from the non-optimal region to the optimal region Y', where S represents the problem space and NGES_tIs the number of GES, and ν (S) is the lux metric value.
Figure BDA0002301781310000151
The variable to the right of the formula is positive, P1>0. Then, Markov random process according to PRA
Figure BDA0002301781310000152
Obtaining the formula (16), wherein P2(t) is the probability that the GES reaches the optimal region Y'.
Figure BDA0002301781310000153
Therefore, the temperature of the molten metal is controlled,
Figure BDA0002301781310000154
since PRA satisfies lemma 1, we can obtain formula (17), which represents
Figure BDA0002301781310000155
P{α(t)∈Y′}＝1-(1-P1(t))tFormula (17)
From the above-described proving process, it can be known that the markov process of PRA can converge to an optimal state. The algorithm provided by the invention belongs to a novel group intelligent algorithm, and can be applied to the complex optimization problems of various industries, such as: the PRA can be used for optimizing the selection of parameters of the artificial neural network and improving the learning ability of the artificial neural network; the method can also be used for load balancing in the network, improving the overall performance of the network and the like.
While the embodiments of the present invention have been described in detail, the present invention is not limited to the above embodiments, and various changes can be made without departing from the spirit of the present invention within the knowledge of those skilled in the art.

Claims (6)

1. The penicillium breeding algorithm based on the colony intelligent optimization algorithm is characterized by comprising the following steps of:
step 1: initializing parameters of a penicillium propagation algorithm, and setting the total iteration times of the algorithm, the number of individuals in a population in each iteration, the dimension of a problem to be optimized, the upper and lower bounds of a search space, the initial value of a negative feedback factor and the maximum and minimum occupation ratios of local search spores (LES);
step 2: determining the quantity of LES (Lee activating substances) of the locally searched spores, and calculating the fitness value of the locally searched spores to complete the local searching process of the spores;
and step 3: determining the number of globally searched spores GES, and completing the global search process of the spores;
and 4, step 4: evaluating the fitness values of all the positions of the spores, and reserving the position with the best fitness value for the next iteration to select a breeding area;
and 5: through a negative feedback process, changes in fitness value are recorded to adjust the assignment of LES and GES to the algorithm.
2. The penicillium propagation algorithm based on the swarm intelligence optimization algorithm according to claim 1, wherein: initializing parameters of the penicillium breeding algorithm in step 1, and setting the total iteration times of the algorithm as TiterIn each iteration, the number of individuals in the population is set to be N, the dimension of the problem to be optimized is M, the upper and lower boundaries of a search space are UL and LL respectively, and the initial value of a negative feedback factor FD is 0; the maximum ratio and the minimum ratio of the local search spore LES are respectively 0.9 and 0.4; in the initialization process of the penicillium breeding algorithm, the value of each dimension of an individual is mediumRandom numbers at the upper and lower bounds will yield a total of N spores, where the individual position with the best fitness value will be retained as the basis for the next iteration.
3. The penicillium propagation algorithm based on the swarm intelligence optimization algorithm according to claim 1, wherein in step 2:
number of locally searched spore LES NLES_tDetermined by the formulas (1), (2), (3); t represents the current number of iterations, Rs(t) is the propagation radius of the LES in the tth iteration;
Figure FDA0002301781300000021
Figure FDA0002301781300000022
Figure FDA0002301781300000023
propagation radius R of LES in the t-th iterationS(t) calculation according to the formula (4)
Figure FDA0002301781300000024
Wherein δ and γ are greedy factor and shrinkage factor, respectively, δ is set to 1.1, and γ is set to 0.9; f. ofspore(t) is the fitness value of t iterations; when the fitness value of the spores is smaller than that of the previous generation, a better solution is found, the conidia have greedy behaviors at the moment, the search of a propagation area is enlarged, and when the fitness value of the spores is larger than or equal to that of the previous generation, the spores do not find a more suitable propagation area.
4. The penicillium propagation algorithm based on the swarm intelligence optimization algorithm according to claim 1, wherein: the number of global search spores CES is calculated according to equation (5):
NGES_t＝N-NLES_t(5)
in the global searching process, an algorithm randomly selects one dimension of the position of the spore, and then the value of the dimension is adjusted through a random number generated by Gaussian distribution; this random number is generated by the global heuristic variable GEV, which follows a gaussian distribution as follows:
GEV～N(S(n)-Rs(t)，SD2) GEV≤S(n)-Rs(t) (6)
GEV～N(S(n)+Rs(t)，SD2) GEV≤S(n)+Rs(t) (7)
s (n) is information on the location of a spore, S (n). + -. Rs(t) the sign of the operation symbol depends on the flying direction of the spore, and the probabilities of the sign are the same; during local search, spores will fall on (-R)s(t)，Rs(t)) interval, and during the global search, the CES avoids the local search area; the position is calculated according to the formula (8) or (9):
S(n)ρ＝Posρ-Rs(t)-|N(0，SD2)| (8)
S(n)ρ＝Posρ+Rs(t)+|N(0，SD2)| (9)
calculating the standard deviation of Gaussian distribution according to the GEV according to a formula (10); SD represents an adjustment parameter of a global search position of the spore, and the change of the adjustment parameter can influence the search range of CES;
Figure FDA0002301781300000031
5. the penicillium propagation algorithm for the swarm intelligence optimization algorithm according to claim 1, wherein the specific selection strategy in step 4 is that after steps 2 and 3, the algorithm evaluates the fitness values of all the positions of the spores, the position of the spore with the best fitness value is retained, and at the beginning of the next iteration, all the positions of the spores are set to the position worth the best fitness value in the previous iteration.
6. The penicillium propagation algorithm for the swarm intelligent optimization algorithm according to claim 1, wherein the negative feedback process in step 5 is to adjust the distribution of LES and GES to jump out of the local optimal solution by recording the value change of the fitness value in the iterative process; when the fitness value is not changed for a plurality of consecutive generations, the LES is reduced, the number of GES is increased, and the negative feedback factor FD is set according to a specific optimization problem.
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