CN110399589B - NMDAFSA-based power system optimal power flow calculation method - Google Patents
NMDAFSA-based power system optimal power flow calculation method Download PDFInfo
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Abstract
The operation mode of the power system is flexible, efficient, safe and economical, and is pursued in the construction of the power system. The intelligent power grid is built more economically and effectively, the running method in the power grid is decided, so that the energy management and other technologies are more intelligent, and the intelligent power grid is a requirement for the construction of the modern intelligent power grid. Therefore, the invention provides an NMDAFSA-based power system optimal power flow calculation method. The power flow calculation method can better optimize the power flow calculation of the power system, has relatively simple implementation process and has good practical value.
Description
Technical Field
The invention relates to a method for calculating optimal power flow of an electric power system based on NMDAFSA, and belongs to the technical field of power flow calculation of power grids.
Background
In recent years, the rapid development of social economy and the continuous improvement of social productivity are realized, the living standard of people is rapidly improved, and the power load of a power supply network is rapidly increased. In order to cope with the continuous increase of loads, the country has increased the construction of power systems, and the coverage area of power grids is increasing year by year. However, the problem of power system loss and the problem of economic operation of the power system are increasingly prominent due to the increase of the power grid scale. One has to consider the problem of power consumption caused by network loss while the power system is being developed and built. Especially in the large background of rapid development of new energy technology in the recent years, such as large-scale grid connection of new energy with uncertain high stability and poor stability in wind power generation, solar photovoltaic power generation and the like, the problem of grid loss of a power grid is more serious, and certain difficulty is caused to power dispatching. The waste of electric power is greatly generated.
Therefore, the flexible, efficient, safe and economical power system operation mode is pursued in power system construction, a more economical and effective smart grid is constructed, and the operation method in the power grid is decided, so that the energy management and other technologies are more intelligent, and the method is a requirement for modern smart grid construction.
Disclosure of Invention
The invention aims to provide a method for calculating the optimal economic power flow of an electric power system, and provides references for running methods in a power grid for decision makers.
In order to achieve the above purpose, the technical scheme of the invention is to provide an optimal power flow calculation method of an electric power system based on NMDAFSA, which is characterized by comprising the following steps:
wherein P is gi And Q is equal to gi The active output and the reactive output of a power generation unit i of the power system are respectively; p (P) di And Q is equal to di Active load and reactive load of the power generation unit i respectively; g ij And B is connected with ij The real part and the imaginary part of the j-th column element of the ith row of the admittance matrix of the power generation unit i are respectively; v (V) i And theta i The voltage amplitude and phase angle of the node i are respectively; θ ij ＝θ i -θ j Is the phase difference between node i and node j;
step 2, converting the inequality constraint condition into an inequality constraint function g (t), wherein the inequality constraint condition is as follows:
P gi_min ≤P gi ≤P gi_max ，i∈S g
V i_min ≤V i ≤V i_max ，i∈S d
|P ij |＝|V i V j (G ij cosθ ij +B ij sinθ ij )-V i 2 G ij |≤|P ij_max |
p in the formula gi_min And P gi_max The upper limit constraint condition and the lower limit constraint condition of the active output of the corresponding power generation unit i; v (V) i_min And V is equal to i_max Corresponding to upper and lower limit constraint conditions of the system node i voltage; p ij_max The I corresponds to the upper limit constraint condition of the active power flow of the line between the nodes i and j; p (P) ij The active power flow of the line between the corresponding nodes i and j; v (V) i And theta i The voltage amplitude and phase angle of the node i; v (V) j And theta j The voltage amplitude and phase angle of the node j; θ ij ＝θ i -θ j Is the phase difference between the nodes; s is S d The method comprises the steps of collecting all nodes of a system; s is S g Collecting all power generation units;
step 3, processing the converted G (t) and h (t), comparing the processed G (t) and h (t) with 0 to obtain the violation constraint degree of the individual, and introducing G (t) function representation:
then calculate the individual violation constraint degree as +.>
In the formula, h k (t) represents an inequality constraint function, g, resulting from the equality constraint processing k (t) represents an inequality constraint function obtained by inequality constraint condition processing, converting an optimization objective function minf in a power system into +.>
In the above formula: u (u) k >0 is a penalty coefficient, andis large enough;
step 4, for artificial fish group x i Initializing and according to the objective function
Food concentration Y as area of fish shoal i Selecting x in the visual field of each artificial fish n Setting the maximum iteration number T max ；
Step 5, calculating the visual field range V 'and the moving step length K' of the t-th iteration of the artificial fish according to the formulas K '=K.beta and V' =V.lambda, wherein K represents the moving step length of the t-1 th iteration of the artificial fish, and V represents the visual field range of the t-1 th iteration of the artificial fish; beta represents the nonlinear coefficient of the step size,
λ represents the nonlinear coefficient of the step size of the field of view,
calculating average status of artificial fish in the region of each artificial fish field of view +.>
Wherein X is i (t) represents the state of the artificial fish i, and n represents the total number of artificial fish within the visual field range V';
step 6, judging
Whether or not the concentration is less than the crowding factor alpha, N represents the total number of artificial fish, if the concentration is less than the food concentration Y i,a (t)>Y i (t)，Y i,a (t) represents the average food concentration in the region where the ith artificial fish is located at the present moment, Y i (t) representing the optimal food concentration in the region of the ith artificial fish at the present moment, then +.>
To calculate the tendency X of artificial fish i,a Displacement of movement X of (t) 1 A=random number of a e (0, 1) generated by rand (); if less than and at a food concentration of Y i,b (t)>Y i (t)，Y i,b (t) representing the optimal food concentration in the region of the ith artificial fish at the present moment, then +.>
To calculate the optimal solution X of each artificial fish tending to be in the current visual field i,b Displacement of movement X of (t) 2 Is then ∈according to the formula->
To calculate the downward moving state of the artificial fish, wherein X i,b (t) the optimal state of the field in which the ith artificial fish is located;
step 7, executing random behavior under the condition that the adaptability of the artificial fish is not improved after the foraging behavior reaches the maximum times, and taking the state as the next state of the artificial fish and X in a random swimming visual field i (t+1)＝X i And (t) +V'. A updating the current optimal individual and the position thereof, repeating until the algorithm ending condition is met, and outputting an optimal solution.
The power flow calculation method can better optimize the power flow calculation of the power system, has relatively simple implementation process and has good practical value.
Drawings
Fig. 1 is a graph of artificial fish movement displacement relation of power system optimal power flow calculation based on NMDAFSA;
fig. 2 is a flowchart of an NMDAFSA-based power system optimal power flow calculation method provided by the invention.
Detailed Description
The invention is further elucidated below in conjunction with the accompanying drawings. It is to be understood that these examples are illustrative of the present invention and are not intended to limit the scope of the present invention. Further, it is understood that various changes and modifications may be made by those skilled in the art after reading the teachings of the present invention, and such equivalents are intended to fall within the scope of the claims appended hereto.
The invention is based on an artificial fish swarm algorithm and the improvement of the algorithm, and comprises the following contents:
first, artificial Fish Swarm Algorithm (AFSA):
part1 foraging behavior of artificial fish school:
the initial number is N artificial fish { X } 1 ,X 2 ,...,X N The current state of each artificial fish is X i The random state in the visual field of each artificial fish is X n ；
X n ＝X i +V·a (1)
A epsilon (0, 1) random number generated by a=rand (), V represents the visual field range of each artificial fish;
if the food concentration Y is satisfied n >Y i The artificial fish will be oriented to X n The area where the moving object is located;
in the above formula, i represents the current iteration number; k represents the step size of the movement; a=random number of a e (0, 1) generated by rand ();
if the food concentration Y is satisfied i (t)>Y n (t) then randomly selecting X again n (T) repeating the updating in this way, if the maximum foraging times T are reached max If the advancing condition is not reached, carrying out random foraging behavior;
X i (t+1)＝X i (t)+V·a (3)
part2 group aggregation behavior of artificial fish school:
the current state of each artificial fish is X i (t) the number of artificial fish adjacent to the artificial fish is n, and then the average state of the artificial fish in the region is:
if it is
N is the total number of artificial fish; alpha is congestion factor alpha E (0, 1), and food concentration Y i,a (t)>Y i (t) description X a The food concentration in the area of (t) is high and not crowded, and the artificial fish can move to X a (t) advancing in the area, otherwise continuing to forge;
y in the above i,a (t) represents the average state of the food concentration in the region where the i-th artificial fish is located at the present moment; y is Y i (t) the food concentration at the position of the ith artificial fish at the current moment; i represents the current iteration number; k represents the step size of the movement; a=random number of a e (0, 1) generated by rand ();
part3 rear-end collision behavior of artificial fish school:
the current state of each artificial fish is X i (t) X in the field of the artificial fish i,b (t) is in an optimal state if it meets
And food concentration Y i,b (t)>Y i (t) description X i,b The area where (t) is located is the area where the food concentration is high and the artificial fish is not crowded, and the artificial fish moves to X b Moving the area where (t) is located, otherwise, continuing to find food;
y in the above i,b (t) represents the optimal state of the food concentration in the region where the i-th artificial fish is located at the present moment; i represents the current iteration number; k represents the step size of the movement; a=random number of a e (0, 1) generated by rand (); part4 random behavior:
after the foraging behavior of the artificial fish reaches the maximum times, under the condition that the adaptability is not improved yet, executing random behavior and followingOne state in the machine-run visual field is taken as the next state of the machine, X i (t+1)＝X i The (t) +V.a random behavior can lead the artificial fish to jump out of a local optimal state to achieve global optimal. Second, improvement of algorithm:
the artificial fish algorithm is used as a novel optimizing strategy and is widely applied to a large number of projects once proposed, but the traditional artificial fish algorithm has the defects of lower solving precision, smaller moving step length in the later stage of the algorithm, poorer local searching capability and easy occurrence of premature convergence phenomenon due to the fact that the traditional artificial fish algorithm is easy to sink into local optimum, so that the convergence precision in the later stage of the algorithm is improved, the sinking into local optimum is avoided, and the premature convergence of the algorithm is prevented. The design improves the existing artificial fish swarm algorithm, is used for enhancing the searching breadth of the algorithm and searching the global optimal solution; aiming at the improved artificial fish swarm algorithm, the invention relates to a Nonlinear multi-displacement artificial fish swarm algorithm (Nonlinear multi-displacement artificial fish swarm algorithm), which comprises the following specific measures:
1) The conventional artificial fish algorithm converges with a fixed step size K in the aspect of the movement of the fish shoal, so that the algorithm cannot flexibly converge and a random state X in the visual field range of each artificial fish is determined n In this case, the field of view V of the artificial fish cannot be changed according to the change of the fish school range, and the accuracy of the search is lowered, and the search speed is not high. Therefore, the nonlinear coefficient is processed aiming at the two parameters, so that the convergence speed in the initial stage of the algorithm is improved, and the accuracy of the algorithm is improved when the fish shoal range is reduced in the later stage of the algorithm. The specific improvement is as follows:
K'＝K·β (7)
V'＝V·λ (9)
2) In the case of an artificial fish algorithm,due to the reduction of the convergence area, the optimal solution is easily trapped in the later stage of the algorithm, and the phenomenon of premature is easy. To improve the global nature of the algorithm, the local optimal solution is jumped out. Improving the problem of the fish shoal convergence direction, and introducing an approach mode of two targets, namely aiming at X i,a Region (t) and X i,b (t) simultaneous approximation of regions while taking into account optimal region X i,b (t) the probability of being a globally optimal solution is greater, so the selection is more biased toward the optimal region X in terms of the angle of movement i,b And (t) the search range of the algorithm can be enlarged while ensuring that the optimal solution is approached, so that the possibility of sinking into the locally optimal solution is reduced. The specific improvement measures are as follows:
in the above formula, i represents the current iteration number; k represents the step size of the movement; a=random number of a e (0, 1) generated by rand ().
The invention provides a method for calculating optimal power flow of an electric power system based on NMDAFSA, which comprises the following steps:
1. power flow calculation of the power system:
optimizing the operation of the power system, wherein the operation cost of the system is the minimum operation target, and the mathematical expression is as follows:
p in the formula gi Is the active power of the ith generator, a i ,b i ,c i The constraint conditions for the consumption characteristic parameters are:
P gi_min ≤P gi ≤P gi_max ；i∈S g (17)
V i_min ≤V i ≤V i_max ；i∈S d (18)
|P ij |＝|V i V j (G ij cosθ ij +B ij sinθ ij )-V i 2 G ij |≤|P ij_max | (19)
in the above formula: node power balance constraint in the first two corresponding power systems; s is S d The method comprises the steps of collecting all nodes of a system; s is S g Aggregate for all generators; p (P) gi_min And P gi_max The upper limit constraint condition and the lower limit constraint condition of the active output of the corresponding power generation unit i; v (V) i_min And V is equal to i_max Corresponding to upper and lower limit constraint conditions of system node i voltage; p ij_max The I corresponds to the upper limit constraint condition of the active power flow of the line between the nodes i and j; p (P) ij The active power flow of the line between the corresponding nodes i and j; p (P) gi And Q is equal to gi The active output and the reactive output of the corresponding power generation unit i; p (P) di And Q is equal to di The active load and the reactive load of the corresponding node i; g ij And B is connected with ij Real and imaginary parts of the j-th column element of the i-th row of the node admittance matrix; v (V) i And theta i The voltage amplitude and phase angle of the node i; θ ij ＝θ i -θ j Is the phase difference between the nodes;
2. solving an optimization problem and a model:
when solving an actual problem, the solution to the objective function is often accompanied by a constrained problem, for which reason the solution to the objective function can be generalized to a problem that determines a set of decision variables so that the objective function takes an optimal value.
For optimization problems with constraints, the solution method can be roughly divided into two kinds of deterministic algorithms and algorithms based on randomness. The deterministic algorithm mainly comprises a Lagrange multiplier method, a sequence quadratic programming method, a gradient method and the like. In practical engineering, the optimization objective is often non-convex, non-linear, non-microscopically and non-continuous; in addition, the feasible search space for decision variables tends to be non-contiguous due to constraints. Therefore, such algorithms are difficult to find, and the result is often a locally optimal solution. Aiming at the constraint optimization problem, the invention adopts a penalty function method to process.
The equality constraint is:
p in the above gi And Q is equal to gi The active output and the reactive output of the corresponding power generation unit i; p (P) di And Q is equal to di The active load and the reactive load of the corresponding node i; g ij And B is connected with ij Real and imaginary parts of the j-th column element of the i-th row of the node admittance matrix; v (V) i And theta i The voltage amplitude and phase angle of the node i; θ ij ＝θ i -θ j Is the phase difference between the nodes.
The equality constraint relation function f (t) is obtained from equality constraint condition processing as follows:
adding a tolerance value delta into the equality constraint f (t), and converting the equality constraint into an inequality constraint function h (t);
h 1 (t)＝f 1 (t)-δ≤0 (24)
h 2 (t)＝f 2 (t)-δ≤0 (25)
where δ is the tolerance of the equation constraint, and is typically a small positive number.
The inequality constraint is:
P gi_min ≤P gi ≤P gi_max ；i∈S g (26)
V i_min ≤V i ≤V i_max ；i∈S d (27)
|P ij |＝|V i V j (G ij cosθ ij +B ij sinθ ij )-V i 2 G ij |≤|P ij_max | (28)
p in the above gi_min And P gi_max The upper limit constraint condition and the lower limit constraint condition of the active output of the corresponding power generation unit i; v (V) i_min And V is equal to i_max Corresponding to upper and lower limit constraint conditions of system node i voltage; p ij_max The I corresponds to the upper limit constraint condition of the active power flow of the line between the nodes i and j; p (P) ij The active power flow of the line between the corresponding nodes i and j; v (V) i And theta i The voltage amplitude and phase angle of the node i; θ ij ＝θ i -θ j Is the phase difference between the nodes; s is S d The method comprises the steps of collecting all nodes of a system; s is S g Aggregate for all generators;
the inequality constraint function g (t) is obtained by inequality constraint condition processing as follows;
g 3 (t)＝P gi_min -P gi ≤0；g 4 (t)＝P gi -P gi_max ≤0；i∈S g (29)
g 5 (t)＝V i_min -V i ≤0；g 6 (t)＝V i -V i_max ≤0；i∈S d (30)
g 7 (t)＝|P ij |-|P ij_max |＝|V i V j (G ij cosθ ij +B ij sinθ ij )-V i 2 G ij |-|P ij_max |≤0 (31)
processing the converted G (t) and h (t) to compare with 0 so as to obtain the violation constraint degree of the individual, and introducing G (t) function representation:
the individual violation constraint can be calculated from the above equation as:
optimizing the operation of the power system, wherein the operation cost of the system is the minimum operation target, and the mathematical expression is as follows:
p in the formula gi Is the active power of the ith generator, a i ,b i ,c i As consumption characteristic curve parameter, lambda is net loss cost
The problem of unconstrained optimization after transformation can thus be described as such a similar function:
in the above formula: u (u) k >0 is the penalty coefficient and is large enough.
The invention provides a method for calculating optimal power flow of an electric power system based on IAFSA, which comprises the following steps as shown in a flow chart:
(1) In calculating the power flow of a power system
And (3) with
The equality constraint translates into an inequality constraint function h (t). P in the above gi And Q is equal to gi The active output and the reactive output of the corresponding power generation unit i; p (P) di And Q is equal to di The active load and the reactive load of the corresponding node i; g ij And B is connected with ij Real and imaginary parts of the j-th column element of the i-th row of the node admittance matrix; v (V) i And theta i The voltage amplitude and phase angle of the node i; θ ij ＝θ i -θ j Is the phase difference between the nodes.
(2) Constraint P of inequality gi_min ≤P gi ≤P gi_max ；i∈S g V i_min ≤V i ≤V i_max ；i∈S d ；|P ij |＝|V i V j (G ij cosθ ij +B ij sinθ ij )-V i 2 G ij |≤|P ij_max I (I); p in the above gi_min And P gi_max The upper limit constraint condition and the lower limit constraint condition of the active output of the corresponding power generation unit i; v (V) i_min And V is equal to i_max Corresponding to upper and lower limit constraint conditions of system node i voltage; p ij_max The I corresponds to the upper limit constraint condition of the active power flow of the line between the nodes i and j; p (P) ij The active power flow of the line between the corresponding nodes i and j; v (V) i And theta i The voltage amplitude and phase angle of the node i; θ ij ＝θ i -θ j Is the phase difference between the nodes; s is S d The method comprises the steps of collecting all nodes of a system; s is S g For all generator sets. Is converted into an inequality constraint function g (t).
(3) Processing the converted G (t) and h (t), comparing the processed G (t) and h (t) with 0 to obtain the violation constraint degree of the individual, and introducing G (t) function representation:
from the above formula, it can be calculated that the individual violating constraint degree is + ->
In this way, the optimized objective function minf in the power system can be converted into
In the above formula: u (u) k >0 is the penalty coefficient and is large enough.
(4) Initializing artificial fish shoals x i And according to the objective function
Food concentration Y as area of fish shoal i . Selecting x in the visual field range of each artificial fish n . Setting the maximum iteration number T max 。
(5) According to the formula
To calculate the current visual field range and moving step length of the artificial fish according to the formula +.>
And calculating the average state of the artificial fish in the area in the visual field of each artificial fish. Wherein i represents the current iteration number; k represents the step size of the movement; a=random number of a e (0, 1) generated by rand ();
(6) Judging
Whether or not it is smaller than the crowding factor alpha, if it is smaller than and at the food concentration Y i,a (t)>Y i (t), then according to the formula
To calculate the tendency X of artificial fish i,a Displacement of movement X of (t) 1 . If less than and at a food concentration of Y i,b (t)>Y i (t), then according to the formula->
To calculate each stripArtificial fish tends to have an optimal solution X in its current field of view i,b Displacement of movement X of (t) 2 Is a value of (2). Then can be according to the formula->
To calculate the downward moving state position of the artificial fish. Wherein N is the total number of artificial fish; alpha is congestion factor alpha epsilon (0, 1); x is X i,b (t) is the optimal state of the field in which the artificial fish is located; i represents the current iteration number; k represents the step size of the movement; a=random number of a e (0, 1) generated by rand (); y is Y i,a (t) represents the average state of the food concentration in the region where the i-th artificial fish is located at the present moment; y is Y i,b (t) represents the optimal state of the food concentration in the region where the i-th artificial fish is located at the present moment;
(7) Executing random behavior under the condition that the adaptation degree is not improved after the foraging behavior of the artificial fish reaches the maximum number of times, randomly swimming to a certain state in the visual field, taking the state as the next state of the artificial fish, and taking the state as X i (t+1)＝X i And (t) +V'. A updating the current optimal individual and the position thereof, repeating until the algorithm ending condition is met, and outputting an optimal solution. Wherein V represents the current visual field range of the artificial fish; a=random number of a e (0, 1) generated by rand ().
Claims (1)
1. An NMDAFSA-based power system optimal power flow calculation method is characterized by comprising the following steps of:
step 1, converting an equality constraint condition in power flow calculation of a power system into an inequality constraint function h (t), wherein the equality constraint condition is as follows:
wherein P is gi And Q is equal to gi The active output and the reactive output of a power generation unit i of the power system are respectively; p (P) di And Q is equal to di Active load and reactive load of the power generation unit i respectively; g ij And B is connected with ij The real part and the imaginary part of the j-th column element of the ith row of the admittance matrix of the power generation unit i are respectively; v (V) i And theta i The voltage amplitude and phase angle of the node i are respectively; θ ij ＝θ i -θ j Is the phase difference between node i and node j;
step 2, converting the inequality constraint condition into an inequality constraint function g (t), wherein the inequality constraint condition is as follows:
P gi_min ≤P gi ≤P gi_max ，i∈S g
V i_min ≤V i ≤V i_max ，i∈S d
|P ij |＝|V i V j (G ij cosθ ij +B ij sinθ ij )-V i 2 G ij |≤|P ij_max |
p in the formula gi_min And P gi_max The upper limit constraint condition and the lower limit constraint condition of the active output of the corresponding power generation unit i; v (V) i_min And V is equal to i_max Corresponding to upper and lower limit constraint conditions of the system node i voltage; p ij_max The I corresponds to the upper limit constraint condition of the active power flow of the line between the nodes i and j; p (P) ij The active power flow of the line between the corresponding nodes i and j; v (V) i And theta i The voltage amplitude and phase angle of the node i; v (V) j And theta j The voltage amplitude and phase angle of the node j; θ ij ＝θ i -θ j Is the phase difference between the nodes; s is S d The method comprises the steps of collecting all nodes of a system; s is S g Collecting all power generation units;
step 3, processing the converted G (t) and h (t), comparing the processed G (t) and h (t) with 0 to obtain the violation constraint degree of the individual, and introducing G (t) function representation:
then calculate the individual violation constraint degree as +.>
In the formula, h k (t) represents an inequality constraint function, g, resulting from the equality constraint processing k (t) represents an inequality constraint function obtained by inequality constraint condition processing, and converts an optimization objective function minf in the electric power system into
In the above formula: u (u) k >0 is a penalty coefficient and is large enough; f, expressing the running cost of the system;
step 4, for artificial fish group x i Initializing and according to the objective function
Food concentration Y as area of fish shoal i Selecting x in the visual field of each artificial fish n Setting the maximum iteration number T max ；
Step 5, calculating the visual field range V 'and the moving step length K' of the t-th iteration of the artificial fish according to the formulas K '=K.beta and V' =V.lambda, wherein K represents the moving step length of the t-1 th iteration of the artificial fish, and V represents the visual field range of the t-1 th iteration of the artificial fish; beta represents the nonlinear coefficient of the step size,
λ represents the nonlinear coefficient of the field of view, +.>
Calculating average status of artificial fish in the region of each artificial fish field of view +.>
Wherein X is i (t) represents the state of the artificial fish i, and n represents the total number of artificial fish within the visual field range V'; />
Step 6, judging
Whether or not the concentration is less than the crowding factor alpha, N represents the total number of artificial fish, if the concentration is less than the food concentration Y i,a (t)>Y i (t)，Y i,a (t) represents the average food concentration in the region where the ith artificial fish is located at the present moment, Y i (t) representing the optimal food concentration in the region of the ith artificial fish at the present moment, then +.>
To calculate the tendency X of artificial fish i,a Displacement of movement X of (t) 1 A=random number of a e (0, 1) generated by rand (); if less than and at a food concentration of Y i,b (t)>Y i (t)，Y i,b (t) representing the optimal food concentration in the region of the ith artificial fish at the present moment, then +.>
To calculate the optimal solution X of each artificial fish tending to be in the current visual field i,b Displacement of movement X of (t) 2 Is then ∈according to the formula->
To calculate the downward moving state of the artificial fish, wherein X i,b (t) the optimal state of the field in which the ith artificial fish is located;
step 7, executing random behavior under the condition that the adaptability of the artificial fish is not improved after the foraging behavior reaches the maximum times, and taking the state as the next state of the artificial fish and X in a random swimming visual field i (t+1)＝X i And (t) +V'. A updating the current optimal individual and the position thereof, repeating until the algorithm ending condition is met, and outputting an optimal solution.
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