CN112836423A - Microgrid capacity optimization configuration method based on improved differential evolution algorithm - Google Patents
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Abstract
The invention relates to a microgrid capacity optimal configuration method based on an improved differential evolution algorithm. And establishing a microgrid capacity optimization configuration method based on an improved differential evolution algorithm with the aim of lowest total cost. The method comprises the following steps: 1. and determining a microgrid object, and performing mathematical modeling on the microgrid. 2. And determining an energy scheduling strategy of the system according to the characteristics of the load and the characteristics of the wind, light, diesel and energy storage complementary power generation system. 3. And constructing an objective function equation of the system by taking the lowest cost as an objective function. 4. And programming and simulating a mathematical model of the system by utilizing matlab software, and optimally solving the problem by adopting a group intelligent algorithm in an algorithm part. And respectively improving the differential evolution algorithm in a population initialization stage and a variation stage. And applying the improved differential evolution algorithm to capacity optimization configuration of the microgrid. The problems of low solving precision and low speed of a traditional optimization algorithm are solved, and the scientificity and the economy of the micro-grid capacity configuration are improved.
Description
Technical Field
The invention relates to the technical field of microgrid capacity optimization configuration, in particular to an economic optimization method for capacity configuration of a microgrid by using a group optimization algorithm under the condition of participation of various power generation modes.
Technical Field
The capacity optimization configuration of the microgrid is a first link in the design and construction of the whole microgrid, and due to the volatility of renewable energy, the instability of charging and discharging of energy storage equipment and the uncertainty of investment cost of related equipment, the capacity configuration problem of the microgrid has the characteristics of multiple targets, multiple constraints and nonlinearity.
Conventional system capacity allocation designs often rely on the human experience of designers. The method is lack of strict scientificity, and has the characteristics of high investment cost, poor economy, poor stability and the like. In recent years, more and more intelligent optimization algorithms have been applied to solve this problem. For example, algorithms such as genetic and universal gravitation search are adopted to perform microgrid capacity optimization configuration. Such conventional optimization algorithms tend to fall into local optima and fail to find a true global optimum solution. Therefore, the method for finding the global optimal solution faster and more accurately by jumping out of the local optimal is the improved target of the algorithm.
Disclosure of Invention
The method aims to solve the problems that a mathematical model of each power generation mode is established for the capacity optimization configuration problem of the independent wind-solar-diesel-storage micro grid; establishing an objective function equation by taking the lowest total cost as a target; aiming at the problems of low solving precision and low speed of the original algorithm, an improved differential evolution algorithm is constructed to optimally plan the microgrid capacity optimal configuration problem and obtain a microgrid capacity configuration scheme with the lowest total cost.
According to the technical scheme adopted by the invention, the microgrid capacity optimal configuration method based on the improved differential evolution algorithm comprises the following steps:
Specifically, in the step 1, a microgrid model formed by a fan, a photovoltaic, a diesel generator and an energy storage device on a power generation side is established; the number of fans, photovoltaics, diesel generators and energy storage devices is used as the variable to be planned.
Specifically, in step 2, according to the characteristics of the load and the characteristics of the wind, light, diesel and energy storage complementary power generation system, the energy scheduling strategy of the system is determined as follows:
(2.1) calculating the difference value delta P between the sum of the electric energy output by the wind and light power generation modes and the load powerre-Pload；
(2.2) checking the residual electric energy in the storage battery, judging whether delta P is larger than 0, if so, entering the step (2.3), otherwise, entering the step (2.4);
(2.3) if the residual electric quantity in the storage battery exceeds an upper limit value, stopping charging the energy storage device, limiting power output by photovoltaic, and starting an unloading load by a fan to ensure the operation safety of the micro-grid system; if the residual electric quantity in the storage battery does not reach the upper limit value, the storage battery is charged;
(2.4) if the residual electric quantity in the storage battery reaches a lower limit value or the sum of the output power of the storage battery and the wind and light output power is smaller than the load power, scheduling and starting a diesel generator to ensure the load to supply power; otherwise, entering the step (2.5);
and (2.5) if the residual electric quantity of the storage battery does not reach the lower limit value and the sum of the wind-solar energy storage output power is larger than the load power, only the storage battery is required to discharge to make up for the power shortage value, and the diesel generator is not required to be started.
Specifically, in step 3, the total cost of the microgrid system
min f(x)＝Cshort+Cwaste+Cinvestment+Cpollution (1)
Wherein, CshortPenalty charge for annual power outages of the system, CwasteFor waste of energy, CinvestmentInvestment and operation and maintenance costs for microgrid, CpollutionThe pollution control cost for the environmental protection of the system is saved.
Specifically, in step 4, chromosome coding is performed, and the configuration numbers of the fan, the photovoltaic, the energy storage and the diesel generator are respectively used as a chromosome individual to perform chromosome coding.
In steps 4 (1) to (3), the improved differential evolution algorithm is to improve the initialization and mutation links of the differential evolution algorithm, so as to improve the performance of the algorithm, and the specific steps include:
(4.1) population initialization applying a reverse learning strategy: for individual X in the populationi＝{x1,x2,…, x D1,2, …, NP, where D denotes the dimension of the individual, here 4, NP is the number of individuals in the population; between the upper and lower limits of the range, for solving xiExistence of its inverse solution xi', the set of inverse solutions constitutes the inverse individual Xi'＝{x1'，x2'，…，xD' }, the calculation formula is expressed as:
xi'＝xmax+xmin-xi (2)
wherein x ismaxAnd xminRespectively the upper and lower limits of the value range; generating individuals corresponding to reverse individuals of the current individuals between the upper limit and the lower limit of the values, mixing the individuals in the two populations, and comparing the individuals to select the better individuals to finally form an initialization population;
(4.2) parameter adaptation: the algorithm realizes the variation among individuals through variation operation, and finds excellent solutions through searching new generation individuals; scaling factor FGThe change of the adaptation as the iteration progresses is expressed as:
wherein G is the number of current iterations, GmaxTo the maximum number of iterations, FmaxAnd FminUpper and lower limits of mutation operator F, respectivelymax＝1,Fmin0, F as the number of iterations increasesGFrom FmaxDown to Fmin；
(4.3) a double mutation strategy improved by adopting an elite selection mechanism:
combining two variation strategies of a differential evolution algorithm, and dividing a population iterated to the G generation currently into an elite population and a non-elite population by using an elite selection mechanism according to the fitness value of an individual; NP individuals exist in the G generation population, the fitness of each individual is calculated and arranged in a descending order, and the first SEP individuals are divided into elite population EPGThe SEP value is set manually, and the rest of the individuals are assigned to the NEP of the non-elite populationG(ii) a Elite population EPGAiming at providing the most desirable direction of evolution, the NEP of the non-elite populationGThe method is used for adjusting the search direction so as to increase the diversity of the population; xr1,G,Xr2,G,Xr4,GFrom elite populations EPGIn (1) random selection, Xr3,GAnd Xr5,GNEP from non-elite populationsGSelecting randomly; the double mutation strategy is shown below:
improved mutation strategy 1:
Vi,G+1＝Xr1,G+FG·(Xr2,G-Xr3,G)+FG·(Xr4,G-Xr5,G) (4)
improved mutation strategy 2:
Vi,G+1＝Xbest,G+FG·(Xr2,G-Xr3,G)+FG·(Xr4,G-Xr5,G) (5)
the two mutation strategies are combined into a unified double mutation strategy as follows:
the proportion of the scale to the scale of the whole population is set to be 0.4, namely SEP: NP is 0.4; wherein, FGAs mutation operator, Xbest,GIs the optimal individual in the population to iterate through the G-th generation, and rand (0,1) is the interval [0,1 ]]Random number between, MPGIs a two-way change of the above typeA probability of being selected in the hetero-policy; xr1,G,Xr2,G,Xr3,G,Xr4,G,Xr5,GAre in the interval [1, NP respectively]Randomly selecting mutually different numbers, V, within the rangei,G+1Representing the individuals after each iteration through the mutation operation.
The invention has the advantages that: the improved differential evolution algorithm is applied to capacity optimization configuration of the micro-grid, a mathematical model of the wind-solar-diesel-storage independent micro-grid is established, the lowest total cost is taken as a target function, and the optimal combination of the number of fans, the number of photovoltaic generators, the number of stored energy and the number of diesel generators is obtained by establishing a target function equation of the system under the condition that constraint conditions are met. By improving the differential evolution algorithm, the overall optimization capability and the later convergence speed of the algorithm are improved, the problems of low solving precision and low speed of the traditional optimization algorithm are solved, and the scientificity and the economy of the capacity configuration of the microgrid are improved.
Drawings
Fig. 1 is a diagram of a microgrid system architecture.
Fig. 2 is a schematic diagram of a reverse learning generation initialization population.
FIG. 3 is a schematic diagram of the mechanism for selecting elite.
FIG. 4 is a schematic diagram of the individual mutation process after modification of mutation strategy 1.
FIG. 5 is a schematic diagram of the individual mutation process after modification of mutation strategy 2.
FIG. 6 is a flow chart of an improved differential evolution algorithm of the present invention.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and examples.
As shown in fig. 1, the microgrid system is composed of a fan, a photovoltaic, a diesel generator, and a storage battery. The invention takes the number of the wind driven generator, the photovoltaic cell panel, the diesel generator and the storage battery as planning variables. Wind power generators have been rapidly developed due to their characteristics of cleanliness, environmental protection and reproducibility. The output power of the fan changes along with the change of the wind speed. The solar photovoltaic cell converts light energy into electric energy through the photovoltaic module and the power generation device, and the generated energy is mainly influenced by the ambient temperature and the illumination intensity. The storage battery is mainly used for solving the problem of unbalanced supply and demand in new energy power generation. The diesel generator has the characteristics of simple operation and quick start, and is used for ensuring the operation of a load when the illumination resources and the wind resources are insufficient and the residual electric energy in the energy storage device cannot meet the load requirement in the actual operation.
The microgrid capacity optimal configuration method based on the improved differential evolution algorithm comprises 4 steps:
step 1: determining a specific research object, and establishing a mathematical model of the wind-solar-diesel-storage independent micro-grid;
step 2: determining an energy scheduling strategy of the system according to the characteristics of the load and the characteristics of the wind, light, diesel and energy storage complementary power generation system;
and step 3: and constructing an objective function equation of the system by taking the lowest total cost as an objective function. The total cost of the system consists of investment, operation and maintenance cost, power failure punishment, energy waste cost and environmental protection cost of each power generation system, and the optimal configuration scheme of the number of fans, the number of photovoltaic devices, the number of stored energy and the number of diesel generators is obtained under the condition that each power supply of the wind-light diesel generator meets constraint conditions.
And 4, step 4: programming and simulating a mathematical model of the system by using Matlab software, and applying an improved differential evolution algorithm to capacity optimization configuration of the microgrid; the configuration number of the fans, the photovoltaic, the energy storage and the diesel generator is used as a chromosome individual, and an optimal individual is obtained through calculation by improving a differential evolution algorithm and is correspondingly an optimal scheme of micro-grid capacity configuration.
In step 1, the power generation side of the microgrid system is composed of multiple power generation modes, including wind power generation, photovoltaic power generation, diesel generator power generation and charging and discharging of stored energy. Performing mathematical modeling on 4 power generation forms in the microgrid; and establishing a mathematical model of the wind-solar-diesel-storage independent micro-grid by taking the number of the wind driven generator, the number of the photovoltaic cell panel, the number of the diesel generator and the number of the storage batteries as planning variables.
In the step 2, according to the characteristics of the load and the characteristics of the wind, light, diesel and energy storage complementary power generation system, determining an energy scheduling strategy of the system as follows:
(2.1) calculating the difference value delta P between the sum of the electric energy output by the wind and light new energy power generation mode and the load powerre-Pload；
(2.2) checking the residual electric energy in the storage battery, judging whether delta P is larger than 0, if so, entering the step (2.3), otherwise, entering the step (2.4);
(2.3) if the residual electric quantity in the storage battery exceeds an upper limit value, stopping charging the energy storage device, limiting power output by photovoltaic, and starting an unloading load by a fan to ensure the operation safety of the micro-grid system; if the residual electric quantity in the storage battery does not reach the upper limit value, the storage battery is charged;
and (2.4) if the residual electric quantity in the storage battery reaches a lower limit value or the sum of the output power of the storage battery and the wind-solar output power is less than the load power, scheduling and starting the diesel generator to ensure the load power supply. Otherwise, entering the step (2.5);
and (2.5) if the residual electric quantity of the storage battery does not reach the lower limit value and the sum of the wind-solar energy storage output power is larger than the load power, only the storage battery is required to discharge to make up for the power shortage value, and the diesel generator is not required to be started.
In step 3, the system optimization aims at solving the number N of the fans by taking the lowest total cost as the target when each wind, light and diesel storage power supply meets the constraint conditionwtNumber N of solar panelspvAnd the number of storage batteries NbatThe optimum combination of (a). The total cost of the microgrid system mainly comprises the penalty cost of power failure of the system, the energy waste cost, the investment cost and the operation and maintenance cost of the microgrid and the environmental protection and pollution control cost, and a formula is expressed as follows.
min f(x)＝Cshort+Cwaste+Cinvestment+Cpollution (1)
Wherein, CshortPenalty charge for annual power outages of the system, CwasteFor waste of energy, CinvestmentInvestment and operation and maintenance costs for microgrid, CpollutionThe pollution control cost for the environmental protection of the system is saved.
In step 4, the method for solving the optimal scheme of the microgrid capacity configuration by using the improved differential evolution algorithm comprises the following processes:
and (4.0) firstly, carrying out chromosome coding, and carrying out chromosome coding by taking the configuration number of the fan, the photovoltaic, the energy storage and the diesel generator as chromosome individuals.
And (4.1) applying population initialization of a reverse learning strategy. In a general evolutionary algorithm, a pure random mechanism is adopted for population initialization. For individual X in the populationi＝{x1,x2,…,xD1,2, …, NP between the upper and lower limits of the range for solution xiExistence of its inverse solution xi', the set of inverse solutions constitutes the inverse individual Xi'＝{x1'，x2'，…，xD', the calculation formula can be expressed as:
xi'＝xmax+xmin-xi (2)
wherein x ismaxAnd xminRespectively, the upper and lower limits of the value range. And generating individuals corresponding to the reverse individuals of the current individuals between the upper limit and the lower limit of the values, mixing the individuals in the two populations, and comparing the individuals to select the better individuals to finally form the initialization population. Compared with the initialized population generated in a pure random mode, the quality of individuals in the population is greatly improved. The process of reverse learning to generate the initialization population is shown in fig. 2.
And (4.2) parameter self-adaptation. The scaling factor F in the differential evolution algorithm is a definite value, i.e. the same F is used for each individual to perform crossover operation in the whole calculation process. The invention adopts an improved method of parameter self-adaptation, which is expressed as follows:
wherein G is the number of current iterations, GmaxTo the maximum number of iterations, FmaxAnd FminUpper and lower limits of mutation operator F, respectivelymax＝1,Fmin0, the scaling factor F used by the invention increases with the number of iterationsGFrom FmaxDown to FminTherefore, the global searching capability of the algorithm can be enhanced in the early stage of the algorithm, the searching range is expanded, and the convergence speed of the algorithm can be improved in the later stage.
(4.3) a double mutation strategy improved by an elite selection mechanism.
The differential evolution algorithm realizes variation and improvement among individuals through variation operation, and then finds an excellent solution through searching new generation of individuals. For a single individual, there are 5 variation strategies for the differential evolution algorithm. Different strategies of variation have different emphasis. In the whole iteration process, if the selected mutation strategy mainly focuses on global exploration, the convergence rate is reduced, and the iteration frequency is increased, and conversely, if the selected strategy focuses on local exploration capacity, a higher convergence rate is obtained, but the diversity of the population is not favorably maintained. In the invention, two variation strategies are combined to balance the global exploration capability and the local optimization capability. The elite selection mechanism is a strategy for dividing and selecting the population, and divides the population iterated to the G generation currently into an elite population and a non-elite population by using the elite selection mechanism according to the fitness value of an individual. NP individuals exist in the G generation population, the fitness of each individual is calculated and arranged in a descending order, and the first SEP individuals are divided into elite population EPGThe remaining individuals are assigned to the non-elite population NEPG. A schematic diagram of the elite selection mechanism is shown in fig. 3.
The principle of the elite guiding mechanism is to realize the improvement of the performance of the algorithm by the cooperation of the elite population and the non-elite population. Elite population EPGThe method aims to provide the most expected evolution direction, thereby enhancing the local searching capability of the algorithm. Non-elite population NEPGFocusing on adjusting the search direction to increase the diversity of the population, increase the global search capability and avoid premature convergence. In the mutation strategy of the improved differential evolution algorithm, Xr1,G,Xr2,G,Xr4,GFrom Elite population EPGIn (1) random selection, Xr3,GAnd Xr5,GFrom non-elite populations NEPGIs randomly selected. The improved double mutation strategy using the elite strategy is as follows:
improved mutation strategy 1:
Vi,G+1＝Xr1,G+FG·(Xr2,G-Xr3,G)+FG·(Xr4,G-Xr5,G) (4)
improved mutation strategy 2:
Vi,G+1＝Xbest,G+FG·(Xr2,G-Xr3,G)+FG·(Xr4,G-Xr5,G) (5)
the two mutation strategies are combined into a unified double mutation strategy as follows:
the ratio of the size to the size of the entire population is set to 0.4, i.e., SEP: NP is 0.4, and rand (0,1) is the interval [0,1 ]]A random number in between. MP (moving Picture experts group)GIs the probability of being selected in the two variant strategies above. Wherein, FGAs mutation operator, Xbest,GIs the best individual in the population to iterate through the G-th generation. Xr1,G,Xr2,G,Xr3,G,Xr4,GAnd Xr5,GAre in the interval [1, NP respectively]The numbers different from each other are randomly selected within the range. Vi,G+1Is an individual after each iteration through a mutation operation.
The improved individual variation evolution is shown in fig. 4 and 5, wherein the hollow dots are random points selected in the elite range, the black solid dots are random points selected in the whole range, fig. 4 is a schematic diagram of the individual variation process after the improvement of the variation strategy 1, and fig. 5 is a schematic diagram of the individual variation process after the improvement of the variation strategy 2. It can be seen that, after the elite selection strategy is used for improvement, compared with the defect that the directions are scattered due to the prior random distribution, the evolution direction of an individual is more definite, each iteration is closer to the global optimum point, the evolution effect of the individual is better, and the global optimum point is easier to search.
An algorithm flow chart of the improved differential evolution algorithm is shown in fig. 6, and the main process can be summarized as follows: 1. initializing a population, and generating an initialized population by applying a reverse learning strategy, wherein each individual represents a capacity configuration scheme; 2. updating the population, dividing the population by using an elite strategy, and applying different variation strategies to the elite population and the non-elite population for cross operation to obtain a new generation of population; 3. and repeating iteration, and when the iteration times reach the set maximum value, finishing the iteration and outputting the optimal individual, wherein the optimal individual corresponds to the optimal scheme of the microgrid capacity configuration.
Claims (6)
1. The microgrid capacity optimization configuration method based on the improved differential evolution algorithm is characterized by comprising the following steps of:
step 1, the power generation side of the micro-grid system consists of a plurality of power generation modes, including wind power generation, photovoltaic power generation, diesel generator power generation and energy storage charging and discharging, and mathematical modeling is carried out on 4 power generation modes in the micro-grid; the method comprises the steps that the quantity of a wind driven generator, a photovoltaic cell panel, a diesel generator and stored energy is used as a planning variable, and a mathematical model of the wind-solar-diesel-storage independent micro-grid is established;
step 2, determining an energy scheduling strategy of the system according to the characteristics of the load and the characteristics of the wind, light, diesel and energy storage complementary power generation system;
step 3, the total cost of the system is composed of investment, operation and maintenance cost, power failure punishment, energy waste cost and environmental protection cost of each power generation system, the lowest total cost is taken as a target function, and the optimal configuration of the number of fans, the number of photovoltaic generators, the number of stored energy generators and the number of diesel generators is obtained under the condition that a target function equation of the constructed system meets constraint conditions;
step 4, programming and simulating a mathematical model of the system by utilizing Matlab software, and applying an improved differential evolution algorithm to capacity optimization configuration of the microgrid; the process of the improved differential evolution algorithm applied to the microgrid capacity optimization configuration mainly comprises the following steps: (1) applying a reverse learning strategy to generate an initialization population, wherein each individual represents a capacity allocation scheme; (2) the scaling factors in the differential evolution algorithm realize variation among individuals through variation operation, and an excellent solution is found through searching for a new generation of individuals; the scaling factor is adaptively changed along with the iteration; (3) dividing the current population into an elite population and a non-elite population by using an elite selection mechanism according to the fitness value of the individual; combining two variation strategies of a differential evolution algorithm, and applying different variation strategies to an elite population and a non-elite population for cross operation to obtain a new generation of population; (4) and repeating iteration, and when the iteration times reach the set maximum value, finishing the iteration and outputting the optimal individual, wherein the optimal individual corresponds to the optimal scheme of the microgrid capacity configuration.
2. The microgrid capacity optimization configuration method based on the improved differential evolution algorithm as claimed in claim 1, wherein in step 1, a microgrid model formed by a fan, a photovoltaic, a diesel generator and an energy storage device on a power generation side is established; the number of fans, photovoltaics, diesel generators and energy storage devices is used as the variable to be planned.
3. The method for optimizing and configuring the capacity of the microgrid based on the improved differential evolution algorithm of claim 1, wherein in step 2, according to the characteristics of the load and the characteristics of the wind, light, diesel and storage hybrid power generation system, the energy scheduling strategy of the system is determined as follows:
(2.1) calculating the difference value delta P between the sum of the electric energy output by the wind and light power generation modes and the load powerre-Pload；
(2.2) checking the residual electric energy in the storage battery, judging whether delta P is larger than 0, if so, entering the step (2.3), otherwise, entering the step (2.4);
(2.3) if the residual electric quantity in the storage battery exceeds an upper limit value, stopping charging the energy storage device, limiting power output by photovoltaic, and starting an unloading load by a fan to ensure the operation safety of the micro-grid system; if the residual electric quantity in the storage battery does not reach the upper limit value, the storage battery is charged;
(2.4) if the residual electric quantity in the storage battery reaches a lower limit value or the sum of the output power of the storage battery and the wind and light output power is smaller than the load power, scheduling and starting a diesel generator to ensure the load to supply power; otherwise, entering the step (2.5);
and (2.5) if the residual electric quantity of the storage battery does not reach the lower limit value and the sum of the wind-solar energy storage output power is larger than the load power, only the storage battery is required to discharge to make up for the power shortage value, and the diesel generator is not required to be started.
4. The microgrid capacity optimization configuration method based on improved differential evolution algorithm of claim 1, wherein in step 3, the total cost of the microgrid system
min f(x)＝Cshort+Cwaste+Cinvestment+Cpollution (1)
Wherein, CshortPenalty charge for annual power outages of the system, CwasteFor waste of energy, CinvestmentInvestment and operation and maintenance costs for microgrid, CpollutionThe pollution control cost for the environmental protection of the system is saved.
5. The microgrid capacity optimization configuration method based on the improved differential evolution algorithm as claimed in claim 1, wherein in step 4, chromosome coding is performed firstly, and the configuration numbers of the fan, the photovoltaic, the energy storage and the diesel generator are respectively used as a chromosome individual to perform chromosome coding.
6. The method for optimizing and configuring capacity of the microgrid based on the improved differential evolution algorithm of claim 5, wherein in the steps (1) to (3) of step 4, the improved differential evolution algorithm is used for improving the initialization and variation links of the differential evolution algorithm so as to improve the performance of the algorithm, and the specific steps include:
(4.1) population initialization applying a reverse learning strategy: for individual X in the populationi＝{x1,x2,…,xD1,2, …, NP, where D denotes the dimension of the individual, here 4, NP is the number of individuals in the population; between the upper and lower limits of the range, for solving xiIn the presence of its inverseSolve x toi', the set of inverse solutions constitutes the inverse individual Xi'＝{x1'，x2'，...，xD' }, the calculation formula is expressed as:
xi'＝xmax+xmin-xi (2)
wherein x ismaxAnd xminRespectively the upper and lower limits of the value range; generating individuals corresponding to reverse individuals of the current individuals between the upper limit and the lower limit of the values, mixing the individuals in the two populations, and comparing the individuals to select the better individuals to finally form an initialization population;
(4.2) parameter adaptation: the algorithm realizes the variation among individuals through variation operation, and finds excellent solutions through searching new generation individuals; scaling factor FGThe change of the adaptation as the iteration progresses is expressed as:
wherein G is the number of current iterations, GmaxTo the maximum number of iterations, FmaxAnd FminUpper and lower limits of mutation operator F, respectivelymax＝1,Fmin0, F as the number of iterations increasesGFrom FmaxDown to Fmin；
(4.3) a double mutation strategy improved by adopting an elite selection mechanism:
combining two variation strategies of a differential evolution algorithm, and dividing a population iterated to the G generation currently into an elite population and a non-elite population by using an elite selection mechanism according to the fitness value of an individual; NP individuals exist in the G generation population, the fitness of each individual is calculated and arranged in a descending order, and the first SEP individuals are divided into elite population EPGThe SEP value is set manually, and the rest of the individuals are assigned to the NEP of the non-elite populationG(ii) a Elite population EPGAiming at providing the most desirable direction of evolution, the NEP of the non-elite populationGThe method is used for adjusting the search direction so as to increase the diversity of the population; xr1,G,Xr2,G,Xr4,GFrom elite populations EPGIn (1) random selection, Xr3,GAnd Xr5,GNEP from non-elite populationsGSelecting randomly; the double mutation strategy is shown below:
improved mutation strategy 1:
Vi,G+1＝Xr1,G+FG·(Xr2,G-Xr3,G)+FG·(Xr4,G-Xr5,G) (4)
improved mutation strategy 2:
Vi,G+1＝Xbest,G+FG·(Xr2,G-Xr3,G)+FG·(Xr4,G-Xr5,G) (5)
the two mutation strategies are combined into a unified double mutation strategy as follows:
the proportion of the scale to the scale of the whole population is set to be 0.4, namely SEP: NP is 0.4; wherein, FGAs mutation operator, Xbest,GIs the optimal individual in the population to iterate through the G-th generation, and rand (0,1) is the interval [0,1 ]]Random number between, MPGIs the probability of being selected in the two variant strategies above; xr1,G,Xr2,G,Xr3,G,Xr4,G,Xr5,GAre in the interval [1, NP respectively]Randomly selecting mutually different numbers, V, within the rangei,G+1Representing the individuals after each iteration through the mutation operation.
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