Economic dispatching method for multi-region interconnected power system based on elite reverse dynamic learning differential evolution algorithm

Abstract

The invention discloses a multi-region interconnected power system economic dispatching method based on an elite reverse dynamic learning differential evolution algorithm. The invention provides an elite reverse dynamic learning differential evolution algorithm (TSDE) aiming at the technical problems that a traditional differential evolution algorithm is insufficient in search capability, slow in convergence speed, easy to fall into local optimum and the like in multi-region economic dispatching considering a valve point effect. The method comprises the following steps: establishing a scheduling model by taking the minimum power generation cost as a target under a multi-region constraint condition; optimization is carried out based on an elite reverse dynamic learning differential evolution algorithm, and the algorithm integrates a dynamic elite guide reverse learning mechanism, a dynamic parameter oscillation strategy and a temperature-driven dual-strategy stage division and dual-gender population cooperation mechanism in a snake optimization algorithm (SO). Experimental results show that the provided elite reverse dynamic learning differential evolution algorithm shows excellent search performance in the aspect of multi-region economic dispatching.

Description

Technical Field

[0001] The present invention belongs to the technical field of power system dispatching, and relates to an economic dispatching method for a multi-region interconnected power system based on an elite reverse dynamic learning differential evolution algorithm. Background Art

[0002] With the continuous advancement of the global industrialization process, achieving the coordinated unity of economy and green and low-carbon goals has become an important issue in the current power industry. Economic dispatch (ED) refers to minimizing the cost of power generation by optimizing the output of each generator while satisfying the power balance and unit constraints. The cost function of a generator set is usually expressed as a differentiable quadratic convex function. However, when the valve point effect is considered, the ED problem gradually evolves into a non-convex, nonlinear, and multimodal complex optimization problem. Traditional differential evolution algorithms usually only use a single strategy for iteration. However, a single strategy is difficult to take into account the dynamic needs of global exploration and local development in complex optimization problems.

[0003] The present invention proposes an optimization algorithm based on the elite reverse dynamic learning differential evolution algorithm, which integrates the dynamic parameter oscillation strategy, the elite reverse learning strategy, and the temperature-driven dual-strategy stage division and dual-sex population collaboration mechanism in the snake optimization algorithm (SO). It effectively achieves a dynamic balance between global exploration and local development, significantly improves the economic operation efficiency of the power system, promotes the safe and stable operation of the power grid, and contributes to ensuring energy security. Summary of the Invention

[0004] The present invention proposes an elite reverse dynamic learning differential evolution algorithm, which integrates a dynamic parameter oscillation strategy, an elite reverse learning strategy, and the temperature-driven dual-strategy stage division and dual-sex population collaboration mechanism of the snake optimization algorithm (SO). It solves the problems of traditional differential evolution algorithms in high-dimensional and complex constrained optimization problems of power system economic dispatch, such as insufficient search capability, slow convergence speed, easy falling into local optimality, and lack of dynamic adaptability, thereby improving solution efficiency and the ability to find the global optimality.

[0005] The present invention adopts a method for economic dispatch of a multi-region interconnected power system based on an elite reverse dynamic learning differential evolution algorithm, comprising the following steps:

[0006] Step 1: Establish a mathematical model with the goal of minimizing the unit power generation cost while satisfying the constraints related to the multi-region economic dispatch of the power system;

[0007] Step 2: Obtain the parameters of the generator set and the system constraints;

[0008] Step 3: Use the elite reverse dynamic learning differential evolution algorithm to optimize and solve the mathematical models established in steps 1 and 2 to obtain the optimal scheduling solution;

[0009] Step 4: output the obtained optimal scheduling scheme, and determine the actual power output of each generator set in the system and the corresponding optimal cost according to the optimal scheduling scheme;

[0010] The multi-region interconnected power system economic dispatch method based on the elite reverse dynamic learning differential evolution algorithm according to claim 1, characterized in that step 3 comprises the following specific steps:

[0011] Step 3.1: initialize parameters, set the population size, the maximum number of function evaluations FEs max and the current number of evaluations FEs=0, and the initial value of the iteration number t=1.

[0012] Step 3.2: initialize a population containing popsize individuals in the constraint space of each decision variable. The population can be represented as: pop=[x1,x2,x3,...,x popsize ] (1) Where x i =[x i,1 ,x i,2 ,...,x i,D ] is the i-th individual, and the dimension D of each individual corresponds to the sum of the number of generator units and tie lines in the system.

[0013] Uniformly randomly initialize the j-th variable (unit power) of the individual x i,j : x i,j =P j min +rand·(P j max -P j min ) (1≤i≤46,1≤j≤D) (2) Where P j max and P j min represent the maximum and minimum output of the j-th unit allowed, respectively, and rand represents a random number in [0,1].

[0014] Step 3.3: calculate the objective function of the population, complete the objective function evaluation, and update the current evaluation number FEs=FEs+popsize.

[0015] Step 3.4: based on the dynamic parameter oscillation strategy, periodically oscillate the mutation factor F and the crossover probability CR, so as to realize the dynamic balance of global exploration and local development.

[0016] Step 3.5: Use the dual-sex population coordination mechanism to divide the population into male and female sub-groups. Different from the snake optimization algorithm's proportional gender division, this invention simulates the dynamic balance of the sex ratio of the biological population and adjusts the male sub-group (N) every 10 iterations. m ) and female subgroup (N f ) ratio: Make the sex ratio fluctuate between 40% and 60%, sort the population in ascending order according to the individual fitness value, and put the first N m The high-quality individuals are first retained in the male subgroup; the remaining individuals are assigned to the female subgroup.

[0017] Step 3.6: Introduce the temperature-driven dual-strategy stage division mechanism of the Snake Optimizer (SO) algorithm, and divide the exploration phase into a high-temperature phase and a low-temperature phase according to the temperature value.

[0018] Step 3.7: Use a hybrid DE / rand / 1 and current-to-best / 1 mutation strategy and add a male-female gender-guided mechanism for mutation.

[0019] Step 3.8: With a probability of 50%, generate a reverse solution by combining the current global optimal information with the elite-guided reverse learning mechanism. Compare the objective function value of the newly generated offspring with the reverse solution of the offspring, and take the better solution as the new offspring.

[0020] Step 3.9: Perform the selection operation and compare the objective function value of the newly generated offspring with that of the parent. If the offspring's objective function value is better than that of the parent, the offspring replaces the parent to form a new population.

[0021] Step 3.10: Determine whether the maximum number of function evaluations has been reached. If so, go to step 3.10; otherwise, repeat steps 3.3 to 3.9.

[0022] Step 3.11: Output the optimal solution and its corresponding unit output;

[0023] The method for economic dispatch of a multi-regional interconnected power system based on an elite reverse dynamic learning differential evolution algorithm according to claim 2 is characterized in that the dynamic parameter oscillation strategy in step 3.4 is specifically:

[0024] Normalize the iterative process to the progress factor progress = FEs / FEs max By introducing a periodic perturbation based on a sine function, the mutation factor F and the crossover probability CR are dynamically adjusted, so that F and CR fluctuate periodically with the progress of the iteration. The update formula of the mutation factor F and the crossover probability CR is as follows: Among them, F base is the scaling factor F base value, set to 0.8; and CR base is the reference value of the crossover probability CR, which is set to 0.2.

[0025] The exploration weight e of the mating mode in the low temperature stage w Using a linear decay strategy: e w = 0.9×(1-0.3×progress) (6)

[0026] According to step 3.6 of claim 2, the dual-strategy execution mechanism based on the dual-threshold is specifically described as follows: The temperature formula is defined as: Among them, mod is the modulo function, which modifies the number of evaluations FEs to 2000 to simulate the periodic "heating-cooling" behavior.

[0027] When Temp>0.5 (high temperature stage), the radical sex-guided DE hybrid mutation strategy is fully adopted to enhance the convergence speed. When Temp<0.2 (low temperature stage), the conservative mating / fighting conservative strategy is switched to, and the exploration weight e of the mating mode is generated using formula (4) w In contrast, the exploration weight of combat mode is 1-e w . Selective enforcement of mating and fighting patterns by exploration weights.

[0028] In the mating mode, the DE hybrid mutation strategy guided by sex in the high temperature phase is used. In the combat mode, the position update method in the SO algorithm is used. i The position update formula is: x i =x i +2×cw i ×rand×(Q×x best -x i ) (8) Among them, the calculation method of competitive weight cw (Competitive Weight) and dynamic attenuation factor Q is: Q=0.6×exp(progress-1) (10)

[0029] By the competition weight cw of the i-th individual i Dynamically adjust the individual step size so that individuals with better fitness tend to move towards the global optimal individual x bestAccelerated convergence. As the progress factor increases, Q decays exponentially, allowing wide-area exploration in the early stages and gradually narrowing to localized, refined search in the later stages.

[0030] In step 3.7 of claim 2, the hybrid DE / rand / 1 and current-to-best / 1 mutation strategy is specifically: A hybrid DE / rand / 1 and current-to-best / 1 mutation strategy is used. The DE / rand / 1 strategy is executed with a probability of 70%, and the population diversity is maintained by the random difference vector. Otherwise, the current-to-best / 1 strategy is executed, and the global optimal individual x is introduced. best The traction item forms a search trend that shrinks towards the elite area. The hybrid mutation strategy is: where x r1 and x r2 are randomly selected from different parent x i The r1-th and r2-th individuals, and r1 is not equal to r2.

[0031] Different from the traditional differential evolution algorithm generation method, the generation mechanism of r here adopts the relative gender generation method: where x male and x female Represents male and female snakes respectively, N m and N f The numbers of male and female snakes are generated in step 3.5. Male and female snakes are randomly selected for mutation and crossover operations, so that the offspring contains information about both male snakes (the superior subpopulation) and female snakes (the inferior subpopulation).

[0032] To further reduce the risk of failing to generate high-quality offspring during the mutation process in step 3.7 due to insufficient genetic information in the hermaphroditic population or limited local search capabilities, step 3.8 enhances the stability and robustness of the algorithm by introducing the guidance of the global optimal solution. The specific steps are as follows: The dynamic elite-guided reverse learning mechanism is performed on individuals in the temporary offspring (TemPop) with a probability of 50% to generate a reverse solution: k=0.7+0.5×rand(0,1) (14) Among them, k is a dynamic scaling factor used to adjust the spatial range of the inverse solution; x best is the current global optimal solution; P i max and P imin They represent the maximum and minimum output allowed for the i-th unit respectively.

[0033] After the reverse solution is generated, calculate its fitness value The number of evaluations FEs is increased by 1, compared with the fitness of the temporary solution, and the better individuals are retained to update the temporary offspring; BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 This is a schematic diagram of 4 zones and 40 units of the present invention

[0035] Figure 2 Violin plots of the present invention and three other existing algorithms

[0036] Figure 3 Convergence curve of the present invention and three other existing algorithms

[0037] Figure 4 Flowchart of the operation of the present invention and three other existing algorithms Specific implementation examples

[0038] A method for economic dispatch of multi-region interconnected power systems based on elite reverse dynamic learning differential evolution algorithm is proposed. First, a mathematical model of multi-region economic dispatch of 40 units in 4 regions is established. Figure 1 As shown, the system's total power load demand is 10,500 MW. Zone 1 includes the first 10 generators, with a demand load of 15% of the total load. Zone 2 includes the next 10 generators, with a demand load of 40% of the total load. Zone 3 consists of the third 10 generators, with a demand load of 30% of the total load. Zone 4 contains the last 10 generators, with a demand load of 15% of the total load. Table 1 Unit characteristics of the MAED system for 40 units in 4 regions

[0039] Step 1: With the goal of minimizing fuel costs, establish a multi-region economic dispatch model for the power dispatch system. The specific form of minimizing fuel costs is: Among them, FC ij (P ij ) is the power generation cost of the j-th generator set in region i, a ij ,b ij and c ij is the cost coefficient of the j-th generator set in region i; M is the number of regions; N iis the number of generators in region i; P ij is the actual output power of the jth generator in region i; e ij 、f ij is the coefficient of the valve point effect of the jth unit in region i.

[0040] Step 2: Determine the system constraints. The inequality constraints in the system include actual power balance constraints, tie line performance constraints, and generator group constraints.

[0041] Step 2.1: The actual power balance constraints between generation, load and network losses are as follows: Among them, PD i is the actual power demand of area i; PL i is the transmission loss in area i; T i,k is the actual power of the tie line from area i to area k. When power is transmitted from i to k, T i,k Take a positive value; otherwise take a negative value, B qj i 、B 0j i 、B 00 i is the transmission loss coefficient.

[0042] Step 2.2: Tie line performance constraints are as follows: in is the maximum value of the transmission power from area i to area k, is the minimum value of the power flow from region k to region i.

[0043] Step 2.3: Each generator output must be within the technical capability and meet the operating characteristics. The generator set constraints are as follows: in, are the minimum and maximum power generation capacity of each generator set respectively.

[0044] Step 2.4: For the regional actual power balance constraint, use the power balance repair operator to repair it so that the generator output, load demand and transmission power in each region are balanced. The power repair of the i-th region is as follows:

[0045] (1) Calculate the violation degree dif of the power balance constraint of the i-th region iWhen the constraint violation degree is greater than zero, it means that the total power of the current area is less than the actual required power, and the power output of the unit needs to be increased; when the constraint violation degree is less than zero, it means that the total power of the current area is greater than the actual required power, and the power output of the unit needs to be reduced. The numbers of all generator units in the current area are counted into set I, dif i The calculation is as follows: in is the total power generation of region i, PD i is the load demand of area i, PL i is the network loss in area i, T ik is the transmission power between area i and area k;

[0046] (2) When the power balance constraint violation degree dif i > 0, randomly select a generator set j in region i, that is, randomly select the j-th generator set from set I, and increase its power output so that its power output is P ij =max(P ij -dif i ,P ij min ) (twenty one)

[0047] (3) When the power balance constraint violation degree dif i When <0, randomly select a generator set j in region i, that is, randomly select j generator sets from set I, and reduce its power output so that its output power is P ij =min(P ij +dif i ,P ij max ) (twenty two)

[0048] (4) Recalculate the violation degree dif of the power balance constraint of the i-th region i , when dif i Zero or dif i If the sign of changes, the repair is stopped, otherwise the selected unit numbered j in set I is deleted and (2) and (3) are repeated.

[0049] Step 3.1: Initialize a population of popsize individuals within the constraint space of each decision variable. The population can be expressed as: pop=[x1,x2,x3,...,x popsize ] (twenty three) where x i =[x i,1 ,xi,2 ,...,x i,D ] is the i-th individual, and the dimension D of each individual corresponds to the sum of the number of generator sets and tie lines in the system.

[0050] For individual x i,j The j-th variable (unit power) is initialized uniformly randomly: x i,j =P j min +rand·(P j max -P j min )(1≤i≤46,1≤j≤D) (24) Among them, P j max and P j min They represent the maximum and minimum output allowed for the j-th unit respectively, and rand represents a random number in [0,1].

[0051] Step 3.3: Calculate the objective function of the population, complete the objective function evaluation, and update the current number of evaluations FEs = FEs + popsize.

[0052] Step 3.4: Based on the dynamic parameter oscillation strategy, perform periodic oscillation adjustment on the mutation factor F and the crossover probability CR. The update formulas of the mutation factor F and the crossover probability CR are as follows: Among them, F base is the scaling factor F base value, set to 0.8; and CR base is the reference value of the crossover probability CR, which is set to 0.2.

[0053] The exploration weight e of the mating mode in the low temperature stage w Using a linear decay strategy: e w = 0.9×(1-0.3×progress) (27)

[0054] Step 3.5: Use the dual-sex population coordination mechanism to divide the population into male and female subgroups. The male subgroup (N m ) and female subgroup (N f ) ratio: Make the sex ratio fluctuate between 40% and 60%, sort the population in ascending order according to the individual fitness value, and put the first N m The high-quality individuals are first retained in the male subgroup; the remaining individuals are assigned to the female subgroup.

[0055] Step 3.6: The temperature formula is defined as: Among them, mod is the modulo function, which modifies the number of evaluations FEs to 2000 to simulate the periodic "heating-cooling" behavior.

[0056] When Temp>0.5 (high temperature stage), the radical sex-guided DE hybrid mutation strategy is fully adopted to enhance the convergence speed. When Temp<0.2 (low temperature stage), the conservative mating / fighting conservative strategy is switched to, and the exploration weight e of the mating mode is generated using formula (4) w In contrast, the exploration weight of combat mode is 1-e w . Selective enforcement of mating and fighting patterns by exploration weights.

[0057] In the mating mode, the DE hybrid mutation strategy guided by sex in the high temperature phase is used. In the combat mode, the position update method in the SO algorithm is used. i The position update formula is: x i =x i +2×cw i ×rand×(Q×x best -x i ) (30) Among them, the calculation method of competitive weight cw (Competitive Weight) and dynamic attenuation factor Q is: Q=0.6×exp(progress-1) (32) By the competition weight cw of the i-th individual i Dynamically adjust the individual step size so that individuals with better fitness tend to move towards the global optimal individual x best Accelerated convergence. As the progress factor increases, Q decays exponentially, allowing wide-area exploration in the early stages and gradually narrowing to localized, refined search in the later stages.

[0058] Step 3.7: Use a hybrid DE / rand / 1 and current-to-best / 1 mutation strategy and add a male-female gender-guided mechanism for mutation: where x r1 and x r2 are randomly selected from different parent x ithe r1, r2th individual, and r1 is not equal to r2. Unlike the generation method of the traditional differential evolution algorithm, the generation mechanism of r here adopts a relative gender generation method: where x male and x female represent the male and female snakes respectively, N m and N f represent the number of male and female snakes respectively generated by step 3.5. Randomly select male individuals and female snakes for mutation and crossover operations, so that the offspring have both male (superior subpopulation) and female (inferior subpopulation) information at the same time.

[0059] Step 3.8: Perform dynamic elite-guided reverse learning mechanism on individuals in the temporary offspring (TemPop) with a probability of 50% to generate reverse solutions: k = 0.7 + 0.5 x rand(0, 1) (36) where k is a dynamic scaling factor used to adjust the spatial range of the reverse solution; x best is the current global optimal solution; P i max and P i min represent the allowed maximum and minimum output of the ith unit.

[0060] Prevent mutation in step 3.7, both male and female subpopulations do not carry excellent genetic information, x m and x f There is no better solution near the better solution, which cannot generate better offspring individuals. At the same time, through global optimal guidance, the result is more stable, and the robustness of the algorithm is improved.

[0061] After the reverse solution is generated, its fitness value is calculated and compared with the fitness of the temporary solution, the better individual is retained to update the temporary offspring, and the evaluation number FEs is increased by 1;

[0062] Step 3.9: Perform selection operation, compare the objective function value of the newly generated offspring with the objective function value of the parent, if the offspring objective function value is better than the parent, then the offspring replaces the parent to form a new population;

[0063] Step 3.10: Determine whether the maximum function evaluation number is reached, if reached, go to step 3.11, otherwise repeat steps 3.3-3.9.

[0064] Step 3.11: Output the optimal solution and its corresponding unit output;

[0065] Step 4: Output the optimal scheduling plan obtained in step 3, and determine the actual power output of each generator set in the system and the corresponding optimal cost based on the optimal scheduling plan;

[0066] The optimal scheduling scheme obtained by solving the example of 40 units in 4 regions using the method of the present invention has a fuel cost of 121,609.0878 $ / h. The output of each unit and the inter-regional transmission power are shown in Table 2.

[0067] To verify the effectiveness of the method, the present invention is compared with SpadePSO, ISO (an improved snake optimization algorithm) and traditional differential evolution algorithm. By arranging the simulation data, corresponding tables, violin plots and convergence curves are obtained.

[0068] As shown in Table 2, the minimum cost, maximum cost, and average cost of this algorithm are all lower than those of the other three algorithms. The minimum cost of this algorithm is 121,605.32$ / h, which is 1.51% and 4.32% lower than SpadePSO (123,469.67$ / h) and ISO (127,094.37$ / h), respectively. Its average cost (121,605.32$ / h) is also the lowest. Figure 2 、 Figure 3 It can be seen that the violin algorithm of the present invention is significantly narrower than SpadePSO, ISO and other algorithms, while converging faster than other algorithms.

[0069] In summary, this algorithm rarely falls into local optima during the iteration process, has high solution quality consistency, and converges significantly faster than other algorithms. This shows that the method provided by the present invention has great advantages in solving multi-region economic dispatch problems, and the determined dispatch scheme can effectively solve multi-region economic dispatch problems.

[0070] Table 2 Power generation of each unit and transmission power of tie line

[0071] Table 3 Comparison results of the optimal scheduling solutions solved by the optimization algorithm

Claims

1. The present invention provides a method for economic dispatch of a multi-region interconnected power system based on an elite reverse dynamic learning differential evolution algorithm, which specifically includes the following steps: Step 1: Establish a mathematical model with the goal of minimizing the unit power generation cost while satisfying the constraints related to the multi-region economic dispatch of the power system; Step 2: Obtain the parameters of the generator set and the system constraints; Step 3: Use the elite reverse dynamic learning differential evolution algorithm to optimize and solve the mathematical model established in steps 1 and 2 to obtain the optimal scheduling solution; Step 4: Output the optimal scheduling plan, and determine the actual power output of each generator set in the system and the corresponding optimal cost based on the optimal scheduling plan.

2. The method for economic dispatch of a multi-regional interconnected power system based on an elite reverse dynamic learning differential evolution algorithm according to claim 1 is characterized in that: Step 3 includes the following specific steps: Step 3.1: Initialize parameters, set population size, and the maximum number of evaluations of the objective function FEs max The current evaluation times FEs=0, and the starting value of the iteration times t=1. Step 3.2: Initialize a population of popsize individuals within the constraint space of each decision variable. The population can be expressed as: pop=[x1,x2,x3,...,x popsize ] (1) Among them, x i =[x i,1 ,x i,2 ,...,x i,D ] is the i-th individual, and the dimension D of each individual corresponds to the sum of the number of generator sets and tie lines in the system. i,j The j-th variable (unit power) is initialized uniformly randomly: x i,j =P j min +rand·(P j max -P j min )(1≤i≤46,1≤j≤D) (2) Among them, P j max and P j min They represent the maximum and minimum output allowed for the j-th unit respectively, and rand represents a random number in [0,1]. Step 3.3: Calculate the objective function of the population, complete the objective function evaluation, and update the current number of evaluations FEs = FEs + popsize. Step 3.4: Based on the dynamic parameter oscillation strategy, the mutation factor F and the crossover probability CR are periodically adjusted to achieve a dynamic balance between global exploration and local development. Step 3.5: Use the dual-sex population coordination mechanism to divide the population into male and female sub-groups. Different from the snake optimization algorithm's proportional gender division, this invention simulates the dynamic balance of the biological population's gender ratio and adjusts the male sub-group (N) every 10 iterations. m ) and female subgroup (N f ) ratio, and the adjustment method is as follows: Make the sex ratio fluctuate between 40% and 60%, sort the population in ascending order according to the individual fitness value, and put the first N m High-quality individuals are first retained in the male subgroup; the remaining N f Individuals are classified into the female subgroup. Step 3.6: Use the temperature-driven dual-strategy stage division mechanism to divide the exploration phase into a high-temperature phase and a low-temperature phase according to the temperature value. Step 3.7: Use a hybrid DE / rand / 1 and current-to-best / 1 mutation strategy and add a male-female gender-guided mechanism for mutation. Step 3.8: Trigger elite reverse learning with a probability of 50%, generate a reverse solution based on the global optimum, compare the objective function values ​​of the original solution and the reverse solution, retain the better one as the new offspring, and increase the number of evaluations FEs by 1. Step 3.9: Perform the selection operation and compare the objective function value of the newly generated offspring with that of the parent. If the offspring's objective function value is better than that of the parent, the offspring replaces the parent to form a new population. Step 3.10: Determine whether the maximum number of function evaluations has been reached. If so, go to step 3.11; otherwise, repeat steps 3.3 to 3.

9. Step 3.11: Output the optimal solution and its corresponding unit output.

3. According to the multi-regional interconnected power system economic dispatch method based on the elite reverse dynamic learning differential evolution algorithm of claim 2, in step 3.4, the dynamic parameter oscillation strategy is specifically: Normalize the iterative process to the progress factor progress = FEs / FEs max By introducing a periodic perturbation based on a sine function, the mutation factor F and the crossover probability CR are dynamically adjusted, so that F and CR fluctuate periodically with the progress of the iteration. The update formula of the mutation factor F and the crossover probability CR is as follows: in, F base is the scaling factor F base value, set to 0.8; and CR base is the reference value of the crossover probability CR, which is set to 0.

2. The exploration weight e of the mating mode in the low temperature stage w Using a linear decay strategy: and w =0.9×(1-0.3×progress) (6)。 4. According to step 3.6 of claim 2, the dual-strategy execution mechanism based on the dual-threshold is specifically described as follows: The temperature Temp is calculated as follows: in, mod is the modulo function, which modulates the evaluation times FEs with respect to 2000 to simulate the periodic "heating-cooling" behavior. When Temp>0.5 (high temperature stage), the radical sex-guided DE hybrid mutation strategy is fully adopted to enhance the convergence speed. When Temp<0.2 (low temperature stage), the conservative mating / fighting conservative strategy is switched to, and the exploration weight e of the mating mode is generated using formula (4) w In contrast, the exploration weight of combat mode is 1-e w . Selective enforcement of mating and fighting patterns by exploration weights. In the mating mode, the DE hybrid mutation strategy guided by sex in the high temperature stage is used. In the combat mode, the position update method in the SO algorithm is used. i The position update formula is: x i =x i +2×cw i ×rand×(Q×x best -x i ) (8) Among them, the calculation method of competitive weight cw (Competitive Weight) and dynamic attenuation factor Q is: Q=0.6×exp(progress-1) (10) By the competition weight cw of the i-th individual i Dynamically adjust the individual step size so that individuals with better fitness tend to move towards the global optimal individual x best Accelerated convergence. As the progress factor increases, Q decays exponentially, allowing wide-area exploration in the early stages and gradually narrowing to localized, refined search in the later stages.

5. In step 3.7 according to claim 2, the hybrid DE / rand / 1 and current-to-best / 1 mutation strategy is specifically: A hybrid DE / rand / 1 and current-to-best / 1 mutation strategy is used. The DE / rand / 1 strategy is executed with a probability of 70%, and the population diversity is maintained by the random difference vector. Otherwise, the current-to-best / 1 strategy is executed, and the global optimal individual x is introduced. best The traction item forms a search trend that shrinks towards the elite area. The hybrid mutation formula is: where x r1 and x r2 are randomly selected from different parent x i The r1th and r2th individuals of the set are generated, and r1 is not equal to r2. Different from the generation method of the traditional differential evolution algorithm, the generation mechanism of r here adopts the relative gender generation method: in, x male and x female Represents male and female snakes respectively, N m and N f The numbers of male and female snakes are generated in step 3.

5. Male and female snakes are randomly selected for mutation and crossover operations, so that the offspring contains information about both male snakes (the superior subpopulation) and female snakes (the inferior subpopulation).

6. To further reduce the risk of failing to generate high-quality offspring during the mutation process in step 3.7 due to insufficient genetic information in the hermaphroditic population or limited local search capabilities, and to enhance algorithm stability and robustness by introducing the guiding role of the global optimal solution, the specific steps of step 3.8 according to claim 2 are as follows: The dynamic elite-guided reverse learning mechanism is triggered with a probability of 50% for individuals in the temporary offspring (TemPop) to generate a reverse solution: x i =k×(P i min +P i min )-TemPop i +0.3×(x best -v i ) (13) k=0.7+0.5×rand(0,1) (14) in, k is a dynamic scaling factor used to adjust the spatial range of the inverse solution; x best is the current global optimal solution; P i max and P i min They represent the maximum and minimum output allowed for the i-th unit respectively. After the reverse solution is generated, calculate its fitness value f(x i ), and compare it with the fitness of the temporary solution, retain the better individuals to update the temporary offspring, and increase the number of evaluations FEs by 1.

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