A method for optimizing the structural parameters of a reducer based on the shuffled frog leaping algorithm

Abstract

A method for optimizing the structural parameters of a speed reducer based on the shuffled frog leaping algorithm, belonging to the technical field of speed reducer structural design optimization, includes the following steps: Step 1: The individual coding is divided into three parts. The first part is continuous real variables, the second part is integer variables, and the third part is discrete variables; Step 2: Initialize the population; Step 3: Use the penalty function to transform the constrained optimization problem into an unconstrained optimization problem and establish the objective function of the speed reducer structural optimization problem; Step 4: Calculate the objective function value of the speed reducer, sort and group, and divide the population into two groups; Step 5: Update the individuals in the first group; Step 6: Perform a combined mutation operation on the individuals in the first group; Step 7: Update the individuals in the second group; Step 8: Combine the first group and the second group as the new population, sort and record the optimal solution and the optimal value, and continue the iteration until the iteration termination condition is met, and output the optimal solution and the optimal value.

Description

Technical Field

[0001] The present invention relates to the technical field of reducer structure design optimization, and in particular to a method for optimizing the structure parameters of a reducer based on the shuffled frog leaping algorithm. Background Art

[0002] At present, the replacement of automobiles is accelerating and the R & D cycle is relatively short. In order to reduce material loss, lower costs and improve vehicle performance, the R & D department usually improves on the basis of the original component model in the later stage of R & D. However, this has led to a situation of excessive strength in the empirical design in the early stage of R & D. In the past vehicle development, the reducers selected by engineers according to experience have problems such as excessive strength, large mass and large volume, which have a certain impact on the fuel economy, handling performance of the vehicle, including the layout of the internal space, and cannot reach the ideal state of lightweight. In addition, using traditional optimization methods requires re-modeling and optimizing on the original design, which is often more complex in actual situations and cannot achieve the minimum quality. At the same time, the existing reducer optimization methods are costly and cannot meet customer requirements. Therefore, it is of great significance to optimize the structure parameters of automotive reducers. Summary of the Invention

[0003] The technical problem to be solved by the present invention is to provide a method for optimizing the structure parameters of a reducer based on the shuffled frog leaping algorithm, which can reduce material loss, lower costs and improve the performance of the vehicle reducer while reducing the production cost of the reducer and improving the performance of the reducer.

[0004] The technical problem to be solved by the present invention is realized through the following technical solutions. The present invention is a method for optimizing the structure parameters of a reducer based on the shuffled frog leaping algorithm, characterized in that it includes Step 1: The chromosome is encoded in a segmented manner, and the chromosome is divided into three parts. The first part is a continuous real variable, the second part is an integer variable, and the third part is a discrete variable;

[0005] Step 2: Initialize the population. The variables therein include continuous real variables, integer variables and discrete variables, and they need to be initialized separately. For the i-th individual X in the population i The initialization method is as follows:

[0006] The initialization method of the continuous real variable is randomly generated, that is, X i1 = Lb i +(Ub i - Lb i )×rand(1, D - N iv - N dv ), where Lb i and Ub i are respectively the lower and upper limit vectors of the i-th variable value, and N ivis the number of integer variables, N dv is the number of discrete variables, rand is a random number uniformly distributed between [0, 1], and D is the number of variables in the optimization problem;

[0007] The initialization method of the integer variables is randomly generated, that is, X i2 = Lb i + randperm(Ub i - Lb i , N iv ), randperm(Ub i - Lb i , N iv ) is to randomly generate N i - Lb i non-repeating integers between [1, Ub iv ;

[0008] The initialization method of the discrete variables is as follows: First, the value set of the i-th discrete variable X i3 is S i = {s 1 , s 2 , …, s Qi}, and each number in S i is mapped to the continuous integer interval Z i , Z i ∈ [1, 2, …, Q i , i = 1, 2, …, N dv ; Then, randomly generate 1 integer in the set Z i , let the randomly generated integer be k, then the discrete variable takes the k-th value s i in S k ;

[0009] The i-th individual X i in the population generated according to the above method is = [X i1 , X i2 , X i3 , repeat the above steps N times to generate an initial population containing N individuals;

[0010] Step 3: Construct the objective function for the reducer optimization, establish the objective function according to the sum of the volumes of the shafting components, and the objective function is to find the minimum value; use the penalty function method to handle the constraints; the objective function is:

[0011]

[0012] The variables therein include: the transmission ratio i 1 of the first-stage gear set, the number of teeth z 1 of the pinion of the first-stage gear set, the number of teeth z3 、Module m of the first - stage gear set n1 、Module m of the second - stage gear set n2 、Helix angle β of the helical gear in the first - stage gear set 1 、Helix angle β of the helical gear in the second - stage gear set 2 、Tooth width coefficient of the first - stage gear set Tooth width coefficient of the second - stage gear set Diameter d of the input shaft 1 '、Diameter d' of the intermediate shaft 2 、Diameter d of the output shaft 3 ' z 1 and z 3 are integers, m n1 and m n2 are discrete variables;

[0013] The penalty function method processes the constraint conditions through the following formula:

[0014]

[0015] In the formula, M 1 、M 2 take sufficiently large constants, f(X c ) is the objective - function term, G i (X c ) = max(0, g i (X c )),H j (X c ) = max(0, |h j (X c )| - ξ), ξ = 10 -4 ,g i (X c ) is the inequality - constraint penalty term, h j (X c ) is the equality - constraint penalty term;

[0016] Step 4: Calculate the individual fitness values and sort them in descending order of fitness values. Group them according to the improved grouping method. Divide the individuals in the population into two groups. The first N / 2 individuals are grouped into one group, and the last N / 2 individuals are grouped into another group;

[0017] The improved grouping method is to sort according to the quality of fitness and divide them into two groups according to the predation method. The individuals with better fitness are used as the first group and prey by the method of local search in place, simulating local exploitation; the individuals with worse fitness are used as the second group and jump - move towards the place with more food (the first group) to prey, simulating global exploration;

[0018] Step 5: Update the positions of the individuals in the first group and adopt an elitist retention evolutionary strategy;

[0019] Step 6: Perform a combinatorial mutation operation on the individuals in the first group, including the following steps:

[0020] The first step: Set the mutation probability p m = 0.8, randomly select individuals in the first group except the optimal individual, and randomly generate a random number r 1 between [0, 1]. When r 1 ≤ p m , perform a mutation operation on the selected individual;

[0021] The second step: Set the dynamic adaptive adjustment conversion probability p, p(t) = p max -(p max - p min )×Rt(t) / MaxRt, let p max = 1, p min = 0, Rt(t) is the running time from the start to the t-th iteration, and MaxRt is the maximum running time;

[0022] The third step: Randomly generate a random number r 2 between [0, 1]. When r 2 < p, perform Cauchy mutation; otherwise, perform Lévy mutation;

[0023] Step 7: Update the individuals in the second group. First, set the step size adjustment coefficient c i , Runtime(t) is the running time from the start of the program to the t-th iteration, c i (t) is the step size adjustment coefficient, α 1 , α 2 and α 3 are adjustment coefficients. Take α 1 = 0.9, α 2 is a 1×D random vector uniformly distributed between [0.2, 0.8], α 3 = 2, bF(t) is the fitness value of the optimal individual in the second group at the t-th iteration, wF(t) is the fitness value of the individual with the worst fitness in the second group at the t-th iteration, and f i (t) is the fitness value of the i-th individual in the second group at the t-th iteration; then, perform an elite-guided strategy to update the positions of the individuals in the second group;

[0024] Step 8: Combine the individuals in the first group and the second group as the new population, sort and record the optimal solution and the optimal value; determine whether the iteration termination condition is satisfied. If it is satisfied, stop the iteration and output the optimal solution and the optimal value; if not, repeat Steps 4 to 8 until the iteration termination condition is satisfied.

[0025] The technical problem to be solved by the present invention can also be further realized by the following technical solution. The update formula in Step 5 is:

[0026] NewXl i =N D (Xl i ,σ 2 )

[0027]

[0028] In the formula, NewXl i is the offspring generated after the update of the i-th frog in the first group, Xl i,j is the j-th component of the i-th frog, N D (Xl i ,σ 2 ) is a D-dimensional random row vector that follows a normal distribution with Xl i as the mean and σ 2 as the variance;

[0029] Round and take the integer value for the updated integer variables and discrete variables. The processed integer needs to be verified whether it is within the solution space. If it exceeds the solution space range, a new integer value needs to be randomly generated within the solution space.

[0030] The technical problem to be solved by the present invention can also be further realized by the following technical solution. After the random individual in the first group is mutated by Cauchy, the movement to the new position is expressed as:

[0031] NewXl rand =Xl rand +δ·s Cauchy

[0032] After being mutated by Lévy, the movement to the new position is expressed as:

[0033] NewXl rand =Xl rand +δ·s Lévy

[0034] In the formula, Xl rand is the individual randomly selected from the first group except the optimal individual, and δ is the adjustment parameter taken as 1;

[0035] Round the mutated integer variables and discrete variables. The processed integers need to be verified whether they are within the solution space. Those exceeding the solution space range need to randomly generate a new integer value within the solution space.

[0036] The technical problem to be solved by the present invention can also be further realized by the following technical solution. The elite guiding strategy in step seven includes the following steps: First, divide the individuals in the first group and the second group into two parts on average. That is, the individuals in the first group are divided into [1, 2, …, 0.5N 1 and [0.5N 1 + 1, 0.5N 1 + 2, …, N 1 , and the individuals in the second group are divided into [1, 2, …, 0.5N 2 and [0.5N 2 + 1, 0.5N 2 + 2, …, N 2 ; Then, when updating the position of an individual in [1, 2, …, 0.5N 2 in the second group, randomly select an elite individual from [1, 2, …, 0.5N 1 in the first group to guide the position update of an individual in [1, 2, …, 0.5N 2 in the second group. The position update formula for the individuals in the second group is:

[0037]

[0038] In the formula, c i is the step size adjustment coefficient, Xfo i is the i-th individual in the second group, Xl r is an individual randomly selected from the first group, Xl elite is an individual randomly selected from the first 20% of the individuals in the first group, and Xl elite ≠ Xl r , N 2 is the number of individuals in the second group;

[0039] Round the updated integer variables and discrete variables. The processed integers need to be verified whether they are within the solution space. Those exceeding the solution space range need to randomly generate a new integer value within the solution space.

[0040] Compared with the prior art, the beneficial effects of the present invention are:

[0041] (1) The reducer structure is optimized. Based on theoretical research, the method for optimizing the structural parameters of the reducer based on the shuffled frog leaping algorithm is applied to the production of various reducers, which has multiple important significances for improving the overall performance of the vehicle and reducing costs and increasing efficiency. It can reduce production costs, improve the power transmission efficiency of the vehicle, extend the service life, enhance design flexibility, save production materials, and improve product quality.

[0042] (2) In the research of the improved shuffled frog leaping algorithm, adding mutation operations and improving the update strategy can reduce the occurrence of premature convergence, increase population diversity, and improve the global search ability. For such complex engineering optimization problems, it can avoid the defects of the traditional optimization method's own architecture. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 is a flowchart of the present invention;

[0044] Figure 2 is a schematic diagram of the individual structure of the population;

[0045] Figure 3 is a simplified diagram of the structural dimensions of the shafting components of the reducer;

[0046] Figure 4 is a simplified diagram of the structural dimensions of the reducer; DETAILED DESCRIPTION OF THE INVENTION

[0047] The following further describes the specific technical solutions of the present invention to facilitate those skilled in the art to further understand the present invention without limiting its rights.

[0048] Referring to Figures 1-4 , a method for optimizing the structural parameters of a reducer based on the shuffled frog leaping algorithm includes:

[0049] Step 1: Referring to Figure 2 Encode individuals using a segmented coding method. There are D variables in the optimization problem, including N iv integer variables, N dv discrete variables, and the remaining variables are continuous real variables. Use a segmented coding method to encode individuals. Each individual is divided into three parts. The first part is continuous real variables, the second part is integer variables, and the third part is discrete variables. The structure of the i-th individual X i in the population is represented as (X i1 , …, X i(D-Niv-Ndv) , X i(D-Niv-Ndv+1) , …, X i(D-Ndv) , X i(D-Ndv+1) , …, X iD );

[0050] Step 2: Population initialization. Different types of variables use different initialization methods, including continuous real variables, integer variables, and discrete variables;

[0051] The \(i\)-th individual \(X\) i The continuous real variable \(X\) i1 is initialized randomly, i.e., \(X\) i1 = \(Lb\) i + (\(Ub\) i − \(Lb\) i ) × \(rand(1, D - N\) iv − \(N\) dv ), where \(Lb\) i and \(Ub\) i are the lower and upper bound vectors of the \(i\)-th variable's value respectively, \(N\) iv is the number of integer variables, \(N\) dv is the number of discrete variables, and \(rand\) is a random number uniformly distributed between \([0, 1]\);

[0052] The initialization method of the integer variable is to generate randomly, i.e., \(X\) i2 = \(Lb\) i + \(randperm(Ub\) i − \(Lb\) i , \(N\) iv ), where \(randperm(Ub\) i − \(Lb\) i , \(N\) iv ) generates \(N\) i non-repeating integers between \([1, Ub\) i − \(Lb\) iv ;

[0053] The initialization method of the discrete variable is as follows: First, let the value set of the \(i\)-th discrete variable \(X\) i3 be \(S\) i = \(\{s\) 1 , \(s\) 2 , …, \(s\) Qi \}, and map each number in \(S\) i to the continuous integer interval \(Z\) i , where \(Z\) i ∈ \([1, 2, …, Q\) i , \(i = 1, 2, …, N\) dv ; Then, randomly generate 1 integer in the set \(Z\) i , let the randomly generated integer be \(k\), then the discrete variable takes the \(k\)-th value \(s\) i in \(S\) k ;

[0054] The \(i\)-th individual \(X\) i in the population generated according to the above method is \([X\)i1 ,X i2 ,X i3 , repeat the above steps N times to generate an initial population containing N individuals.

[0055] Step 3: Construct the objective function for the reducer optimization. The smaller the volume of the shafting components, the smaller the mass of the reducer. First, establish the objective function based on the sum of the volumes of the shafting components, and the objective function is to find the minimum value. Then, handle the constraint conditions, and use the penalty function method to punish the solutions that do not meet the constraint conditions, and finally turn the infeasible solutions into feasible solutions.

[0056] Step 4: Calculate the fitness values of all N individuals in the population and sort them in descending order, and group them according to the improved grouping method. The first N individuals in the sorted population are the first group, denoted as Xl, and the last N individuals in the sorted population are the second group, denoted as Xfo, where N and N are equal and equal to N / 2. 1 individuals are the first group, denoted as Xl, and the last N 2 individuals in the sorted population are the second group, denoted as Xfo, where N 1 and N 2 are equal and equal to N / 2;

[0057] The improved grouping method is to sort according to the quality of the fitness and divide them into two groups according to the predation method. The individuals with better fitness are the first group and adopt the method of searching in place to prey, simulating local development; the individuals with worse fitness are the second group and jump and move towards the place with more food (the first group) to prey, simulating global exploration.

[0058] Step 5: Update the individuals in the first group according to the position update formula and adopt the elite retention strategy. The update formula generates offspring through normal distribution, with the position of the individual to be updated as the mean value, and controls the distance of the individual's updated position by controlling the variance value. As the number of iterations increases, the variance value changes from large to small, and the exploration ability of the algorithm gradually weakens and the development ability gradually increases.

[0059] Step 6: Perform the combined mutation operation on the individuals in the first group. The combined mutation operation includes the following steps:

[0060] The first step: Set the mutation probability p m , randomly select the individuals in the first group except the optimal individual, and randomly generate a random number r between [0,1] 1 , when r 1 ≤p m , perform the mutation operation on the selected individual;

[0061] The second step: Set the dynamically adaptive adjustment conversion probability p, p(t) = p max -(p max -p min )×Runtime(t) / MaxRuntime, let pmax = 1, p min = 0, Runtime(t) is the running time from the start to the t-th iteration, and MaxRuntime is the maximum running time;

[0062] Step 3: Randomly generate a random number r between [0, 1] 2 , when r 2 < p, perform Cauchy mutation; otherwise, perform Lévy mutation;

[0063] Step 7: Update the individuals in the second group according to the update formula. First, set the step size adjustment coefficient c i , the step size has a great impact on the algorithm performance. To better balance the global exploration ability and the local development ability, an adaptive step size adjustment coefficient c that is independent of the maximum number of iterations and the maximum running time and changes continuously is set i , c i is used in the update formula for the individuals in the second group, so that the algorithm performs global search with a high probability in the early stage of iteration and local search with a low probability, and vice versa in the later stage of iteration, but the global search ability at this time is weaker than that in the early stage of iteration. The calculation formula of c i is as follows: α 1 、α 2 and α 3 are adjustment coefficients, α 1 = 0.9, α 2 is a 1-row D-column random vector uniformly distributed between [0.2, 0.8], α 3 = 2, bF(t) is the fitness value of the best individual in the second group at the t-th iteration, wF(t) is the fitness value of the individual with the worst fitness in the second group at the t-th iteration, f i (t) is the fitness value of the i-th individual in the second group at the t-th iteration; then, execute the elite guiding strategy to update the individuals in the second group;

[0064] The position update formula for the individuals in the second group is:

[0065]

[0066] In the formula, c i is the step size adjustment coefficient, Xfo i is the i-th individual in the second group, Xl r is an individual randomly selected from the first group, Xl elite is an individual randomly selected from the first 20% of the individuals in the first group, and Xl elite ≠ Xl r , N 2 is the number of individuals in the second group;

[0067] Step 8: Combine the first group and the second group as the new population, sort them in ascending order according to the individual fitness values, and record the optimal solution and the optimal value; determine whether the iteration termination condition is satisfied. If it is satisfied, stop the iteration and give the optimal value and the optimal solution; if not, repeat Steps 4 to 7 until the iteration termination condition is satisfied.

[0068] The technical problem to be solved by the present invention can also be further realized by the following technical solution. The continuous real variable X i in the i-th individual X i1 in Step 2 is initialized randomly, that is, X i1 = Lb i + (Ub i - Lb i ) × rand(1, D - N iv - N dv ), where Lb i and Ub i are the lower and upper bound vectors of the i-th variable value respectively, N iv is the number of integer variables, N dv is the number of discrete variables, and rand is a random number uniformly distributed between [0, 1];

[0069] The i-th integer variable X i2 is initialized randomly, that is, X i2 = Lb i + randperm(Ub i - Lb i , N iv ), and randperm(Ub i - Lb i , N iv ) is N i randomly generated and non-repeating integers between [1, Ub i - Lb iv ;

[0070] The initialization method of the i-th discrete variable X i3 is as follows: First, if the value set of the i-th discrete variable X i3 is S i = {s 1 , s 2 , …, s Qi}, map each number in S i to the continuous integer interval Z i , Z i ∈ [1, 2, …, Q i , i = 1, 2, …, N dv ; then, in the set Zi Randomly generate an integer. Let the randomly generated integer be k. Then the discrete variable takes the k-th value s i in S k ;

[0071] The i-th individual X in the population generated according to the above method i = [X i1 , X i2 , X i3 . Repeat the above steps N times to generate an initial population containing N individuals;

[0072] Round the updated integer variable and discrete variable to an integer. The processed integer needs to be verified whether it is within the solution space. If it exceeds the solution space range, a new integer value needs to be randomly generated within the solution space.

[0073] The technical problem to be solved by the present invention can also be further realized by the following technical solution. The penalty function method in step three includes: when dealing with the constraint conditions of the mixed discrete variable problem, converting the equality constraint into an inequality constraint. At the same time, in order to avoid the penalty function from failing due to too small a penalty term, the formula of the penalty function method is as follows:

[0074]

[0075] In the formula, M 1 , M 2 Take sufficiently large constants, f(X c ) is the objective function term, G i (X c ) = max(0, g i (X c ))), H j (X c ) = max(0, |h j (X c )| - ξ), ξ = 10 -4 , g i (X c ) is the inequality constraint penalty term, h j (X c ) is the equality constraint penalty term.

[0076] The technical problem to be solved by the present invention can also be further realized by the following technical solution. The objective function in step three is:

[0077]

[0078] The variables therein include: the transmission ratio i of the first-stage gear set 1 , the number of teeth z of the pinion of the first-stage gear set 1 , the number of teeth z of the pinion of the second-stage gear set3 , module m of the first - stage gear set n1 , module m of the second - stage gear set n2 , helix angle β of the helical gears in the first - stage gear set 1 , helix angle β of the helical gears in the second - stage gear set 2 , face - width coefficient of the first - stage gear set Face - width coefficient of the second - stage gear set Diameter d’ of the input shaft 1 , diameter d’ of the intermediate shaft 2 , diameter d’ of the output shaft 3 , z 1 and z 3 are integers, and m n1 and m n2 are discrete variables.

[0079] The technical problem to be solved by the present invention can also be further realized by the following technical solution. The update formula in step five is:

[0080] NewXl i = N D (Xl i , σ 2 )

[0081]

[0082] In the formula, NewXl i is the offspring generated after the update of the position of the i - th individual in the first group, Xl i,j is the j - th component of the i - th individual, and N D (Xl i , σ 2 ) is a D - dimensional random row vector that follows a normal distribution with Xl i as the mean and σ 2 as the variance.

[0083] The technical problem to be solved by the present invention can also be further realized by the following technical solution. After the random individuals in the first group in step six are mutated by Cauchy, the movement to the new position is expressed as:

[0084] NewXl rand = Xl rand + δ·s Cauchy

[0085] After being mutated by Lévy, the movement to the new position is expressed as:

[0086] NewXl rand = Xl rand + δ·s Lévy

[0087] Wherein, Xl rand is an individual randomly selected from the first group other than the optimal individual, and δ is a regulation parameter taking 1.

[0088] The technical problem to be solved by the present invention can also be further realized by the following technical solution. The elite guiding strategy in step seven includes the following steps: First, divide the individuals in the first group and the second group into two parts on average, that is, the individuals in the first group are divided into [1, 2, …, 0.5N 1 and [0.5N 1 + 1, 0.5N 1 + 2, …, N 1 , and the individuals in the second group are divided into [1, 2, …, 0.5N 2 and [0.5N 2 + 1, 0.5N 2 + 2, …, N 2 ; Then, when updating the position of a certain individual in [1, 2, …, 0.5N 2 in the second group, randomly select an elite individual from [1, 2, …, 0.5N 1 in the first group to guide the position update of a certain individual in [1, 2, …, 0.5N 2 in the second group. The position update formula for the individuals in the second group is:

[0089]

[0090] Round and take the integer for the updated integer variable and discrete variable. The processed integer needs to be verified whether it is within the solution space. If it exceeds the solution space range, a new integer value needs to be randomly generated within the solution space.

[0091] Example 1: In order to give the optimal structural parameters of the reducer, take the optimization of the structural parameters of a certain type of reducer as an example; First, establish a mathematical model for the optimization problem of the reducer structural parameters; Second, use the proposed shuffled frog leaping algorithm (ISFLA) to solve the mathematical model of the optimization problem of the reducer structural parameters, and find the optimal structural parameters of the reducer that minimize the volume of the reducer;

[0092] The objective function of the optimization problem of the reducer structural parameters is:

[0093]

[0094] Let the maximum running time MaxTime of the solution of the shuffled frog leaping algorithm (ISFLA) be 20s, the penalty factor M = 10 8 , the population size N = 100, p m = 0.8, and the corresponding relationship between the standard module and the mapping value is shown in the following table:

[0095]

[0096] The mathematical model for solving the structural optimization problem of the reducer by the shuffled frog leaping algorithm (ISFLA), and the obtained optimal structural parameters are: the transmission ratio i of the first-stage gear set 1 equals 3.3, the number of teeth z of the first-stage pinion 1 equals 17, the number of teeth z of the second-stage pinion 3 equals 17, the module m of the first-stage gear set n1 equals 2 mm, the module m of the second-stage gear set n2 equals 2 mm, the helix angle β of the first-stage gear set 1 equals 8°, the helix angle β of the second-stage gear set 2 equals 8°, the tooth width coefficient of the first-stage gear set equals 0.6, the tooth width coefficient of the second-stage gear set equals 0.6, the shaft diameter d′ of the input shaft 1 equals 20 mm, the shaft diameter d′ of the intermediate shaft 2 equals 25 mm, the shaft diameter d′ of the output shaft 3 equals 23.3 mm, and the volume of the optimized reducer is 529011.373 mm 3 while the actual volume of the reducer before optimization is 717646.8 mm 3 . The volume of the optimized reducer is significantly reduced, which can save the consumption of raw materials and reduce costs. In addition, the reduction in volume can reduce the weight of the reducer, thereby reducing the vehicle mass and helping to reduce fuel consumption.

Claims

1. An optimization method for the structural parameters of a reducer based on the shuffled frog leaping algorithm, characterized in that: Step 1: The chromosome is encoded in a segmented manner. The chromosome is divided into three parts. The first part is a continuous real variable, the second part is an integer variable, and the third part is a discrete variable; Step 2: Initialize the population. The variables therein include continuous real variables, integer variables, and discrete variables, and they need to be initialized separately; Step 3: Construct the objective function for the reducer optimization. Establish the objective function according to the sum of the volumes of the shafting components. The objective function is to find the minimum value; Use the penalty function method to handle the constraint conditions; Step 4: Calculate the individual fitness values and sort them in descending order of fitness values. Group them according to the improved grouping method. Divide the individuals in the population into two groups. The first N / 2 individuals are divided into one group, and the last N / 2 individuals are divided into another group; The improved grouping method is to sort according to the quality of fitness and divide them into two groups according to the predation method. The individuals with better fitness are used as the first group and prey by the method of local search in place to simulate local development; the individuals with worse fitness are the second group and jump and move towards the place with more food to prey, simulating global exploration; Step 5: Update the positions of the individuals in the first group and adopt the evolutionary strategy of elitist retention; Step 6: Perform a combined mutation operation on the individuals in the first group, including the following steps: Step 1: Set the mutation probability p m =0.8, randomly select individuals from the first group except the best individual, and randomly generate a random number r1 between [0,1]. When r1≤p m When , mutation operation is performed on the selected individuals; Step 2: Set the dynamic adaptive adjustment conversion probability p, p(t) = p max -(p max -p min )×Rt(t) / MaxRt, let p max =1, p min =0, Rt(t) is the running time from the beginning to the tth iteration, and MaxRt is the maximum running time; Step 3: Randomly generate a random number r2 between [0, 1]. When r2 < p, perform Cauchy mutation; otherwise, perform Lévy mutation; Step 7: Update the individuals in the second group. First, set the step size adjustment coefficient c i , Runtime(t) is the running time from the start of the program to the tth iteration, c i (t) is the step adjustment coefficient, α1, α2 and α3 are adjustment coefficients, α1 = 0.9, α2 is a random vector of 1 row and D columns uniformly distributed between [0.2, 0.8], α3 = 2, bF(t) is the fitness value of the best individual in the second group at the tth iteration, wF(t) is the fitness value of the worst individual in the second group at the tth iteration, f i (t) is the fitness value of the i-th individual in the second group in the t-th iteration; then, the elite guidance strategy is executed to update the position of the individuals in the second group; Step 8: Combine the individuals in the first group and the second group as a new population, sort and record the optimal solution and the optimal value; judge whether the iteration termination condition is satisfied. When it is satisfied, stop the iteration and output the optimal solution and the optimal value; when it is not satisfied, repeat steps 4 to 8 until the iteration termination condition is satisfied.

2. The method for optimizing reducer structural parameters based on the frog leaping algorithm according to claim 1 is characterized in that: The position update formula for the individuals in the first group in step 5 is: NewXl i =N D (Xl i ,σ 2 ) In the formula, NewXl i is the offspring generated after the position of the i-th frog in the first group is updated, Xl i,j is the jth component of the ith frog, N D (Xl i ,σ 2 ) is Xl i is the mean, σ 2 is the variance, a D-dimensional random row vector that follows a normal distribution; Round and take the integer value for the updated integer variable and discrete variable. The processed integer needs to be verified whether it is within the solution space. If it exceeds the solution space range, a new integer value needs to be randomly generated within the solution space.

3. The method for optimizing reducer structural parameters based on the frog leaping algorithm according to claim 1 is characterized in that: After the individuals in the first group in step 6 are mutated by Cauchy, the position they move to is expressed as: NewXl rand =Xl rand +δ·s Cauchy After being mutated by Lévy, the position they move to is expressed as: NewXl rand =Xl rand +δ·s Lévy Where Xl rand is the individual other than the best individual randomly selected from the first group, δ is the adjustment parameter and takes 1; Round and take the integer value for the mutated integer variable and discrete variable. The processed integer needs to be verified whether it is within the solution space. If it exceeds the solution space range, a new integer value needs to be randomly generated within the solution space.

4. The method for optimizing reducer structural parameters based on the frog leaping algorithm according to claim 1 is characterized in that: The elite guidance strategy in step seven includes the following steps: first, the individuals in the first group and the second group are evenly divided into two parts, that is, the individuals in the first group are divided into [1,2,…,0.5N1] and [0.5N1+1,0.5N1+2,…,N1], and the individuals in the second group are divided into [1,2,…,0.5N2] and [0.5N2+1,0.5N2+2,…,N2]; then, when the position of an individual [1,2,…,0.5N2] in the second group is updated, an elite individual is randomly selected from [1,2,…,0.5N1] in the first group to guide an individual [1,2,…,0.5N2] in the second group to update its position. The position update formula of the second individual is: In the formula, c i is the step length adjustment coefficient, Xfo i is the i-th individual in the second group, Xl r is an individual randomly selected from the first group, Xl elite An individual is randomly selected from the first 20% of the individuals in the first group, and Xl elite ≠Xl r , N2 is the number of individuals in the second group; The updated integer variables and discrete variables are rounded to the nearest integer. The processed integers need to be verified to see if they are within the solution space. If they are outside the solution space, a new integer value needs to be randomly generated within the solution space.

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