Athletic performance optimization method based on dynamic multi-objective optimization

Abstract

The invention discloses an athletic performance optimization method based on dynamic multi-objective optimization. The method comprises the following steps: initializing parameters and populations, and establishing a to-be-optimized objective function; detecting whether the environment is changed and detecting a corresponding response strategy; when an initial population in a new environment is generated, the population is divided into two sub-populations; different environment corresponding strategies are adopted for different sub-populations, the influence of historical information on the current environment is considered in a linear prediction strategy, and the prediction accuracy is improved; in the diffusion model, the generation model is fused into a dynamic response strategy, an initial noise sample is generated in the trained model, and denoising is performed step by step to generate a high-quality initial population adaptive to the current environment. According to the method, a set of personalized running training plans can be customized for each runner, and it is ensured that the runner can run at the most appropriate stride frequency, stride width, speed and breathing frequency in different time periods, so that the optimal exercise performance is achieved.

Description

Technical Field

[0001] The present invention belongs to the technical field of sports performance optimization, and in particular relates to a sports performance optimization method based on dynamic multi-objective optimization. Background Art

[0002] In real life, we often encounter situations where multiple problems need to be optimized simultaneously. Such problems are usually called multi-objective optimization problems (MOPs). Due to the conflict between multiple objectives, it is impossible to obtain a single optimal solution, but a set of trade-off solutions, called the Pareto optimal solution set (PS). The mapping of this set of solutions in the objective space is called the Pareto front (PF). In actual optimization problems, many MOPs are dynamic in nature. That is, the objective function, constraint relationship or other parameters of this MOP change over time, then such problems are called dynamic multi-objective problems (DMOPs). Unlike static multi-objective optimization problems, the optimal solution of dynamic multi-objective optimization problems is not a fixed solution set, but a set of Pareto optimal solutions that change over time. This requires the designed dynamic multi-objective evolutionary algorithm to be able to quickly track the latest Pareto frontier. However, in the actual optimization process, when the environment changes, all individuals in the evolving population are likely to have converged to the PS in the previous environment. At this time, the diversity of the population is low, and cross-breeding between individuals is difficult to produce new individuals that are out of the PS, resulting in a slow search for the optimal solution in the new environment. This is the main challenge faced in solving DMOPs. It is worth noting that the key to solving dynamic multi-objective problems is how to generate a high-quality initial population in the new environment after detecting environmental changes, ensuring that the newly generated population can quickly converge to the Pareto frontier in the new environment, and at the same time achieving a good balance between convergence and diversity.

[0003] Running performance is a complex multi-dimensional optimization problem. It not only depends on the runner's speed, but also involves many considerations such as the adjustment of stride length and frequency, the adjustment of breathing frequency, etc. In the actual running process, these factors will change dynamically with the passage of time and the change of running state. Therefore, when solving the problem of running performance optimization, multiple goals need to be considered at the same time. Assuming that in a running process, it is necessary to maximize running speed, minimize energy consumption, and minimize joint burden, there are usually conflicts between these goals. For example, increasing speed may increase energy consumption, while reducing energy consumption may lead to a decrease in speed, and these goals should change over time. Summary of the invention

[0004] The purpose of the present invention is to provide a sports performance optimization method based on dynamic multi-objective optimization, which solves the problem that existing optimization methods are difficult to accurately improve sports performance.

[0005] The technical solution adopted by the present invention is: a sports performance optimization method based on dynamic multi-objective optimization, comprising the following steps:

[0006] Step 1: Parameter initialization;

[0007] Step 2: Initialize the population Pop, establish the function to be optimized F(x, t) with the maximum running speed, minimum energy consumption, and minimum joint burden as the goals, and calculate the target value F(x, t) of the population Pop;

[0008] Step 3: Check whether the target value has changed. If it has changed, execute steps 5 to 7; otherwise, execute step 4.

[0009] Step 4: Use MOEA / D static optimization to obtain the optimal Pareto solution set, and go to step 8;

[0010] Step 5: Divide the population Pop into two sub-populations pop 1 and pop 2 ;

[0011] Step 6: Pop the population 1 and pop 2 Generate populations in new environments using improved linear and diffusion model prediction strategies and

[0012] Step 7: Merge populations and Get the population pop t+1 And perform local optimization to obtain the initial population under the new environment and input it into the MOEA / D algorithm, and go to step 4;

[0013] Step 8: After reaching the maximum number of iterations, output the optimal solution in each environment, that is, the running plan that changes over time.

[0014] The present invention is also characterized in that:

[0015] The initialization parameters in step 1 include population size N, dimension D, upper and lower bounds of decision variables lu, target number objNum, and maximum number of iterations FESMAX.

[0016] The function to be optimized F(x, t) established in step 2 is:

[0017] F(x,t)=max{-f 1 (x,t),f 2 (x,t),f 3(x,t)}

[0018] In the formula, f 1 (x,t),f 2 (x,t),f 3 (x, t) represents maximizing running speed, minimizing energy consumption, and minimizing joint burden, respectively, and is expressed as:

[0019]

[0020] Where t is the running time, and x represents the stride length C, speed S, step frequency SL, and breathing frequency BR during running.

[0021] Step 4 specifically includes the following steps:

[0022] Step 4.1, Initialization: Generate N weight vectors: λ 1 ,λ 2 ,…,λ N ; Generate the initial population: P = {x 1 ,x 2 ,…,x N}; For each weight vector λ i , find its nearest T neighbors;

[0023] Step 4.2: For each subproblem i∈{1,2,…,N}, randomly select two parent individuals x from the neighbor set. k and x j , perform crossover and mutation operations to generate new offspring individuals y, and calculate the objective function value f(y) of the new individuals;

[0024] Step 4.3: For each subproblem j∈B(i) in each set, if f(y) is better than the current optimal solution f(x j ), then replace x with y j ; Otherwise, no replacement;

[0025] Step 4.4, update the external archive and record the non-dominated solution;

[0026] Step 4.5: Determine whether the termination condition is met. If so, terminate; otherwise, return to step 4.2 to continue iterating.

[0027] In step 5, Spearman correlation analysis is used to divide the population Pop into two sub-populations pop 1 and pop 2 , specifically including the following steps:

[0028] Step 5.1: Calculate the center point C of the population at time t-1 and t t-1 and C t , and the difference between the center points W0 =C t -C t-1 Considered as variable M in Spearman's coefficient;

[0029] Step 5.2: For each individual at time t-1 and t, calculate the distance between them and select the individual The closest individual Where t-1 and t represent the t-1th and tth environments respectively, and the difference between the two individuals associated Considered as variable N;

[0030] Step 5.3: Sort the data of variables M and N to get the ranking and

[0031] Step 5.4: For each pair of data points and Calculating rank differences in and are the rankings of the i-th observation in variables M and N, respectively, and the ranking difference d i After the calculation is completed, the Spearman correlation coefficient ρ is calculated using the following formula:

[0032]

[0033] Step 5.5: Divide the population Pop into two sub-populations according to the calculated ρ value. The sub-population with high correlation is recorded as pop. 1 , and the other subpopulation is denoted as pop 2 .

[0034] Step 6 specifically includes the following steps:

[0035] Step 6.1: Pop subpopulation 1 Using an improved linear prediction strategy to generate subpopulations in new environments The calculation method of the linear prediction strategy is as follows:

[0036] x t+1 =λΔC t1 +(1-λ)ΔC t2 +x t +Gaussion(0,d)

[0037] Where, ΔC t1 =C t -C t-1 , ΔC t2 =C t-1 -C t-2,λ∈[0,1], used to balance adjacent information and historical information Gaussion(0,d) is a Gaussian noise term, which is used to locally perturb individuals and help them escape from local optimality.

[0038] Step 6.2: Pop subpopulation 2 The diffusion model prediction strategy is adopted. The diffusion model is based on the joint probability distribution p θ (x 0 )=∫p θ (x 0:T )dx 1:T To approximate the data distribution p 0 , by introducing the KL divergence D KL , the training objective of the neural network is equivalent to minimizing the variational bound of the negative log-likelihood. The training objective L is simplified to L simple It is expressed as:

[0039]

[0040] In the formula, x 0 represents the initial value of running; ∈ represents the noise added during the diffusion process; ∈ θ represents the output of the diffusion model, i.e., the prediction of the noise; represents the cumulative noise proportionality coefficient in the diffusion process; β t represents the diffusion rate at time step t, that is, the increase in noise intensity; T represents the total number of diffusion time steps; σ represents the standard deviation of the noise during the diffusion process;

[0041] After the diffusion model is trained, an initial noise sample is generated from the Gaussian distribution, and the initial noise sample is gradually denoised to generate an initial population that adapts to the current environment.

[0042] Step 7 specifically includes the following steps:

[0043] Step 7.1: Merge populations and Get the population pop t+1 ;

[0044] Step 7.2: Pick any two points δ in the decision space 1 ,δ 2 , respectively, with δ 1 ,δ 2 Draw a circle S with a fixed length and radius as the center 1 , S 2 , then the areas of the two regions are equal;

[0045] Step 7.3: Calculate the number of cells that fall in area S 1 , S2 The number of individuals ξ 1 , 2 ;

[0046] Step 7.4: Determine ξ 1 , 2 If the size of 1 > 2 , then according to the super volume contribution from area S 1 Delete a certain number of individuals in area S 2 The mutation generates the same number of individuals if S 2 If there is no individual in the area, a reference point is generated first, and then mutation is performed until |ξ 1 -ξ 2 |≤1;

[0047] Step 7.5: After local adjustment, the final initial population is obtained The initial population As input to the MOEA / D algorithm.

[0048] Step 8 is specifically as follows: determine whether the number of fitness evaluations FES is less than the maximum number of iterations FESMAX. If so, proceed to step 3; otherwise, output the optimal solution in each environment, which is a series of personalized running plans that change over time.

[0049] The beneficial effects of the present invention are as follows: the sports performance optimization method based on dynamic multi-objective optimization of the present invention abstracts the objectives that need to be optimized during exercise, such as maximizing running speed, minimizing energy consumption, minimizing joint burden, etc., into a set of minimization objective functions, and generates a high-quality initial population by combining an improved linear prediction method with a diffusion model, which can ensure that it can converge to the Pareto front quickly and accurately in a new environment, so that the optimal cadence, stride, speed and breathing rate can be found in each time period, thereby maximizing the overall performance of the runner and ensuring that the conflicts between the various objectives are reasonably balanced. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 is a flow chart of a sports performance optimization method based on dynamic multi-objective optimization of the present invention;

[0051] Figure 2 is a schematic diagram of a process of improving sports performance in a sports performance optimization method based on dynamic multi-objective optimization of the present invention;

[0052] Figure 3 It is a schematic diagram of the local optimization process in the sports performance optimization method based on dynamic multi-objective optimization of the present invention. DETAILED DESCRIPTION

[0053] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0054] Example 1

[0055] The present invention provides a sports performance optimization method based on dynamic multi-objective optimization, such as Figure 1 As shown, the following steps are included:

[0056] Step 1: Parameter initialization, including population size N, dimension D, upper and lower bounds of decision variables lu, target number objNum, and maximum number of iterations FESMAX.

[0057] Step 2: Initialize a population Pop of N individuals, establish the function to be optimized F(x, t) with the maximum running speed, minimum energy consumption, and minimum joint burden as the goals, and calculate the target value F(x, t) of the population Pop:

[0058] F(x,t)=max{-f 1 (x,t),f 2 (x,t),f 3 (x,t)} (1)

[0059] In the formula, f 1 (x,t),f 2 (x,t),f 3 (x, t) represents maximizing running speed, minimizing energy consumption, and minimizing joint burden, respectively, expressed as:

[0060]

[0061] In the formula, t is the running time (min), x represents the stride C, speed S, step frequency SL and breathing frequency BR during running, where:

[0062] C min ≤C≤C max

[0063] S min ≤S≤S max

[0064] SL min ≤SL≤SL max

[0065] BR min ≤BR≤BR max

[0066] When establishing the objective function, in addition to the decision information closely related to the running process, the runner's BMI index, maximum heart rate HR max , maximum oxygen consumption Resting heart rate HRresting The changes in heart rate and oxygen consumption during running also have a certain impact on the final result. Therefore, these auxiliary information and decision information are comprehensively considered to model the objective function, such as Figure 2 shown.

[0067] Step 3: Randomly select 20% N individuals to detect whether the target value has changed. If the target value has changed, it is determined that the environment has changed and steps 5 to 7 are executed; if the target value has not changed, step 4 is executed.

[0068] Step 4: Use MOEA / D for static optimization to obtain the optimal Pareto solution set under this environment, and then go to step 8.

[0069] Step 5: Use Spearman correlation analysis to divide the population into two sub-populations pop 1 and pop 2 .

[0070] Step 6: Pop the population 1 Generating populations in new environments using an improved linear prediction strategy Pop 2 Using diffusion model prediction strategies to generate populations in new environments

[0071] Step 7: and Merge to get the population pop t+1 , pop t+1 Perform a local optimization to obtain the initial population in the new environment, use the initial population as the input of the MOEA / D algorithm, and go to step 4.

[0072] Step 8: Determine whether the number of fitness evaluations FES is less than the maximum number of function evaluations FESMAX. If so, proceed to step 3; otherwise, terminate and output the optimal solution in each environment, which is a series of personalized running plans that change over time, such as Figure 2 As shown in the figure, the final output solution is the running frequency, running speed, running stride and breathing frequency corresponding to the Pareto optimal solution at the current moment. As the running time T goes by, there will be different running plans at each moment t (min). The time starts from t = 1 and ends at t = n. Each time point t (min) has a corresponding running state and target optimization decision. Personalized running plans are designed according to each person's health needs, sports goals, etc. Figure 2In the process of dynamic multi-objective optimization, a set of compromise solutions are obtained. The compromise solution is to find a suitable balance point among the three objectives so that the speed, energy consumption and joint burden are within a reasonable range. The compromise solution is not a simple average, but the final choice is determined based on factors such as the relative importance of the objectives, the degree of conflict and the needs of the decision maker. Figure 2 The representation of time t-1 and t in the lower left corner is the best running plan selected by the runner at the current moment.

[0073] Example 2

[0074] The present invention provides a sports performance optimization method based on dynamic multi-objective optimization. Based on Example 1, step 4 preferably includes the following steps:

[0075] Step 4.1, Initialization: Generate N weight vectors: λ 1 ,λ 2 ,…,λ N ; Generate the initial population: P = {x 1 ,x 2 ,…,x N}; For each weight vector λ i , find its nearest T neighbors;

[0076] Step 4.2: For each subproblem i∈{1,2,…,N}, randomly select two parent individuals x from the neighbor set. k and x j , perform crossover and mutation operations to generate new offspring individuals y, and calculate the objective function value f(y) of the new individuals;

[0077] Step 4.3: For each subproblem j∈B(i) in each set, if f(y) is better than the current optimal solution f(x j ), then replace x with y j ; Otherwise, no replacement;

[0078] Step 4.4, update the external archive and record the non-dominated solution;

[0079] Step 4.5: Determine whether the termination condition is met. If so, terminate; otherwise, return to step 4.2 to continue iterating.

[0080] Example 3

[0081] The present invention provides a sports performance optimization method based on dynamic multi-objective optimization. Based on Example 1, step 5 preferably includes the following steps:

[0082] Step 5.1: Calculate the center point C of the population at time t-1 and t t-1 and C t , and the difference between the center points W 0 =Ct -C t-1 Considered as variable M in Spearman's coefficient;

[0083] Step 5.2: For each individual at time t-1 and t, calculate the distance between them and select the individual The closest individual At this point, the individual and individuals is considered to be associated, where t-1 and t denote the t-1th and tth environments, respectively. Considered as variable N;

[0084] Step 5.3: Sort the data of variables M and N to get the ranking and

[0085] Step 5.4: For each pair of data points and Calculate the ranking difference in and are the rankings of the ith observation in variables M and N, respectively. The ranking difference d i After the calculation is completed, the Spearman correlation coefficient ρ is calculated using the following formula:

[0086]

[0087] Step 5.5: Divide the population into two sub-populations according to the calculated ρ value. The sub-population with high correlation is recorded as pop 1 , and the other subpopulation is denoted as pop 2 .

[0088] Example 4

[0089] The present invention provides a sports performance optimization method based on dynamic multi-objective optimization. Based on Example 1, step 6 preferably includes the following steps:

[0090] Step 6.1: Pop subpopulation 1 Using an improved linear prediction strategy to generate subpopulations in new environments The calculation method of the linear prediction strategy is as follows:

[0091] x t+1 =λΔC t1 +(1-λ)ΔC t2 +x t +Gaussion(0,d) (4)

[0092] Where, ΔC t1=C t -C t-1 , ΔC t2 =C t-1 -C t-2 ,λ∈[0,1], used to balance adjacent information and historical information The larger the λ, the more significant the impact of recent trends, and vice versa. Gaussion(0,d) is a Gaussian noise term that performs a local disturbance on individuals to help them escape from local optimality.

[0093] Step 6.2: Pop subpopulation 2 The diffusion generation model prediction strategy is adopted. The calculation method of the diffusion model to generate new solutions is as follows:

[0094] Forward diffusion stage: The final PS obtained in each environment is regarded as a sample, and a series of noise addition processes are performed on each sample until the sample is destroyed and becomes a complete Gaussian noise. Specifically, in the forward stage, the original sample x 0 The noise is gradually increased, and the x obtained at each step is t Only the result x of the previous step t-1 The process can be regarded as a Markov process, satisfying:

[0095]

[0096] Therefore, the entire forward diffusion can be defined as:

[0097]

[0098] where β t ∈(0,1) is the variance hyperparameter of the Gaussian distribution and satisfies β 1 <β 2 <…<β T , represents a Gaussian distribution with mean μ and variance Σ; is the scaling factor, which means that in the tth step, the t-1 Transfer to x t The mean of t I represents the covariance matrix, which represents the noise variance added in the tth step. Through the entire forward process, the initial sample x 0 Convert to noise x T .

[0099] Backward Diffusion Phase: The backward phase of the diffusion model is defined via a learnable Gaussian kernel (parameterized by θ) as:

[0100]

[0101] Among them, μ θ and Σ θ is the mean and variance of the learnable inverse Gaussian kernel, given by the inverse distribution p θ OK. From x T to x 0 The reverse sequence of steps is defined as:

[0102]

[0103] The diffusion model aims to obtain the θ (x 0 )=∫p θ (x 0:T )dx 1:T To approximate the data distribution p 0 .

[0104] Training objective: By introducing KL divergence D KL , the training objective of the neural network is equivalent to minimizing the variational bound on the negative log-likelihood:

[0105]

[0106] Among them, L T and L 0 represents the prior loss and reconstruction loss; L 1:T-1 represents the sum of the divergences between the posterior distributions of the forward and backward steps at the same time. Simplified L t-1 , we can get the posterior distribution q(x t-1 |x t ,x 0 )’s simplified training objective L simple :

[0107]

[0108] in, Depends on β t , reparameterize x t For x t (x 0 ,σ),L t-1 Represents the l between two mean coefficients 2 Expected value of loss:

[0109]

[0110] By changing μ 0 Reparameterization is written as ∈ θ To simplify L t-1 , the simplified training target is named L simple , then L simple for:

[0111]

[0112] Among them, x 0 represents the initial value of running, ∈ represents the noise added during the diffusion process, ∈ θ represents the output of the diffusion model, represents the prediction of the noise, represents the cumulative noise proportionality coefficient in the diffusion process, β t represents the diffusion rate at time step t, represents the increase in noise intensity, T represents the total number of diffusion time steps, σ represents the standard deviation of the noise during the diffusion process, and the optimization target L simple It is a weighted mean square error loss function that is used to minimize the difference between the noise predicted by the model and the actual noise. By minimizing this loss, the neural network gradually learns how to generate data points that are closer to the actual distribution.

[0113] After the diffusion model is trained, an initial noise sample is generated from the Gaussian distribution, and the initial noise sample is gradually denoised to generate an initial population that adapts to the current environment.

[0114] Example 5

[0115] The present invention provides a sports performance optimization method based on dynamic multi-objective optimization. Based on Example 1, step 7 preferably includes the following steps:

[0116] Step 7.1: Merge populations and Get the population pop t+1 ;

[0117] Step 7.2: Pick any two points δ in the decision space 1 ,δ 2 , respectively, with δ 1 ,δ 2 Draw a circle S with a fixed length and radius as the center 1 , S 2 , then the areas of the two regions are equal;

[0118] Step 7.3: Calculate the number of cells that fall in area S 1 , S 2 The number of individuals ξ 1 , 2 ;

[0119] Step 7.4: Determine ξ 1 , 2 If the size of 1 > 2 , then according to the hypervolume contribution from region S 1 Delete a certain number of individuals in area S 2The mutation generates the same number of individuals if S 2 If there is no individual in the area, a reference point is generated first, and then mutation is performed until |ξ 1 -ξ 2 |≤1, the specific process is as follows Figure 3 As shown;

[0120] Step 7.5: After local adjustment, the final initial population is obtained This population is used as the input of the MOEA / D algorithm.

[0121] Example 6

[0122] The sports performance optimization method based on dynamic multi-objective optimization provided by the present invention solves the problem of optimal sports performance during running. The specific description is:

[0123]

[0124] f 1 (x,t),f 2 (x,t),f 3 (x, t) represent maximizing running speed, minimizing energy consumption, and minimizing joint burden respectively. The three objectives are transformed into minimization problems, and the function to be optimized is:

[0125] F(x)=max{-f 1 (x),f 2 (x),f 3 (x)} (2)

[0126] Assume that during the running process, as time goes by, the runner's physical condition, environmental conditions, and exercise methods will change. Therefore, the optimization process needs to be adjusted in real time during the running process. Through dynamic multi-objective optimization, a personalized running training plan can be tailored for runners to ensure that they can run with the most appropriate stride, stride frequency, speed, and breathing frequency in different time periods, so as to achieve the best sports performance. This method can not only improve the training effect of runners, but also effectively reduce sports injuries and improve the overall health benefits of running.

[0127] The present invention is mainly aimed at multi-objective optimization problems in dynamic environments, that is, obtaining the optimal solution set under different environments. The difficulty in solving dynamic multi-objective optimization problems lies in how to quickly and accurately detect environmental changes and how to generate a higher quality initial population after the environmental changes. The focus of the present invention on the improvement of the existing method is that it has a profound grasp of this key. The population is divided into two populations using Spearman correlation analysis. A large ρ value indicates that the individual is consistent with the moving direction of the center point during the environmental change. In this case, a linear prediction strategy based on the center point can be used to predict individuals with high correlation. On the contrary, if the ρ value is small, it indicates that the individual is not changing regularly during the environmental change. At this time, it is often more effective to use a diffusion model to capture the changing laws of the environment. After obtaining the population, a local adjustment of the population can maintain the diversity of the environment. In the case of similar environmental changes, a simple and fast adjustment strategy can be adopted to reduce the consumption of computing resources. In the case of severe changes, complex global optimization is performed to reasonably allocate computing resources. The present invention can obtain the optimal solution under different environments, which helps to tailor a personalized running training plan for each runner, ensuring that they can run with the most appropriate cadence, stride, speed and breathing rate in different time periods, so as to achieve the best sports performance. This method can not only improve the training effect of runners, but also effectively reduce sports injuries and improve the overall health benefits of running.

Claims

1. A sports performance optimization method based on dynamic multi-objective optimization, characterized in that: The following steps are involved: Step 1: Parameter initialization; Step 2: Initialize the population Pop, establish the function to be optimized F(x, t) with the maximum running speed, minimum energy consumption, and minimum joint burden as the goals, and calculate the target value F(x, t) of the population Pop; Step 3: Check whether the target value has changed. If it has changed, execute steps 5 to 7; otherwise, execute step 4. Step 4: Use MOEA / D static optimization to obtain the optimal Pareto solution set, and go to step 8; Step 5, divide the population Pop into two sub-populations pop1 and pop2; Step 6: Use the improved linear and diffusion model prediction strategies for populations pop1 and pop2 to generate populations in the new environment and Step 7: Merge populations and Get the population pop t+1 And perform local optimization to obtain the initial population under the new environment and input it into the MOEA / D algorithm, and go to step 4; Step 8: After reaching the maximum number of iterations, output the optimal solution in each environment, that is, the running plan that changes over time.

2. The sports performance optimization method based on dynamic multi-objective optimization according to claim 1, characterized in that: The initialization parameters in step 1 include population size N, dimension D, upper and lower bounds lu of decision variables, target number objNum, and maximum number of iterations FESMAX.

3. The sports performance optimization method based on dynamic multi-objective optimization according to claim 1, characterized in that: The function to be optimized f(X, T) established in step 2 is: F(x,t)=max{-f1(x,t),f2(X,t),f3(x,t)} In the formula, f1(x, t), f2(X, T), and f3(x, t) represent maximizing running speed, minimizing energy consumption, and minimizing joint burden, respectively, and are expressed as: Where t is the running time, and x represents the stride length C, speed S, step frequency SL, and breathing frequency BR during running.

4. The sports performance optimization method based on dynamic multi-objective optimization according to claim 1, characterized in that: The step 4 specifically comprises the following steps: Step 4.1, Initialization: Generate N weight vectors: λ 1 ,λ 2 ,…,λ N ; Generate the initial population: P = {x 1 ,x 2 ,…,x N }; For each weight vector λ i , find its nearest T neighbors; Step 4.2: For each subproblem i∈{1,2,…,N}, randomly select two parent individuals x from the neighbor set. k and x j , perform crossover and mutation operations to generate new offspring individuals y, and calculate the objective function value f(y) of the new individuals; Step 4.3: For each subproblem j∈B(i) in each set, if f(y) is better than the current optimal solution f(x j ), then replace x with y j ; Otherwise, no replacement; Step 4.4, update the external archive and record the non-dominated solution; Step 4.5: Determine whether the termination condition is met. If so, terminate; otherwise, return to step 4.2 to continue iterating.

5. The sports performance optimization method based on dynamic multi-objective optimization according to claim 1, characterized in that: In step 5, the population Pop is divided into two sub-populations pop1 and pop2 using Spearman correlation analysis, which specifically includes the following steps: Step 5.1: Calculate the center point C of the population at time t-1 and t t-1 and C t , and the difference between the center points W0 = C t -C t-1 Considered as variable M in Spearman's coefficient; Step 5.2: For each individual at time t-1 and t, calculate the distance between them and select the individual The closest individual Where t-1 and t represent the t-1th and tth environments respectively, and the difference between the two individuals associated Considered as variable N; Step 5.3: Sort the data of variables M and N to get the ranking and Step 5.4: For each pair of data points and Calculating rank differences in and are the rankings of the i-th observation in variables M and N, respectively, and the ranking difference d i After the calculation is completed, the Spearman correlation coefficient ρ is calculated using the following formula: Step 5.5: According to the calculated ρ value, divide the population Pop into two sub-populations. The sub-population with high correlation is recorded as pop1, and the other sub-population is recorded as pop2.

6. The sports performance optimization method based on dynamic multi-objective optimization according to claim 1, characterized in that: The step 6 specifically comprises the following steps: Step 6.1: Use the improved linear prediction strategy for subpopulation pop1 to generate subpopulations under the new environment The calculation method of the linear prediction strategy is as follows: x t+1 =λΔC t1 +(1-λ)ΔC t2 +x t +Gaussian(0,d) Where, ΔC t1 =C t -C t-1 , ΔC t2 =C t-1 -C t-2 ,λ∈[0,1], used to balance adjacent information and historical information Gaussion(0,d) is a Gaussian noise term, which is used to locally perturb individuals and help them escape from local optimality. Step 6.2: Use the diffusion model prediction strategy for the subpopulation pop2. The diffusion model uses the joint probability distribution p θ (x0)=∫p θ (x 0:T )dx 1:T To approximate the data distribution p0, by introducing the KL divergence D KL , the training objective of the neural network is equivalent to minimizing the variational bound of the negative log-likelihood. The training objective L is simplified to L simple It is expressed as: In the formula, x0 represents the initial value of running; ∈ represents the noise added during the diffusion process; ∈ θ represents the output of the diffusion model, i.e., the prediction of the noise; represents the cumulative noise proportionality coefficient in the diffusion process; β t represents the diffusion rate at time step t, that is, the increase in noise intensity; T represents the total number of diffusion time steps; δ represents the standard deviation of the noise during the diffusion process; After the diffusion model is trained, an initial noise sample is generated from the Gaussian distribution, and the initial noise sample is gradually denoised to generate an initial population that adapts to the current environment.

7. The sports performance optimization method based on dynamic multi-objective optimization according to claim 1, characterized in that: The step 7 specifically includes the following steps: Step 7.1: Merge populations and Get the population pop t+1 ; Step 7.2, randomly select two points δ1 and δ2 in the decision space, and draw circles S1 and S2 with δ1 and δ2 as the center and fixed length as the radius, then the areas of the two regions are equal; Step 7.3, calculate the number of individuals ξ1 and ξ2 falling in areas S1 and S2 respectively; Step 7.4: Determine the size of ξ1 and ξ2. If ξ1>ξ2, delete a certain number of individuals from region S1 according to the hypervolume contribution, and generate the same number of individuals in region S2 by mutation. If there are no individuals in region S2, generate a reference point first, and then mutate until |ξ1-ξ2|≤1. Step 7.5: After local adjustment, the final initial population is obtained The initial population As input to the MOEA / D algorithm.

8. The sports performance optimization method based on dynamic multi-objective optimization according to claim 1, characterized in that: The step 8 is specifically as follows: determining whether the number of fitness evaluations FES is less than the maximum number of iterations FESMAX; if so, proceeding to step 3; otherwise, outputting the optimal solution in each environment, which is a series of personalized running plans that change over time.

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