Optimization study of students’ physical training program in volleyball course based on dynamic planning

As one of the important courses of physical education majors, college volleyball course plays an important role in the cultivation of students’ physical training and teamwork ability [1]. In the teaching of college volleyball, physical training as an important course of basic training is always unremitting. Grasping physical training as an important part of students and grassroots sports training work is the need to build a strong sports country [2]. Adolescents are a key period of physical development, but also a key stage in the development of physical athletic ability, and physical training in this period plays a key role in the healthy development of students and the development level of students’ athletic ability [3]. The growth process of students, different stages of their growth and development laws are different, teachers should be based on the growth and development of different stages of the law, effectively grasp the sensitive period of the students’ qualities, in the physical training, we must carry out scientific and dynamic planning for each student’s characteristics and each of the different periods of development of physical qualities, and the training methods adopted in the training must be in line with the physical and mental development law of the students’ stage, the only way to make the students physical fitness to get better. Only in this way can students get better physical performance. At the same time, we must also adhere to the physical training and special training, so as to make the physical level more targeted, and lay a solid foundation for future training [4-7].

Volleyball is a sport that has exploded in a very short period of time, and it is a technical and specialized sport with high requirements for students’ physical quality, such as athletic endurance, bouncing power, body coordination, and body reaction ability [8-9]. Therefore, in the usual sports training, in addition to the students’ technical training, tactical training and other than psychological training, physical training is obviously the most important, the students’ physical quality and psychological quality is a key factor in determining the success or failure of the game. Volleyball is not just a simple team type program, it is a skill sport mainly characterized by physical class, student physical fitness is reflected in the athletes’ technical and tactical level from the micro level [10-11]. Macroscopically, students’ physical fitness determines the success or failure of the game. Therefore, a strong physical strength and technique are needed to win the game. Without good physical fitness, it is impossible to perform skillful techniques and tactics, and without high level of physical training, one cannot become an excellent coach and athlete. In addition, good physical fitness is also necessary to study complex, high-level techniques and tactics [12-14].

Physical fitness essentially specializes in the basic mobility associated with physical fitness and the basic mobility associated with the completion of athletic movements. Physical fitness training is the process of developing physical fitness and athletic ability through purposeful physical exercises [15-16]. In volleyball programs, physical fitness plays a pivotal role in the physical quality of students as the material basis for the improvement of their athletic level. Scientific research has shown that factors such as the ability, function and structure of the athlete’s organism in the process of movement are the main basis for athletes to achieve excellent results. Physical quality plays an important role in students’ competitive level, especially maximum strength, speed, endurance, sensitivity, flexibility, etc., which directly determines students’ tactical level and athletic performance in sports competitions. Therefore, optimizing students’ physical training programs is of great significance to the development of students’ volleyball competitive level [17-20].

Based on the physical training program for students in college volleyball courses, this paper determines the research hypotheses and research variables, establishes a dynamic planning model based on binary coding, and also combines the training time arranged by the school and the training requirements of the school to obtain the constraints of the dynamic planning model. According to the principle of genetic algorithm, the optimal solution problem of the model in this paper is defined as a mathematical function model containing 8 elements, and a series of pre-processing is carried out on the model, and when the iterative training of the model meets the maximization iteration condition, the adaptation of its output is the optimal solution of the model. The corresponding algorithm parameters, experimental platform and research subjects are determined, and the optimal solution of the model and its application effect analysis are jointly explored with the help of the experimental platform and physical training test apparatus.

2

A dynamic planning model for physical training

2.1

Overview of genetic algorithms

This section will provide an overall overview of the basic principles and application process of genetic algorithms in terms of fundamentals, terminology and basic operations.

2.1.1

Basic principles of genetic algorithms

The genetic algorithm process is shown in Fig. 1.The basic principle of genetic algorithm is similar to the principle of natural evolution of organisms, specifically the genetic variation of the genome, the natural selection of individuals, and the superiority and inferiority of the population [21-22]. A population, a result is considered as an individual in the population. Each individual in the population is then encoded with 0 and 1 according to certain rules [23]. The string of 0 and 1 represents the genome of each individual, and then on this basis, simulate the process of biological evolution in nature, perform reproduction, crossover, mutation and other operations, “reproduce” on the basis of the original individual to produce new individuals, and according to the evaluation function to filter out the results of the new individuals with a lower value of the evaluation function, and retain the results with a higher value of the evaluation function, and retain the results with a higher value of the evaluation function. According to the evaluation function, individuals with lower evaluation function values will be screened out, and individuals with higher evaluation function values will be retained, thus completing the evolution of the population. Then a new round of evolution is started on the basis of the new population. In this way, each round of evolution results in the original population based on the higher value of the evaluation function of the population, that is, the model is getting closer and closer to the optimal solution, and ultimately can be “evolved” to get a relatively satisfactory model results.

The basic process of a genetic algorithm is:

1) Initialize the population.

2) Calculate the fitness value of each individual in the population.

3) Evaluate the fitness of individuals, and those with higher fitness values will retain their characteristics and enter the next round of evolution.

4) Perform crossover operation according to the probability Pc.

5) Perform mutation operation according to the probability Pm.

6) If the stopping condition set by the calculation is not reached, return to step 2, otherwise execute step 7.

7) Output the chromosome with the optimal fitness value in the population as a satisfactory or optimal solution to the problem.

2.1.2

Basic terminology of genetic algorithms

Before the genetic algorithm is practiced it is necessary to determine the initial population, choose the appropriate population coding method, and select the appropriate fitness function according to the research problem.In this section, some basic terms and the main work of the genetic algorithm will be introduced.

1)

Population

Genetic algorithm needs to be performed based on a certain population. Therefore, before starting to perform genetic operations, the initial population of the research problem needs to be determined. At the same time, in order to ensure the randomness of the model solution as much as possible, the initial population is generally generated randomly by a certain probability. In practice, depending on the number of individuals in the population, the population of the research problem can be divided into different sizes. Generally speaking, the population size is a constant number, but the selection of the population size should take into account the computational cost and model accuracy, and each solution in the population will be affected by the selection, crossover, mutation and other steps to increase the “adaptability” of the solution. In general, the larger the value of the population size, the broader its representation in all populations, so it is more likely to get or close to one of the optimal solutions in the process of model optimization.

2)

Coding

The coding work converts the potential solution into a representation that can be manipulated by the algorithm, and is also an important work that needs to be done before the implementation of the genetic algorithm, because the genetic operation is not for all the parameters to be processed, but for the parameters after coding, and to a large extent, it will have a direct impact on the scope of the search of the solution space and the efficiency. To put it simply, for an intelligent optimization problem with known control variables and objective function, genetic operation cannot be carried out directly on the variables, i.e., the variables are directly brought into the genetic operation, but the variables need to be encoded, i.e., they are transformed into a finite-length number string consisting of different numbers according to a certain encoding method, which is easy to be accepted by the genetic operation. Therefore, it can be seen that the choice of coding method for the execution of genetic operation has a very close relationship, not only related to whether the genetic operation can be carried out, but also affect the results of parameter optimization. Regarding the choice of coding method, the following principles need to be satisfied: first, the coding method needs to be able to represent all feasible solutions in the solution space, i.e., each feasible solution has its corresponding coding method in the coding space. Secondly, the coding space must be complete and there must be no gaps.Third, the encoding mode and feasible solutions need to correspond sequentially.

3)

Fitness function

The fitness function is a function used to evaluate the fitness of each individual in the population in the evolutionary process of the genetic algorithm, which can reflect the level of individual strengths and weaknesses, and to a certain extent, its value determines the “fitness” of each solution, which determines the possibility of the solution to be affected by the selection, crossover, mutation and other steps, which is very important for the search for optimal solutions. It is very important to find the optimal solution.Therefore, the fitness function is strongly related to the objective function of the optimization problem to be solved, and the latter may be transformed into the former. The fitness function is chosen as the basis for evaluating the fitness of individuals rather than the objective function because the fitness function is the key basis for the genetic algorithm to perform the genetic operation, which only evaluates the individuals in the population and does not need to search for other information in the solution space. In the solution process of genetic algorithms, the choice of fitness function is crucial. On the one hand, the fitness function evaluates the strengths and weaknesses of individuals to carry out the survival of the fittest, so as to retain the better individuals and eliminate the inferior ones, and then continuously approach the optimal solution, only by choosing the appropriate fitness function can an optimal solution be obtained in the end. On the other hand, different fitness functions have different ways of evaluating the level of feasible solutions, which directly affects the convergence speed and solution time of the model.

2.1.3

Basic operation procedure of genetic algorithm

The genetic algorithm has three basic operations in the process of operation implementation: selection operation, crossover operation, and mutation operation.

1)

Selection operation

Selection operation is to select high-quality individuals from the population to enter the next round of evolution, and eliminate the poor quality individuals in the current round of evolution, so as to realize the inheritance of “high-quality genes”, improve the overall fitness function of the population, so as to make the existing feasible solutions on the basis of the original closer to the target optimal solution.

2)

Crossover operation

The process of crossover operation is similar to the genetic recombination process in biological reproduction, i.e., some genes of individuals in the population are crossed and interchanged, which is also called recombination operation, so as to produce new individuals to enter the next round of evolution. In the crossover operation, the key step lies in the ability to select the appropriate crossover operator, and the commonly used selection method is single-point crossover.

3)

Mutation operation

If the genetic operation relies only on selection and crossover operations without other operations, the range of new individuals obtained is limited.Inspired by gene mutation in the field of biological evolution, the introduction of mutation operations has also become an important operation in genetic algorithms.Specifically, the mutation operation involves making a small change to the genes of individuals in the current population, which in turn generates a new genetic composition and creates new individuals.

2.2

Basic assumptions and notation

2.2.1

Basic assumptions

Hypothesis 1: There is no malfunctioning of instruments during volleyball physical training.

Hypothesis 2: There is no human factor affecting the training process during volleyball physical training.

Hypothesis 3: The same kind of training equipment is fully operational during the volleyball physical training.

Hypothesis 4: All students complete the training in one go during the volleyball physical fitness training without reworking.

Hypothesis 5: The students to be trained completely obey the school’s arrangement.

Hypothesis 6: The waiting time for the students to be trained starts from the time they enter the volleyball fitness training field.

Hypothesis 7: The staff of volleyball physical training will not be counted in the total capacity of the venue.

Hypothesis 8: The “first-come, first-served” principle is met during the volleyball fitness training.

2.2.2

Description of main variable symbols

s_k denotes the number of students who accessed the Volleyball Physical Training site during Phase k.

y_k indicates the number of students who entered the volleyball fitness program in phase k.

x_k indicates the number of people who ended up at the volleyball physical training site in phase k.

T_k-1(s) indicates the time taken to complete all physical training programs from the start of training to the end of phase k.

$T_{k - 1}^{*} (s_{k - 1})$ indicates the time taken to complete all training programs from the start of training to the end of phase k − 1.

T_k(s_k,x_k) indicates the time taken to complete all training programs at the end of Phase k with x_k people.

n₀ indicates the maximum capacity of the training site.

N indicates the total number of people trained.

a_j indicates the number of people in class j.

A_ij indicates whether the jth class of the ith phase enters the training ground, if it enters the training ground A_ij = 1, otherwise A_ij = 0.

2.3

Model construction and solution

2.3.1

Construction of dynamic planning models

In the school, the students were given physical training in five events: height and weight, standing long jump, lung capacity, grip strength, and step test. A total of 2325 students from 48 classes in the school participated, and the number of students in each class is shown in Table 1. Where i denotes the class number and C_i denotes the number of students participating in the test in class i. From the table, it can be seen that the number of students in each class is distributed in the interval of 40-55.

Table 1.

The number of classes

i	1	2	3	4	5	6	7	8	9	10	11	12
C_i	54	43	45	50	54	54	54	53	41	52	51	54
i	13	14	15	16	17	18	19	20	21	22	23	24
C_i	52	45	41	52	49	42	42	41	55	49	49	41
i	25	26	27	28	29	30	31	32	33	34	35	36
C_i	43	46	48	48	49	49	53	54	44	50	44	43
i	37	38	39	40	41	42	43	44	45	46	47	48
C_i	51	43	46	51	48	55	49	44	53	45	53	53

The configuration of the training instruments owned by the school and the average training time of each instrument are shown in Table 2, where i indicates the program number of physical training, j indicates the number of sets of the same program, D_i indicates the average training time of each student in the program, and D₀ indicates the time of entering the student number, which is automatically shifted back by one after each student has finished the measurement. Every day 8:00~12:00 and 14:00~16:45 are the training time arranged by the school. The training place is an indoor sports ground with a maximum capacity of 220 students. The school’s training requirement is that all students in the same class complete all training programs within the same time period, and the training programs are not prioritized in any way.The waiting time of students should be minimized as much as possible while minimizing the number of time slots required for the entire training. Give a clear and intuitive optimization algorithm for this training problem and solve it.

Table 2.

Test instrument configuration and average test time

Project	Entry	Height and weight	Fixed jump	Lung capacity	Holding strength	Step Training
D_ij	D₀	D₁₁, D₁₂, D₁₃	D₂₁	D₃₁	D₄₁, D₄₂	D₅₁, D₅₂
Training time	5	20, 20, 20	40	40	30, 30	205, 205

The analysis of the data in Tables 1 and 2 yielded the following constraints and objective functions for building the mathematical model: First, the model assumption that “students in non-training classes do not show up at the training site when they are not on a training assignment” was met by accurately evaluating the training time of the students. Second, in order to minimize the time required for entry, students were arranged to enter the training site in order as much as possible. Third, because the step training is the most time-consuming, in order to effectively reduce the time required for step training, we adopt the class as a unit of five people to arrange other training programs and equipment, in order to make the training process smooth and non-obstructive, we designed two training processes, the training program is shown in Figure 2.

To summarize: generalize to the general process schedule X_ij, i denotes 8 different time slots for process 1 (i takes 1, 3, 5, 7), process 2 (i takes 2, 4, 6, 8), and i denotes the class number scheduled in the corresponding time slot. Build the following 0 to 1 integer planning model: (1) $X_{i j} = {\begin{array}{l} 1, Arrange class j in the corresponding process of the time period \\ 0, The corresponding process of not scheduling the j shift in the time period \end{array}$ $${X_{ij}} = \{ \matrix{ {1,{\rm{Arrange}}\,{\rm{class}}\,j\,{\rm{in}}\,{\rm{the}}\,{\rm{corresponding}}\,{\rm{process}}\,{\rm{of}}\,{\rm{the}}\,{\rm{time}}\,{\rm{period}}} \hfill \cr {0,{\rm{The}}\,{\rm{corresponding}}\,{\rm{process}}\,{\rm{of}}\,{\rm{not}}\,{\rm{scheduling}}\,{\rm{the}}\,j\,{\rm{shift}}\,{\rm{in}}\,\,{\rm{the}}\,\,{\rm{time}}\,\,{\rm{period}}} \hfill \cr } $$

Seeking the Best Arrangement Process X_ij makes: (2) $S_{o p t} (X_{i j}) = \min [\sum_{i = 1}^{8} (205 i n t (\frac{\sum_{j = 1}^{48} c_{j} x_{i j}}{5}) + \sum_{j = 1}^{48} 5 X_{i j})]$ (3) $S . t S_{2} = \sum_{i = 1}^{8} (\sum_{j = 1}^{48} 5 X_{i j})$

The time used for the bench test was: (4) $S_{1} = \sum_{i = 1}^{8} (205 i n t (\sum_{j = 1}^{48} C_{j} X_{i j} / 5))$

The time required to record the breast for the step test is: (5) $S_{2} = \sum_{i = 1}^{0} (\sum_{j = 1}^{48} 5 X_{i j})$

Revise equation (1) as: (6) $S_{o p t} (X *_{i j}) = \min [\sum_{i = 1}^{3} ((\sum_{j = 1}^{48} X_{i j} * C_{j} / 5) * 205) + \sum_{i = 1}^{8} (\sum_{j = 1}^{48} X_{i j} * 5)]$

2.3.2

Solving the model

1)

Structural components

Solving an optimization problem with a genetic algorithm can be defined as a function model with 8 elements: (7) $S G A = (C, f, P_{0}, N, S, p_{c}, p_{m}, T)$

In Eq. 7, C is the coding method, f is the fitness function, P₀ is the initial population, N is the population size, S is the selection operation, p_c is the crossover operation, p_m is the mutation operation, and T is the algorithm stopping condition.

2)

Minimum length coding

Aiming at the problems of low search efficiency and discrete error caused by too long or too short coding length, this paper adopts a minimum coding length based on the value interval of the decision variable and the solution accuracy. For one-dimensional decision variable x, [a,b] is the value interval, c is the solution accuracy, then the minimum coding length L is: (8) $L = ⌈ \log_{2} \frac{(b - a)}{10^{- c}} ⌉$

For a n-dimensional optimization problem, the individual coding length is equal to the sum of the coding lengths of the decision variables in each dimension. Individual coding length L is: (9) $L^{'} = \sum_{i = 1}^{n} L_{i}$

3)

Population initialization

The uniform interval method first distributes the value space of the decision variable equally according to the number of individuals in the population N, thus obtaining N uniform sub-intervals, and then generates an initial individual in each sub-interval in a randomized manner. For a one-dimensional decision variable, the width d of the subintervals is: (10) $d = \frac{M}{N}$ where M is the variable value space and N is the number of individuals in the population.

For the n-dimensional optimization problem, the width of each one-dimensional interval d is: (11) $d = \sqrt[n]{\frac{M}{N}}$ where n is the number of dimensions.

The initial population distributions obtained by the three methods are shown in Fig. 3, where (a)~(c) denote the traditional random method, Logistic chaotic mapping method, and uniform interval method, respectively. From Figs. 3(a) and 3(b), it can be seen that the traditional random method and Logistic chaotic mapping method have randomness, and the operation by crossover and mutation does not jump out of the local optimum well, and it is easy to converge to the local optimum solution in the evolutionary process, so both methods do not improve the nature of the distribution of the initial population. In Fig. 3(c), on the other hand, the distribution of the initial population of the uniform interval method is very uniform and stable, so that the population maintains a high degree of richness, which greatly enhances the possibility of the algorithm to converge to the global optimal solution.

4)

Selection method

In this paper, we adopt a selection strategy that combines an optimal preservation strategy with a parent-child competition mechanism. Although roulette makes the better individuals inherited to the next generation with a greater probability, the optimal individuals may still be missed, so the optimal preservation strategy is adopted so that the optimal individuals of the population can directly enter the next generation cycle without genetic manipulation, so that the evolutionary trend is toward the global optimum.

5)

Adaptive crossover and mutation operators

In this paper, we propose a crossover and variation operator that is adaptively adjusted according to the degree of population dispersion. The operator measures the degree of population dispersion in terms of three dimensions: the minimum fitness of the population f_min, the maximum fitness f_max, and the average fitness f_avg. p_c and p_m are specifically defined as: (12) $p_{c} = {\begin{matrix} (p_{c 1} - p_{c 2}) (1 - \frac{f_{min}}{f_{max}}) + p_{c 2} & \frac{f_{avg}}{f_{max}} > a, \frac{f_{min}}{f_{max}} > b \\ p_{c 1} & o t h e r \end{matrix}$ (13) $p_{m} = {\begin{matrix} (p_{m 1} - p_{m 2}) \frac{f_{\min}}{f_{\max}} + p_{m 2} & \frac{f_{\max}}{f_{\max}} > a, \frac{f_{\min}}{f_{\max}} > b \\ p_{m 2} & o t h e r \end{matrix}$ where P_ò1 ~ P_ò2 ~ P_m1 ~ P_m2 is an adjustment constant and P_ò1 > P_ò2 ~ P_m1 > P_m2, parameter 0.5 < a < 1, parameter 0 < b < 1.

6)

Adaptation function

Sequential transformation of the original fitness function to obtain f ', the construction method is to target two values of the descending order and the arranged individuals in accordance with the mapping relationship to calculate the corresponding fitness value. The sequential transformation of f is obtained as: (14) $f_{i} = \frac{n - i + 1}{n}, i = 1, 2, \dots, n$ where i is the nd individual of the population in order of preference. n is the population size.

In the second step, the final fitness function f is obtained by adaptively transforming f ' obtained in the first step. The final fitness function f obtained by adaptive transformation is: (15) $f_{i} = | f_{i}^{'} - \bar{f} |, i = 1, 2, \dots, n$

Among them: (16) $\bar{f} = α (f_{max}^{'} - f_{min}^{'}) + f_{min}^{'}$ (17) $α = α_{max} - \frac{t}{T} (α_{max} - α_{min})$ (18) ${f^{'}}_{\min} = \min {{f^{'}}_{i}}, i = 1, 2, \dots, n$ (19) ${f^{'}}_{\max} = \max {{f^{'}}_{i}}, i = 1, 2, \dots, n$ where t is the number of contemporary evolutionary generations. T is the maximum number of evolutionary generations. α is the adjustment factor n is the population size.

7)

Algorithm solution

Transform the three constraints in Eqs. (2) to (4): since $Σ_{i = 1}^{n} X_{i j} = 1, X_{i j} = 1, 2, ...8$ can be viewed as a 3-bit binary number Y_j, encode X_ij as a 168-bit binary code. The other two sets of constraints are transformed using the penalty function: $Σ_{i = 1}^{56} C_{j} X_{i j} \leq 348$ can be transformed into an equation with a penalty factor λ_o: (20) $λ_{ϵ} {m a x [(0, Σ_{j = 1}^{48} C_{j} X_{i j}) - 205]}^{2}$

Eq. (15) can be reduced to: (21) $\begin{matrix} S_{apt} = \min [\sum_{i = 1}^{e} ((205 \sum_{j = 1}^{48} \frac{c_{j} x_{i j}}{5}) + \sum_{j = 1}^{48} X_{i j}) \\ + Σ_{ex 1.2.5.}, λ_{e} {^{m a x [(0, \sum_{j = 1}^{48} C_{j} X_{i j}) - 348]} 2} \\ + Σ_{i = 2, i . i . i . 0} λ_{i} {m a x [(0, \sum_{j = 1}^{48} C_{j} X_{i j}) - 269]}^{2}] \end{matrix}$ $$\matrix{ {{S_{{\rm{apt}}}} = \min [\mathop \sum \limits_{i = 1}^{\rm{e}} \left( {\left( {205\mathop \sum \limits_{j = 1}^{48} {{{c_j}{x_{ij}}} \over 5}} \right) + \mathop \sum \limits_{j = 1}^{48} {X_{ij}}} \right)} \cr { + {\Sigma _{{\rm{ex}}1.2.5.}},{\lambda _{\rm{e}}}{{\left\{ {max[(0,\mathop \sum \limits_{j = 1}^{48} {C_j}{X_{ij}}) - 348]} \right\}}^2}} \cr { + {\Sigma _{i = 2,\,i.\,i.\,i.\,0}}{\lambda _i}{{\left\{ {max[(0,\mathop \sum \limits_{j = 1}^{48} {C_j}{X_{ij}}) - 269]} \right\}}^2}]} \cr } $$ Eq. (21) was solved using the Genetic Algorithm tool in the Matlab toolbox.

3

Model solving and application effect analysis

3.1

Analysis of Dynamic Programming Model Solution

3.1.1

Experimental environment

The experimental environment of this paper is: processor 11th Gen Intel(R) Core(TM) i5-1135G7, MATLAB R2022b simulation platform, and the following four parameters are included in the process of solving the dynamic planning model using genetic algorithm:

1) Population size N=100.

2) Crossover probability P_c = 0.08.

3) Mutation probability P_m=0.04.

4) The number of iterations are 100, 200, 300, 400, and 500.

3.1.2

Algorithm evaluation

In this subsection, Table 1 and Table 2 are used as the experimental data to complete the dynamic planning scheme for volleyball course physical training. According to the study of volleyball course physical training, two kinds of dynamic planning model solution methods, conventional method and genetic algorithm, are used respectively, and the two solution methods are evaluated and analyzed by using the MATLAB R2022b simulation platform mentioned in subsection 3.1.1, and the evaluation items contain the number of iterations and the maximum operation time, the number of iterations and the minimum operation time, the number of iterations and the average running time, the number of occurrence of the the number of times of better eigenvalues. The results of the algorithm training evaluation are shown in Fig. 4, where (a) to (d) are the maximum operation time, the minimum operation time, the average running time, and the number of times the better eigenvalues appear, respectively. Comparison in terms of running time reveals that the maximum running time of the traditional algorithm is much larger than the maximum running time of the genetic algorithm as the number of runs increases, while the minimum running time of the genetic algorithm is smaller than that of the traditional algorithm, not to mention the average running speed. Therefore, the genetic algorithm has a greater advantage than the traditional algorithm in terms of faster running speed and shorter running time. Analyzing from the aspect of the number of times the eigenvalues appear, when the number of populations is constant, the number of times the two algorithms appear to have better eigenvalues (later used as eigenvalues) is expressed to be proportional to the number of iterations, i.e., as the number of times the algorithms are run increases, the eigenvalues also increase. In the case of the traditional algorithm, after 300 runs, the eigenvalues did not go up and down. In the genetic algorithm, the eigenvalues do not fluctuate up and down until after 400 runs. It can be seen that the genetic algorithm is more effective in solving the dynamic planning model for volleyball class physical training. The optimal grouping conditions and the optimal results are as follows: for different time periods, the total number of people in each process is 348, 348, 269, 269, 348, 348, 33, 33, and the results are converted into the training schedule, and the classes to be trained only need to enter the training site at the predetermined time and designate the flow of the training program (Fig. 2), that is, they can complete the entire physical training in the shortest possible time, thus realizing the physical training of students. The program ensures that students’ physical training is arranged optimally.

3.2

Analysis of the effect of model application

3.2.1

Objects of study

To verify the optimization effect of physical training in volleyball course based on dynamic programming. This subsection additionally selected 40 students (20 males and 20 females) in the class of 2022 of an undergraduate university, aged 18-21 years old, of which the average height of male students is 172.5 cm and weight 65.3 kg. Female students have an average height of 162 cm and weight of 50.5 kg, and the data studied here does not conflict with the data studied above.

3.2.2

Data acquisition

The cardiopulmonary function of the students after the physical training of the volleyball course was comparatively tested using the TJY-1 high-precision digital display electronic step test tester and the RCS-10000 high-precision digital display electronic spirometer, respectively, and the corresponding cardiopulmonary function data were obtained.

3.2.3

Experimental results

The author used the cardiac function and pulmonary function tester respectively to measure the step test and lung capacity experimental indexes under two teaching training modes (mode 1 is the conventional mode, mode 2 is the dynamic planning program of physical training in this paper) for 40 students (20 males and 20 females) in the class of 2022 of an undergraduate college, and the results of the male and female comparative tests are shown in Table 3 and Table 4. The results show that after applying the dynamic planning program of physical training, the physical fitness indexes after training are significantly better than the traditional teaching and training methods (in terms of male students, the difference between the mean values of the step test indexes: 1.495, the difference between the mean values of the lung capacity experimental indexes: 266, and the same for female students), which shows that the method has obvious effects on enhancing the physical fitness (cardiorespiratory fitness) of the college students, and has practical significance for improving the physical fitness and health of college students. It is of practical significance to improve the physical health of college students. In addition, it can also be seen that the method of applying dynamic planning to optimize the design of college students’ physical training elements has practical value for improving college students’ physical fitness, and it is an objective, effective, and rapid teaching and training method, which can be easily extended to other physical education teaching and training programs, and thus puts forward a new teaching and training mode of enhancing college students’ physical fitness and health from a new perspective.

Table 3.

Comparison of male experimental index

Student	Step test index		Lung capacity test index
Student	Mode 1	Mode 2	Mode 1	Mode 2
1	57.6	59.1	3755	4022
2	49.8	51	4721	4809
3	48.3	50.5	4096	4199
4	48.6	51.4	3603	4319
5	56.9	57.2	4149	4949
6	52.5	54.4	4903	4648
7	56.1	57.3	4399	3950
8	57.2	59.1	4718	4849
9	62.3	63.1	3802	4117
10	54.1	54.9	4932	5001
11	61.2	63.7	4601	4852
12	53.9	54.8	4120	4580
13	53.7	55	4203	4851
14	59.1	60.8	4705	4428
15	43.3	46.1	4203	4375
16	55.1	55.1	3900	4465
17	56.4	57.3	4245	4433
18	52.3	55	3796	4300
19	53	53.4	3297	3974
20	62.4	64.5	3901	4248

Table 4.

Comparison of female experimental index

Student	Step test index		Lung capacity test index
Student	Mode 1	Mode 2	Mode 1	Mode 2
1	57.2	57.8	3249	3314
2	53.3	55.1	3298	3452
3	50.4	53.5	3050	3190
4	50.5	53.6	2752	2982
5	52.9	55.6	3501	3627
6	53.1	54.8	3091	3274
7	52.4	53.7	3015	3337
8	51.5	54	3049	3282
9	52.3	53.8	2956	3215
10	52.4	53.7	3195	3344
11	51	52.4	2904	3280
12	59.5	60.5	3386	3431
13	54.7	57.6	2948	3173
14	50	53.7	2556	2854
15	56.2	58.4	2386	2794
16	53.5	55.7	3519	3662
17	53.2	55.1	3214	3434
18	43.1	48.2	3248	3352
19	53.8	56.6	2583	2751
20	55.9	57.1	3211	3430

4

Conclusion

Although the traditional method can meet basic physical training requirements, there is a lack of an optimized physical training model to further improve the physical teaching and training effects of college students. In this paper, we construct an optimization model for students’ physical training programs based on dynamic planning and use genetic algorithms to find the optimal solution. From the point of view of the number of better eigenvalues, the traditional algorithm has no up and down fluctuations in its eigenvalues after 300 iterations, while the algorithm in this paper runs to 400 iterations before the eigenvalues do not have up and down fluctuations, which indicates that this paper’s algorithm is more effective in solving the problem. In addition, with the help of the genetic algorithm tool in the toolbox of the MATLAB R2022b simulation platform to solve the optimization model, it is concluded that the total number of people arranged in each process is 348, 348, 269, 269, 348, 348, 33, and 33 in different time periods, respectively, which can achieve the optimal arrangement of students’ physical training. Applying the dynamic planning program for physical training results in a significantly better physical performance index after training compared to traditional teaching and training methods. The study’s effectiveness and practicality are fully demonstrated in this document.

Sprache:: Englisch

Zeitrahmen der Veröffentlichung:: 1 Hefte pro Jahr
Fachgebiete der Zeitschrift:: Biologie, Biologie, andere, Mathematik, Angewandte Mathematik, Mathematik, Allgemeines, Physik, Physik, andere

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Optimization study of students’ physical training program in volleyball course based on dynamic planning

Xiaofan Hao

Mingfei Xiao

Songbo Chen

Online veröffentlicht: 17. März 2025

Eingereicht: 25. Okt. 2024

Akzeptiert: 08. Feb. 2025

DOI: https://doi.org/10.2478/amns-2025-0290

SchlüsselwörterGenetic algorithm, Dynamic programming model, Optimal solution, Physical fitness training

© 2025 Xiaofan Hao et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Schlüsselwörter
Genetic algorithm, Dynamic programming model, Optimal solution, Physical fitness training

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