Application and optimization of adaptive genetic algorithm in fencing training load prediction: a data visualization-based analytical approach

The AGA represents an evolution of the traditional GA, specifically designed to enhance adaptability across different evolutionary stages. This improvement is achieved through dynamic adjustments of key parameters, such as crossover and mutation rates, which address common limitations observed in traditional GAs, including premature convergence to local optima and slow convergence speeds. The core implementation process of AGA retains structural similarities with traditional GAs, encompassing several fundamental steps as outlined in Table 1:

The AGA enhances performance across different evolutionary stages through dynamic adjustments of the crossover and mutation rates, thereby adapting to varying optimization phases. In the initial evolutionary stages, a higher crossover rate facilitates a broad exploration of the solution space, strengthening global search capabilities and accelerating the discovery of diverse potential solutions. As the algorithm progresses towards later stages, the crossover rate is gradually reduced to minimize disruptions to high-quality individuals, thereby enhancing local search precision and convergence stability17,18,19. The dynamic adjustment of the crossover rate is expressed by Eq. (1):

In Eq. (1), \(\:{\varvec{P}}_{\varvec{c}\varvec{m}\varvec{a}\varvec{x}}\) and \(\:{\varvec{P}}_{\varvec{c}\varvec{m}\varvec{i}\varvec{n}}\) represent the maximum and minimum crossover rates, respectively. The variable \(\:\varvec{t}\) denotes the current iteration number, while \(\:\varvec{T}\) refers to the maximum number of iterations. The crossover rate \(\:{\varvec{P}}_{\varvec{c}}\) dynamically decreases as the number of iterations increases, promoting a gradual transition from global exploration to local exploitation. The mutation rate is also dynamically adjusted to maintain a balance between population diversity and convergence speed. In scenarios where population diversity is low, an elevated mutation rate is introduced to prevent premature convergence to local optima, thereby sustaining the algorithm’s exploratory capacity. As the population approaches convergence and diversity decreases further, the mutation rate is progressively reduced to stabilize solution quality and prevent unnecessary perturbations. The dynamic adjustment of the mutation rate is defined by Eq. (2):

In Eq. (2), \(\:{\varvec{P}}_{\varvec{m}\varvec{a}\varvec{x}}\) and \(\:{\varvec{P}}_{\varvec{m}\varvec{i}\varvec{n}}\) denote the maximum and minimum mutation rates, respectively, while \(\:\varvec{D}\) represents the population diversity, calculated based on genetic variation within the population. The parameter \(\:\varvec{\alpha\:}\) serves as a control factor, regulating the sensitivity of the mutation rate to fluctuations in diversity. This dynamic adjustment mechanism ensures that the mutation rate remains adaptive to the evolving characteristics of the population, promoting both diversity maintenance and convergence efficiency. To mitigate the risk of generating low-quality initial populations, heuristic methods are utilized to produce a subset of individuals with enhanced distribution quality. This approach ensures that the initial solutions are more diverse and representative of the broader solution space, thereby improving the algorithm’s overall search efficiency from the outset. Additionally, during each iteration, the current optimal solution is directly retained in the next generation. This elitism strategy safeguards high-quality solutions from being lost due to stochastic genetic operations, thereby maintaining solution stability across generations20,21,22. Real-time monitoring of the population’s genetic diversity is implemented to track the evolutionary process. When diversity metrics fall below a predefined threshold, indicating a risk of premature convergence, mutation operations are intensified to introduce greater variability. Alternatively, new individuals are introduced to the population to rejuvenate genetic diversity, thereby sustaining the algorithm’s exploration capability.

The AGA improved global search capability and accelerated convergence by dynamically adjusting crossover and mutation rates, incorporating optimized fitness functions, and applying diversity control strategies. These methodological enhancements provide a solid basis for subsequent experiments, particularly in predicting fencing training load, where capturing complex and dynamic patterns is essential23.

Optimization of the AGA

Improving the efficiency and performance of the AGA in predicting fencing training load involved optimizing key algorithmic components, including the fitness function, crossover and mutation strategies, and both convergence speed and global search capability.

The fitness function serves as the core mechanism for evaluating individual solution quality within the genetic algorithm framework. Traditional fitness functions often exhibit limitations in capturing the complexities of nonlinear optimization problems, leading to premature convergence toward local optima. To address this issue, the fitness function is optimized through the introduction of a dynamic fitness weighting mechanism, which adjusts weight coefficients in response to problem-specific characteristics:

In Eq. (3), \(\:\varvec{F}\left(\varvec{i}\right)\) represents the fitness function, \(\:{\varvec{\omega\:}}_{1}\) and \(\:{\varvec{\omega\:}}_{2}\) are dynamically adjusted weighting coefficients, and \(\:{\varvec{f}}_{1}\left(\varvec{i}\right)\) and \(\:{\varvec{f}}_{2}\left(\varvec{i}\right)\) denote objective functions reflecting different performance metrics. The adjustment of weights is guided by the evolutionary stage of the algorithm and the observed trends in objective function performance. To further mitigate premature convergence, a penalty factor is incorporated into the fitness evaluation, reducing the fitness of individuals that violate predefined constraints. This approach promotes a more directed optimization process, enhancing the algorithm’s capacity to explore feasible regions of the solution space effectively24.

Crossover and mutation operations are critical to generating new solutions and maintaining genetic diversity within the population. The crossover rate is dynamically modulated based on the fitness of individual solutions to balance exploration and exploitation effectively:

In Eq. (4), \(\:{\varvec{F}}_{\varvec{a}\varvec{v}\varvec{g}}\) represents the average fitness of the population, \(\:{\varvec{P}}_{\varvec{c}}\left(\varvec{i}\right)\) denotes the dynamically adjusted crossover probability for the -th individual.

To complement the crossover strategy, a non-uniform mutation operation is introduced. The mutation probability decreases gradually as the algorithm progresses, allowing for more aggressive exploration in the early stages and refined local searches in later iterations:

Enhancing population diversity and preventing premature convergence are critical objectives in optimizing the AGA. To achieve these goals, the number of crossover and mutation points is increased, while elite individuals are retained to preserve high-quality solutions. Addressing the challenges of slow convergence and susceptibility to local optima, the individual with the highest fitness is directly preserved during each iteration. This elite retention strategy ensures that the optimal solution is not lost and improves the stability of algorithm convergence. To enhance local search precision without compromising global search capabilities, local search algorithms such as simulated annealing and particle swarm optimization are integrated into the genetic algorithm framework. This hybrid approach leverages the global exploration strength of the genetic algorithm and the fine-tuning capabilities of local search methods. Additionally, parallel computing techniques are employed to accelerate the evaluation of populations, as well as crossover and mutation operations, thereby significantly reducing the algorithm’s runtime and improving computational efficiency. The key features of the optimized algorithm are summarized in Table 2.

Through the optimization of the fitness function, crossover and mutation strategies, and improvements in convergence speed and global search capability, the performance of the AGA in predicting fencing training load is significantly enhanced. These optimizations strengthen the algorithm’s search capabilities, improve adaptability to complex nonlinear problems, and establish a robust foundation for subsequent experimental validation and practical applications.

Experimental design

The dataset used in this experiment was the Daily and Sports Activities Dataset, which includes data from 19 distinct daily and sports activities performed by eight participants (four females and four males) aged 20 to 30 years. Each activity lasted five minutes and was segmented into five-second intervals, resulting in 480 signal segments per activity. The recorded activities included sitting, standing, lying down, stair climbing (ascending and descending), remaining stationary or moving within an elevator, walking in a parking lot, walking and running on a treadmill, and using various fitness equipment. The dataset is publicly available at: https://archive.ics.uci.edu/dataset/256/daily+and+sports+activities.

Although the Daily and Sports Activities Dataset is not specific to fencing, it possesses several features highly relevant to modeling fencing training load. First, the dataset continuously records time-series signals of various daily and sports activities using wearable sensors. Each activity is segmented into 5-second windows, producing a large number of multi-segment activity samples. This “multiple activity types + continuous time windows” structure resembles the temporal alternation of different session types in actual fencing training (e.g., technical drills, footwork exercises, combat simulations), where load fluctuates within short time windows. This makes the dataset suitable for evaluating the modeling capability of AGAs on intermittent, non-stationary motion signals. Second, the dataset includes a wide range of movement patterns, such as sitting, standing, walking, running, stair climbing, and machine-based exercises. These cover a continuum from low-intensity static postures to moderate- and high-intensity cyclical movements. Although these activities do not represent fencing-specific techniques, their mechanical load patterns and metabolic responses can serve as proxies for “low-load maintenance,” “moderate-intensity reciprocal movement,” and “high-intensity limb-driven” activity types. This provides a controllable and open environment for constructing a mapping between external load features and load-type labels. The core objective of this study is to validate the feasibility and performance of the improved AGA in complex exercise load prediction tasks. Therefore, using a publicly available and well-structured dataset facilitates methodological verification under reproducible conditions and lays the foundation for subsequent transfer to actual fencing data.

For analytical clarity, the dataset was classified into three dimensions based on activity type: strength training, aerobic training, and endurance training. This classification is not arbitrary. It is based on distinctions in energy metabolism and movement characteristics of different load patterns in exercise physiology. Activities that primarily involve large muscle groups overcoming gravity or external resistance, with short bursts of high tension, were classified as “strength training.” These physiological characteristics resemble the short explosive movements in fencing, such as lunging initiations and rapid directional changes. Activities of moderate intensity with rhythmic, cyclical motion and predominantly aerobic energy supply, such as walking or light jogging, were classified as “aerobic training.” These correspond to longer periods of low- to moderate-intensity reciprocal footwork in fencing. Activities with longer duration that place higher demands on cardiovascular endurance and muscular stamina were classified as “endurance training,” reflecting the regulation of cumulative load and recovery rhythms in training plans. These three categories are not intended to prescribe fencing-specific training directly. Instead, they serve as label spaces for supervised learning, allowing evaluation of whether the improved AGA can distinguish load types of different intensities and patterns within the same dataset. The focus of this study is on the algorithm’s sensitivity to load patterns and prediction accuracy, rather than on prescribing specific training programs. Using general load classifications at a macro level maintains correspondence with classical training load theory (e.g., external load/internal load, intensity–time structure) and provides a unified framework for later transfer of the model to fencing-specific data.

To ensure experimental consistency and reproducibility, the hardware configuration is specified as follows:

Processor: Intel Xeon Silver 4216.

Graphics Card: NVIDIA A100.

Memory: Samsung 128GB DDR4.

Storage Device: Samsung 970 EVO Plus NVMe SSD.

Power Supply: Corsair RM850x.

The experimental parameters are configured as follows:

Population size: 50.

Maximum generations: 100.

Crossover and mutation probabilities: Dynamically adjusted based on fitness and diversity metrics.

Objective function weights: (0.3, 0.7) to balance multi-objective optimization.

Penalty factor: 10, applied to constrain violations in optimization.

Elite individual proportion: 10%, ensuring the retention of top-performing solutions.

Random seed: 42, to maintain result reproducibility.

Comparative models employed in the experiment include:

Deep Neural Network – Gated Recurrent Unit (DNN-GRU).

Extreme Gradient Boosting (XGBoost).

Long Short-Term Memory with Attention Mechanism (LSTM-Attn).

Event Adversarial Neural Network (EANN).

Temporal Attention Graph Convolutional Network (TA-GCN).

These models encompass a diverse array of methodologies, ranging from deep learning and ensemble learning to graph neural networks. This diversity ensures comprehensive benchmarking, providing a robust framework for evaluating the performance of the optimized AGA in comparison to state-of-the-art predictive models.