Application of linear programming methods for automated planning of personalized training programs

Context and relevance. We developed a hybrid mixed-integer linear programming (MILP) model to automate training-program planning that combines knowledge extraction from expert plans with a physiological model of fatigue dynamics. The approach enables automatic calibration of recovery parameters from plan structure without medical measurements. Objective. To develop and empirically validate a hybrid MILP model that extracts latent periodization patterns and generates physiologically grounded programs accounting for muscle-fatigue dynamics. Hypotheses. (1) The recovery coefficient of muscle groups can be inferred from the temporal structure of an expert plan. (2) The combination of linear constraints with an exponential fatigue model reproduces microcycle periodization without explicit rule coding. (3) The hybrid approach balances structural fidelity and exercise variability. Methods and materials. We performed a descriptive analysis of a real training plan for the women’s handball team “Rostov-Don” (24 sessions). To assess statistical significance, we simulated a Monte-Carlo null distribution of the metrics (N = 1,000) under the same structural constraints and computed z-scores and normal-approximation p-values (α = 0.05). The model uses 32 binary decision variables (exercises), a 32×8 intensity matrix, dynamic weighting (base utility, diversity bonus, fatigue penalty), and automatic estimation of the recovery coefficient λ. Implementation: Python 3.11, PuLP 2.7, CBC 2.10. Results. Cosine similarity of load distribution = 0.722 (vs 0.634 ± 0.025 for random generation; z = 3.55; p < 0.0002); exact volume match (EMR) = 55.2% (vs 38.1 ± 3.2%; p < 0.001); Jaccard index = 0.37 (vs 0.21 ± 0.08; p < 0.001); 22 microcycle patterns detected. The extracted recovery coefficient λ = 0.345 corresponds to a half-recovery period of ≈ 2.0 sessions. Conclusions. The hybrid approach enables automatic extraction of physiologically meaningful parameters and periodization patterns from real-world plan structure. High computational efficiency (< 0.5 s per plan) and interpretability make the model suitable for practical automation of training-program design.