While chaotic initialization enhances Genetic Algorithm (GA) diversity through ergodic sampling, its inherent boundary effects—systematic clustering of individuals near search space boundaries—are neglected in existing studies. A mathematical framework quantifying boundary effects is established in this paper, through interval-based diversity metrics and chaotic probability density analysis. By defining boundary, variable, and probability intervals, it is proven that the logistic mapping’s invariant distribution \(\rho (z)=1/(\pi \sqrt{z\left(1-z\right))}\) leads to 21.8% theoretical boundary occupancy, which is amplified to 36% empirically due to discretization. To mitigate this, a dimension-adaptive dynamic interval expansion strategy is proposed, achieving a reduction in boundary clustering from 36% to 29.70% in Shubert function tests ( \(\chi 2=27.154\) , \(p<0.001\) ). The dual nature of chaotic initialization is demonstrated: while sensitivity to initial conditions and ergodicity improve global exploration, boundary control is required to prevent diversity loss. Theoretical guarantees for boundary effect mitigation are provided in this study, offering actionable insights for GA and swarm intelligence initialization design.