TC-HUR: A Tri-Phase Cauchy-Assisted Hunger Games Search and Unified Runge-Kutta Optimizer for Robust DNA Data Storage

Although DNA-based data storage theoretically provides an information density of 2 bits per nucleotide, biochemical constraints transform sequence design into a high-dimensional constrained combinatorial optimization problem. The high computational cost and low encoding efficiency of conventional rule-based approaches make metaheuristic methods an effective alternative. This study proposes the TC-HUR hybrid algorithm to simultaneously optimize information density and conflicting biophysical constraints, including homopolymer (HP) length, GC content, melting temperature (Tm), and reverse-complement (RC) similarity. The method escapes local optima using Cauchy jump-enhanced Hunger Games Search (HGS), performs high-precision exploitation via Runge-Kutta (RUN) operators, and refines constraint violations at the nucleotide level through an adaptive intensive mutation mechanism. The algorithm is evaluated on a complex dataset of 1853 nucleotides under different noise regimes. TC-HUR outperforms RUN by 2.5% and HGS by 16.7% in average fitness. While maintaining homopolymer length near the ideal threshold, it reduces reverse-complement similarity to 19.10%, ensuring high sequence diversity. Under high-noise conditions, TC-HUR achieves a normalized edit distance of 0.1290, reducing insertion-deletion (indel) errors by approximately 14%. The results demonstrate that the proposed model effectively generates biophysically synthesizable and noise-resilient DNA codes.