Optimising parent selection in plant breeding: comparing metaheuristic algorithms for genotype building.

Stacking desirable haplotypes across the genome to develop superior genotypes has been implemented in several crop species. A major challenge in Optimal Haplotype Selection is identifying a set of parents that collectively contain all desirable haplotypes, a complex combinatorial problem with countless possibilities. In this study, we evaluated the performance of metaheuristic search algorithms (MSAs)-genetic algorithm (GA), differential evolution (DE), particle swarm optimisation (PSO), and simulated annealing (SA) for optimising parent selection under two genotype building (GB) objectives: Optimal Haplotype Selection (OHS) and Optimal Population Value (OPV). Using a diverse wheat population of 583 lines genotyped for 29,972 SNPs, forming 7645 haplotype blocks and phenotyped for stripe rust scores, we assessed each algorithm's performance across fitness optimisation, convergence speed, and computational efficiency. GA consistently achieved high fitness and rapid convergence, while DE showed robustness but required longer runtime and careful tuning. PSO performed well under the OHS criterion but was less effective for OPV. SA, although computationally lighter, was less consistent in finding optimal solutions. Simulation over 100 breeding cycles showed that OHS outperformed both OPV and GEBV-based selection in long-term genetic gain and diversity retention. OHS maintained heterozygosity and additive variance, which are key for sustainable improvement, while GEBV selection led to early allele fixation. Our findings underscore the potential of GB strategies that prioritise the collective performance of parent sets rather than individual ranking to enhance selection outcomes in genomic-assisted breeding programmes.