This work describes the implementation of a genetic algorithm-based strategy combined with first-principles computations for identifying the structure of the most stable boron 1D structures. We focus our attention on the structure of ultrathin 1D boron structures given the lack of previous experimental and theoretical work on this topic. Our methodology yields reasonable structural candidates for further optimizations at the DFT level with tighter convergence criteria. The simulations involved 1D structures with up to 8 atoms per unit cell. We have identified four main groups of structures: flat nanowires (monatomic-height stripes) with triangular or triangular and "square" motifs, stripes with larger holes, nanowires with an open tubular shape, and regular nanowires. The diameter-dependent structural changes are discussed.