New algorithms for the optimization of alloy nanoparticles (nanoalloys) are presented. The new algorithms are based on the concept of multiple basin-hopping walkers running in parallel, each with its own specialized task—the flying walker, exploring the energy landscape at high temperatures to sample different geometric structures, and the landing and hiking walkers mainly refining the optimization of chemical ordering at low temperatures. These algorithms are referred to as flying-landing (FL) and flying-landing-hiking (FLH). The algorithms are tested against several benchmarks (AuCu and AuRh clusters of 400 atoms and PtNi clusters of 38 and 55 atoms). In all cases, both FL and FLH are shown to perform very well compared to previous results in the literature. In addition, the algorithms are applied to the optimization of larger AgCu nanoparticles, with sizes up to 4000 atoms, in order to establish the behavior of the mixing energy and to compare full global optimization of shape and chemical ordering with optimization of chemical ordering alone at a fixed shape. In general, the results show that the simultaneous optimization of shape and chemical ordering is necessary in many cases, and that the FLH approach is especially efficient for that purpose.