This paper describes the application of genetic algorithms to select a generic set of ground motions that can be used to conduct hazard-consistent incremental dynamic analysis (HC-IDA) on a wide range of structures located at any site. HCIDA is a recently developed procedure that overcomes the primary drawback of traditional incremental dynamic analysis (IDA) by enabling the computation of a hazard-consistent collapse fragility curve. Hence, it offers an alternative to the commonly employed hazard-consistent multiple stripe analysis (MSA) procedure, but without the need for site-specific ground motion selection. The response spectral shapes and durations of the ground motions used to conduct HC-IDA should ideally be uniformly distributed over the range of response spectral shapes and durations likely to be expected at a wide range of representative sites. This uniform distribution of response spectral shapes and durations enables the structural failure surface to be estimated with the least amount of uncertainty. In this study, response spectral shape is quantified using the scalar metric SaRatio, while duration is quantified using 5-75% significant duration (Ds5-75). The ranges of SaRatio and Ds5-75 values anticipated at Wellington, New Zealand are computed using the generalized conditional intensity measure (GCIM) framework. A genetic algorithm is employed to select a suitable record set from a database of 2500 ground motions recorded from both shallow crustal and subduction earthquakes. Genetic algorithms employ operations such as mutation, crossover, and selection, inspired by the process of natural selection in evolution, to optimize highly nonlinear functions. The Latin hypercube sampling technique is used in this study to select the sets of ground motions constituting the first generation of chromosomes that have approximately uniform marginal distributions of SaRatio and Ds5-75. The fitness of the ground motion sets, quantified using the Kolmogorov-Smirnov test, is then optimized over successive generations by crossover and mutation operations. The selected ground motions are demonstrated to be able to predict the failure surface of a steel moment frame building more precisely compared to the FEMA far-field set. Hence, they can be used to compute the hazard consistent fragility curve of a wide range of structures located at a wide range of sites using HC-IDA.