<p>An improved methodology for generative design of microstructures with optimized elastic properties is presented. It employs a generative adversarial network (GAN) adapted to generate three-dimensional two-phase structures together with a genetic algorithm for solution of the multi-objective optimization problem. The proposed GAN architecture is able to model the disentangled design space, which accelerated convergence of the optimization and improved interpretability of the process. A new way for definition of the design space boundaries was proposed. Performance evaluation of the generative model was implemented using an approach that allows to monitor stability of training as well as to simplify the choice of the optimal model. The case study of creation of random porous structures with maximization of the effective elastic modulus and minimization of the volume fraction of a solid phase was considered. The obtained open-cell and closed-cell structures with superior mechanical properties and optimal morphology confirm the effectiveness of the proposed approach.</p>