An optimal design analysis is carried out for an explosives’ detection system (EDS) based on thermal neutron activation (TNA) of a sample under investigation. The objective of this work is to use a genetic algorithm (GA) to obtain the optimized moderator design that would yield the “best” signal in a detection system. In a preliminary analysis, a full Monte Carlo (MC) simulation is carried out to estimate the effectiveness of various moderators, namely, water, graphite, and beryllium with respect to radiative capture reactions in a sample under investigation. Since MC simulation is computationally “expensive,” it is generally not used for random-search-based optimization analysis. Thus, more efficient methods are required for the design of optimal nuclear systems, where neutron transport is accurately modeled and iteratively solved for estimating the effect of independent design parameters. This paper proposes a computational scheme in which GA is coupled with the two-group neutron diffusion equation (DE) for carrying out an optimization analysis. The coupled GA-DE optimization scheme is demonstrated for obtaining the optimal moderator design. It is found that with considerably less computational effort than in an elaborate MC computation, the GA-DE approach can be used for the optimal design of detection systems.