Some pests and vectors of many vector-borne diseases (like mosquitoes for malaria and dengue) are known to invade any homogeneous and favorable territory, following a traveling wave type dynamic. The density of individuals in the field is commonly modeled as the solution of a bistable reaction-diffusion equation on an unbounded domain. In this work, we are interested in finding an optimal strategy to block such a solution by means of a population elimination action in a prescribed subdomain (modeling, for instance the effect of a mechanical action or an insecticide applied in a certain region to reduce the number of individuals in the population). We propose a complete description of the solutions of this problem, based on the precise analysis of the optimality conditions and on arguments for comparison between the possible strategies.