Invasive species are a major threat to global biodiversity and cause considerable economic losses. Often, the main constraint to controlling or eradicating invaders is finding them, rather than eliminating them after they are located. Finding them can be difficult and costly if the focus is on detecting individual organisms over a large area. Enlisting the help of the public through "passive surveillance" can enhance the search effort when resources are limited. The roles of active and passive surveillance and their interaction are investigated here using a spatially explicit simulation model of the spread of a hypothetical invasive species. In the model, the uncontrolled spread of the invasive across the landscape is driven by habitat suitability, a Cauchy dispersal kernel and random long-distance dispersal events. Detection may result from passive surveillance or through supplementary searching by a pest-control agency. Modeling the spread of invaders allows identification of effective management strategies. In this article two measures of success are incorporated in the fitness measure within a genetic algorithm that identifies optimal management strategies. Strategies are defined in terms of search effort applied, the distance that is searched around detections, and the number of repeat visits to previously treated sites.