Explosives, weapons of mass destruction and other contraband smuggled via cargo containers present a significant threat to national security. To combat this threat cargo containers are inspected for various types of contraband upon entering the country. This article presents a genetic algorithm-based technique for developing an optimum inspection strategy capable of detecting two different types of contraband. Experimentation on the behavior of the optimization algorithm is presented, demonstrating how this technique can be used to optimize an inspection strategy for detecting chemical explosives and radiological material, the components of either a nuclear or ''dirty'' bomb.