The size and complexity of containerized shipping across the globe has increased the vulnerability of seaports to the attack of terrorist networks and contraband smuggling. As a result, the creation of inspection strategies to check incoming containers at ports-of-entry has been necessary to enable the detection of containers carrying prohibited items. However, since costs and tardiness considerations related to the inspection process prevent all cargo to be manually checked, including different non-intrusive screening technologies as part of the inspection strategies is essential to optimize inspection needs. In this paper, inspection strategies are represented as decision-tree structures where each node illustrates a screening device, and links represent the two possible classifications a screened container can get (i.e. suspicious or unsuspicious). Based on such classification, one of three actions is taken: to continue screening, release or physically check the container. The contribution of this paper is a mathematical framework that provides an approximation to the Pareto optimal solutions (i.e. inspection strategies) that enable decision-makers to: (1) identify tradeoffs among vulnerability, inspection cost, and tardiness for different inspection strategies, and based on this (2) find the strategy that best suits current inspection needs. The mathematical framework includes: (1) a multi-objective optimization model that concurrently minimizes vulnerability, cost, and tardiness while determining screening device allocation and threshold settings, as well as, (2) an evolutionary approach used to solve the optimization model.