Attacks against computer networks are becoming more sophisticated, with adversaries using new attacks or modifying existing attacks. This research uses three different types of multiobjective approaches, one lexicographic and two Pareto-based, in a multiobjective evolutionary programming algorithm to develop a new method for detecting such attacks. The approach evolves finite state transducers to detect attacks; this approach may allow the system to detect attacks with features similar to known attacks. Also, the approach examines the solution quality of each detector. Initial testing shows the algorithm performs satisfactorily in generating finite state transducers capable of detecting attacks.