A new approach to route planning for joint search and track missions by coordinated unmanned aerial vehicles (UAVs) is presented. The cornerstone is a novel objective function that integrates naturally and coherently the conflicting objectives of target detection, target tracking, and vehicle survivability into a single scalar index for path optimization. This objective function is the value of information gained by the mission on average in terms of a summation, where the number of terms reflects the number of targets detected while how large each term is reflects how well each detected target is tracked. The UAV following the path that maximizes this objective function is expected to gain the most valuable information by detecting the most important targets and tracking them during the most critical times. Although many optimization algorithms exist, we use a modified particle swarm optimization algorithm along with our proposed objective function to determine which trajectory is the best on the average at detecting and tracking targets. For simplicity, perfect communication with centralized fusion is assumed and the problems of false alarm, data association, and model mismatch are not considered. For analysis, we provide several simplified examples along with a more realistic simulation. Simulation results show that by adjusting the parameters of the objective function, solutions can be optimized according to the desired tradeoff between the conflicting objectives of detecting new targets and tracking previously detected targets. Our approach can also be used to update plans in real time by incorporating the information obtained up to the time (and then reusing our approach).