In multi-agent search planning for a randomly moving and camouflaging target,
we examine heterogeneous searchers that differ in terms of their endurance
level, travel speed, and detection ability. This leads to a convex
mixed-integer nonlinear program, which we reformulate using three linearization
techniques. We develop preprocessing steps, outer approximations via lazy
constraints, and bundle-based cutting plane methods to address large-scale
instances. Further specializations emerge when the target moves according to a
Markov chain. We carry out an extensive numerical study to show the
computational efficiency of our methods and to derive insights regarding which
approach should be favored for which type of problem instance