Locust Swarms are a new multi-optima search technique explicitly designed for non-globally convex search spaces. They use "smart" start points to scout for promising new areas of the search space before using particle swarms and a greedy local search technique (e.g. gradient descent) to find a local optimum. These scouts start a minimum distance away from the previous optimum, and this gap is an important part of achieving a non-convergent search trajectory. Equally, the search for "smart" start points centers around the previous local optimum, and this provides the basis for also having a non-random search trajectory. Experiments on a 30-dimensional rotated Schwefel function demonstrate that the ability of Locust Swarms to successfully balance these two search characteristics is an important factor in its ability to effectively explore this non-globally convex search space.