It is widely accepted that feature extraction is quite possibly the most critical step in computer vision. Typically, feature extraction is performed using a method such as the histogram of oriented gradients. In recent years, a shift has occurred from human to machine learned features, e.g., convolutional neural networks (CNNs) and Evolution-COnstructed (ECO) features. An advantage of our improved ECO (iECO) framework is it optimizes features on a per-descriptor basis. Herein, iECO is extended in order to represent a richer class of features, namely arithmetic combinations and compositions of iECOs. This extension, called Genetic prOgramming Optimal Feature Descriptor (GOOFeD) is based on genetic programming (GP). Three experiments are performed on data from a U.S. Army test site that contains multiple target and clutter types, burial depths, and times of day for automatic buried explosive hazard detection. The first two experiments focus on GOOFeD initialization and parameter selection. The last experiment demonstrates that GOOFeD is superior to iECO in terms of the fitness of evolved individuals.