Epistasis refers to the phenomenon where the interaction of multiple genes affects a certain phenotype in addition to their individual additive effects. Similar epistatic effects are also ubiquitous in other application areas, such as gene-environment interactions, where a certain effect is triggered only when a particular combination of genes and environmental components is present. Epistasis detection has been recognized as a major challenge in the field of genetics. Previously proposed methods either focused on finding two-gene interactions using brute force enumeration or resorted to heuristic algorithms to search only a subset of the solution space. Herein we present an optimization approach that can identify the number of explanatory variables responsible for the epistasis as well as the exact combination of these variables. Results from simulation experiments using a soybean data set suggested that the proposed approach had a 95.5% chance of correctly detecting second-order to fifth-order epistases, which was a significant improvement over two alternative approaches in the literature.