Although genetic factors play an important role in most human diseases, multiple genes or genes and environmental factors may influence individual risk. In order to understand the underlying biological mechanisms of complex diseases, it is important to understand the complex relationships that control the process. In this paper, we consider different perspectives, from each optimization, complexity analysis, and algorithmic design, which allows us to describe a reasonable and applicable computational framework for detecting gene-gene interactions. Accordingly, support vector machine and combinatorial optimization techniques (local search and genetic algorithm) were tailored to fit within this framework. Although the proposed approach is computationally expensive, our results indicate this is a promising tool for the identification and characterization of high order gene-gene and gene-environment interactions. We have demonstrated several advantages of this method, including the strong power for classification, less concern for overfitting, and the ability to handle unbalanced data and achieve more stable models. We would like to make the support vector machine and combinatorial optimization techniques more accessible to genetic epidemiologists, and to promote the use and extension of these powerful approaches. Genet. Epidemiol. 2008. © 2007 Wiley-Liss, Inc.