Epistasis, which is the phenomenon of genetic interactions, plays a central role in many scientific discoveries. However, due to the combinatorial nature of the problem, it is extremely challenging to decipher the exact combinations of genes that trigger the epistatic effects. Many existing methods only focus on two-way interactions. Some of the most effective methods used machine learning techniques, but many were designed for special case-and-control studies or suffer from overfitting. We propose three new algorithms for multi-effect and multi-way epistases detection, with one guaranteeing global optimality and the other two being local optimization oriented heuristics.