Causal discovery is essential across various scientific fields to uncover causal structures within data. Traditional methods relying on observational data have limitations due to confounding variables. This paper presents an optimization-based approach using integer programming (IP) to design minimal intervention sets that ensure causal structure identifiability. Our method provides exact and modular solutions, adaptable to different experimental settings and constraints. We demonstrate its effectiveness through comparative analysis across different settings demonstrating its applicability and robustness.