A tractable numerical strategy for robust MILP and application to energy management

Robust optimization has emerged as a tractable methodology for coping with parameter uncertainty in an optimization problem. In order to avoid conservative solutions, i.e. overly protective and expensive solutions, Ben-Tal and Nemirovski introduced the notion of affine adaptability. However, their approach significantly increases the program size and threatens its tractability, especially in the context of mixed-integer programming. In this paper, we focus on robust mixed-integer linear programs. We propose a tractable numerical strategy for solving them and demonstrate the computational efficiency of our method when applied to a real energy management problem. In addition, we propose a practical data-driven methodology for designing the uncertainty set of robust programs.