1. A sequential deep learning algorithm for sampled mixed-integer optimisation problems
- Author
-
Roland Bouffanais and Mohammadreza Chamanbaz
- Subjects
FOS: Computer and information sciences ,Computer Science - Machine Learning ,Information Systems and Management ,Optimization and Control (math.OC) ,Artificial Intelligence ,Control and Systems Engineering ,FOS: Mathematics ,Mathematics - Optimization and Control ,Software ,Machine Learning (cs.LG) ,Computer Science Applications ,Theoretical Computer Science - Abstract
Mixed-integer optimisation problems can be computationally challenging. Here, we introduce and analyse two efficient algorithms with a specific sequential design that are aimed at dealing with sampled problems within this class. At each iteration step of both algorithms, we first test the feasibility of a given test solution for each and every constraint associated with the sampled optimisation at hand, while also identifying those constraints that are violated. Subsequently, an optimisation problem is constructed with a constraint set consisting of the current basis -- namely, the smallest set of constraints that fully specifies the current test solution -- as well as constraints related to a limited number of the identified violating samples. We show that both algorithms exhibit finite-time convergence towards the optimal solution. Algorithm 2 features a neural network classifier that notably improves the computational performance compared to Algorithm 1. We quantitatively establish these algorithms' efficacy through three numerical tests: robust optimal power flow, robust unit commitment, and robust random mixed-integer linear program.
- Published
- 2023