A Sequential Deep Learning Algorithm for Sampled Mixed-integer Optimisation Problems
This work addresses sampled mixed-integer optimization problems, which are incremental improvements for domains like power systems and random linear programming.
The authors tackled computationally challenging mixed-integer optimization problems by introducing two sequential algorithms that converge to optimal solutions in finite time, with Algorithm 2 using a neural network classifier to improve computational performance over Algorithm 1, as demonstrated in numerical tests like robust optimal power flow and unit commitment.
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.