A Sequential Deep Learning Algorithm for Sampled Mixed-integer Optimisation Problems

TL;DR

This paper presents two sequential deep learning algorithms for sampled mixed-integer optimization problems, demonstrating finite-time convergence and improved computational performance through neural network classifiers in practical power and linear programming tests.

Contribution

Introduction of two novel sequential algorithms with neural network enhancement for efficiently solving sampled mixed-integer optimization problems.

Findings

Algorithms converge in finite time to the optimal solution.

Neural network classifier significantly improves computational efficiency.

Validated on power flow, unit commitment, and linear programming problems.

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.