A sequential deep learning algorithm for sampled mixed-integer optimisation problems
Year: 2023
Type: article
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.
Source: Information Sciences
Authors: Mohammadreza Chamanbaz, Roland Bouffanais
Institutions: The University of Sydney, University of Ottawa
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,330
OpenAlex ID: W4324370607