Computationally efficient solution of mixed integer model predictive control problems via machine learning aided Benders Decomposition

TL;DR

This paper introduces a machine learning-enhanced Benders Decomposition method for mixed integer MPC problems, significantly reducing solution time while maintaining high accuracy, demonstrated on chemical process control.

Contribution

It proposes a novel ML-based approach to approximate Benders cuts, improving computational efficiency in solving mixed integer MPC problems.

Findings

Achieves up to 97% reduction in solution time

Maintains about 1% error in solutions

Ensures feasibility when the problem is feasible

Abstract

Mixed integer Model Predictive Control (MPC) problems arise in the operation of systems where discrete and continuous decisions must be taken simultaneously to compensate for disturbances. The efficient solution of mixed integer MPC problems requires the computationally efficient and robust online solution of mixed integer optimization problems, which are generally difficult to solve. In this paper, we propose a machine learning-based branch and check Generalized Benders Decomposition algorithm for the efficient solution of such problems. We use machine learning to approximate the effect of the complicating variables on the subproblem by approximating the Benders cuts without solving the subproblem, therefore, alleviating the need to solve the subproblem multiple times. The proposed approach is applied to a mixed integer economic MPC case study on the operation of chemical processes. We show that the proposed algorithm always finds feasible solutions to the optimization problem, given that the mixed integer MPC problem is feasible, and leads to a significant reduction in solution time (up to 97% or 50x) while incurring small error (in the order of 1%) compared to the application of standard and accelerated Generalized Benders Decomposition.