Dual Dynamic Programming for Multi-Scale Mixed-Integer MPC

TL;DR

This paper introduces a dual dynamic integer programming framework that efficiently solves complex multi-scale mixed-integer MPC problems involving long horizons and discrete controls, outperforming existing solvers.

Contribution

The paper presents a novel nested cutting-plane scheme for multi-scale mixed-integer MPC, capable of handling general formulations and improving scalability and performance.

Findings

The proposed DDIP scheme effectively solves large-scale mixed-integer MPC problems.

It significantly outperforms state-of-the-art mixed-integer solvers in computational efficiency.

Demonstrated on HVAC scheduling, showing practical applicability and scalability.

Abstract

We propose a dual dynamic integer programming (DDIP) framework for solving multi-scale mixed-integer model predictive control (MPC) problems. Such problems arise in applications that involve long horizons and/or fine temporal discretizations as well as mixed-integer states and controls (e.g., scheduling logic and discrete actuators). The approach uses a nested cutting-plane scheme that performs forward and backward sweeps along the time horizon to adaptively approximate cost-to-go functions. The DDIP scheme proposed can handle general MPC formulations with mixed-integer controls and states and can perform forward-backward sweeps over block time partitions. We demonstrate the performance of the proposed scheme by solving mixed-integer MPC problems that arise in the scheduling of central heating, ventilation, and air-conditioning (HVAC) plants. We show that the proposed scheme is scalable and dramatically outperforms state-of-the-art mixed-integer solvers.