(61a) Decision-Focused Surrogate Modeling for Mixed-Integer Optimization (Poster corresponding to plenary presentation)

Efficient and safe process operations require decision-making in real-time. Many online decision-making frameworks involve solving mathematical optimization problems; however, often the computational complexity of the given optimization problem presents a major challenge such that the long solution time renders it ineffective in time-critical online applications. A common approach to tackling this challenge is to perform online optimization with a surrogate model, which is an approximation of the original model that can be solved more efficiently [1, 2]. Typically in surrogate modeling, one tries to replace complicating functions that are embedded in the optimization problem with simpler ones. Here, a major underlying assumption is that a surrogate model that provides a good approximation of the original functions will, once incorporated into the optimization problem, also lead to solutions that are close to the true optimal solutions. However, it is unclear whether or under what conditions this assumption holds and how accurate the surrogate model needs to be.
Recently, we proposed a decision-focused surrogate modeling framework that explicitly aims to construct surrogate models that minimize the decision prediction error defined as the difference between the optimal solutions of the original and the surrogate optimization problems [3]. The proposed approach was successfully applied to construct efficient surrogate models for nonconvex nonlinear programs. In this work, we extend the framework to consider challenging mixed-integer optimization problems, which commonly arise in hybrid model predictive control (MPC) and online scheduling applications [4].

In decision-focused surrogate modeling, we generate data by solving several instances of the original optimization problem offline, which gives us the true optimal solutions for different model inputs. We then try to estimate the parameters of a surrogate optimization model such that it provides the same optimal solutions. The corresponding learning problem can be formulated as a large-scale bilevel program, which we solve using a penalty-based block coordinate descent algorithm [5]. In our case, the original optimization problems are mixed-integer linear programs (MILPs) or mixed-integer quadratic programs (MIQPs) for which we construct surrogate models in the form of convex quadratic programs (QPs). The effectiveness of the proposed approach is demonstrated in multiple computational case studies, including one involving a hybrid vehicle MPC problem. In particular, the results show that the method is relatively data-efficient in learning QPs that achieve near-optimal solutions in significantly less time compared to the original MILPs or MIQPs.

References

[1] L. T. Biegler, Y. Lang, and W. Lin, “Multi-scale optimization for process systems engineering,” Comput. Chem. Eng., vol. 60, pp. 17–30, 2014.

[2] A. Cozad, N. V. Sahinidis, and D. C. Miller, “Learning Surrogate Models for Simulation-Based Optimization,” AIChE J., vol. 60, no. 6, pp. 2211–2227, 2014.

[3] R. Gupta and Q. Zhang, “Decision-focused surrogate modeling with feasibility guarantee,” in Computer Aided Chemical Engineering, 2022, pp. 1717–1722.

[4] D. Bertsimas and B. Stellato, “Online Mixed-Integer Optimization in Milliseconds,” INFORMS J. Comput., vol. 34, no. 4, pp. 2229–2248, 2022.

[5] R. Gupta and Q. Zhang, “Efficient learning of decision-making models : A penalty block coordinate descent algorithm for data-driven inverse optimization,” Comput. Chem. Eng., vol. 170, p. 108123, 2023.