Mixed-Integer Convex Nonlinear Optimization with Gradient-Boosted Trees Embedded

TL;DR

This paper introduces methods for solving large-scale mixed-integer nonlinear optimization problems that incorporate gradient-boosted trees and convex penalties, with applications in chemical process optimization.

Contribution

It develops heuristic and exact algorithms for optimizing models with gradient-boosted trees embedded in mixed-integer nonlinear problems.

Findings

Effective heuristic methods for feasible solutions

An exact branch-and-bound algorithm leveraging structural properties

Successful computational tests on industrial chemical optimization instances

Abstract

Decision trees usefully represent sparse, high dimensional and noisy data. Having learned a function from this data, we may want to thereafter integrate the function into a larger decision-making problem, e.g., for picking the best chemical process catalyst. We study a large-scale, industrially-relevant mixed-integer nonlinear nonconvex optimization problem involving both gradient-boosted trees and penalty functions mitigating risk. This mixed-integer optimization problem with convex penalty terms broadly applies to optimizing pre-trained regression tree models. Decision makers may wish to optimize discrete models to repurpose legacy predictive models, or they may wish to optimize a discrete model that particularly well-represents a data set. We develop several heuristic methods to find feasible solutions, and an exact, branch-and-bound algorithm leveraging structural properties of the gradient-boosted trees and penalty functions. We computationally test our methods on concrete mixture design instance and a chemical catalysis industrial instance.