4,372 research outputs found
Mixed-Integer Convex Nonlinear Optimization with Gradient-Boosted Trees Embedded
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
Using Functional Programming to recognize Named Structure in an Optimization Problem: Application to Pooling
Branch-and-cut optimization solvers typically apply generic algorithms, e.g., cutting planes or primal heuristics, to expedite performance for many mathematical optimization problems. But solver software receives an input optimization problem as vectors of equations and constraints containing no structural information. This article proposes automatically detecting named special structure using the pattern matching features of functional programming. Specifically, we deduce the industrially-relevant nonconvex nonlinear Pooling Problem within a mixed-integer nonlinear optimization problem and show that we can uncover pooling structure in optimization problems which are not pooling problems. Previous work has shown that preprocessing heuristics can find network structures; we show that we can additionally detect nonlinear pooling patterns. Finding named structures allows us to apply, to generic optimization problems, cutting planes or primal heuristics developed for the named structure. To demonstrate the recognition algorithm, we use the recognized structure to apply primal heuristics to a test set of standard pooling problems
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