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

Conic Optimization Theory: Convexification Techniques and Numerical Algorithms

Optimization is at the core of control theory and appears in several areas of this field, such as optimal control, distributed control, system identification, robust control, state estimation, model predictive control and dynamic programming. The recent advances in various topics of modern optimization have also been revamping the area of machine learning. Motivated by the crucial role of optimization theory in the design, analysis, control and operation of real-world systems, this tutorial paper offers a detailed overview of some major advances in this area, namely conic optimization and its emerging applications. First, we discuss the importance of conic optimization in different areas. Then, we explain seminal results on the design of hierarchies of convex relaxations for a wide range of nonconvex problems. Finally, we study different numerical algorithms for large-scale conic optimization problems.Comment: 18 page

Event-Driven Network Model for Space Mission Optimization with High-Thrust and Low-Thrust Spacecraft

Numerous high-thrust and low-thrust space propulsion technologies have been developed in the recent years with the goal of expanding space exploration capabilities; however, designing and optimizing a multi-mission campaign with both high-thrust and low-thrust propulsion options are challenging due to the coupling between logistics mission design and trajectory evaluation. Specifically, this computational burden arises because the deliverable mass fraction (i.e., final-to-initial mass ratio) and time of flight for low-thrust trajectories can can vary with the payload mass; thus, these trajectory metrics cannot be evaluated separately from the campaign-level mission design. To tackle this challenge, this paper develops a novel event-driven space logistics network optimization approach using mixed-integer linear programming for space campaign design. An example case of optimally designing a cislunar propellant supply chain to support multiple lunar surface access missions is used to demonstrate this new space logistics framework. The results are compared with an existing stochastic combinatorial formulation developed for incorporating low-thrust propulsion into space logistics design; our new approach provides superior results in terms of cost as well as utilization of the vehicle fleet. The event-driven space logistics network optimization method developed in this paper can trade off cost, time, and technology in an automated manner to optimally design space mission campaigns.Comment: 38 pages; 11 figures; Journal of Spacecraft and Rockets (Accepted); previous version presented at the AAS/AIAA Astrodynamics Specialist Conference, 201

Integration of process design and control: A review

There is a large variety of methods in literature for process design and control, which can be classified into two main categories. The methods in the first category have a sequential approach in which, the control system is designed, only after the details of process design are decided. However, when process design is fixed, there is little room left for improving the control performance. Recognizing the interactions between process design and control, the methods in the second category integrate some control aspects into process design. With the aim of providing an exploration map and identifying the potential areas of further contributions, this paper presents a thematic review of the methods for integration of process design and control. The evolution paths of these methods are described and the advantages and disadvantages of each method are explained. The paper concludes with suggestions for future research activities