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NASA NTRS2022

Alternative regularizations for Outer-Approximation algorithms for convex MINLP

In this work, we extend the regularization framework from Kronqvist et al. (Math Program 180(1):285–310, 2020) by incorporating several new regularization functions and develop a regularized single-tree search method for solving convex mixed-integer nonlinear programming (MINLP) problems. We propose a set of regularization functions based on distance metrics and Lagrangean approximations, used in the projection problem for finding new integer combinations to be used within the Outer-Approximation (OA) method. The new approach, called Regularized Outer-Approximation (ROA), has been implemented as part of the open-source Mixed-integer nonlinear decomposition toolbox for Pyomo—MindtPy. We compare the OA method with seven regularization function alternatives for ROA. Moreover, we extend the LP/NLP Branch and Bound method proposed by Quesada and Grossmann (Comput Chem Eng 16(10–11):937–947, 1992) to include regularization in an algorithm denoted RLP/NLP. We provide convergence guarantees for both ROA and RLP/NLP. Finally, we perform an extensive computational experiment considering all convex MINLP problems in the benchmark library MINLPLib. The computational results show clear advantages of using regularization combined with the OA method.

Convex Mixed-integer nonlinear programming↗

NASA NTRS2024

A Convexification-Based Outer-Approximation Method for Convex and Nonconvex MINLP

The advancement of domain reduction techniques has significantly enhanced the performance of solvers in mathematical programming. This paper delves into the impact of integrating convexification and domain reduction techniques within the Outer-Approximation method. We propose a refined convexification-based Outer-Approximation method alongside a Branch-and-Bound method for both convex and nonconvex Mixed-Integer Nonlinear Programming problems. These methods have been developed and incorporated into the open-source Mixed-Integer Nonlinear Decomposition Toolbox for Pyomo-MindtPy. Comprehensive benchmark tests were conducted, validating the effectiveness and reliability of our proposed algorithms. These tests highlight the improvements achieved by incorporating convexification and domain reduction techniques into the Outer-Approximation and Branch-and-Bound methods.

Optimization↗

NASA NTRSDate not supplied

Rolling Horizon with K-Position Search Method for Strategic Deconfliction of Package Delivery UAS

This research focuses on the strategic deconfliction of unmanned aircraft systems (UAS) in an urban package delivery environment with two depots and multiple drop-off locations. Since the formulated mixed-integer nonlinear programming (MINLP) problem is non-deterministic polynomial-time (NP) hard, a heuristic algorithm called "rolling horizon with k-position search (KPS)" is used to compute the departure sequence and scheduled time of departure (STD) of each UAS at a depot, considering temporal constraints at en-route crossing waypoints and depots for strategic deconfliction. The simulation studies show that an increase in the value of k (local neighborhood search) in the KPS reduces the average ground delay at the cost of an increase in the computation time for a given number of UAS, size of the rolling horizon window, and number of depots involved in the local neighborhood search. The studies also show that for a given rolling horizon window, the computation time increases exponentially with an increase in the total number of UAS flights when serial processing the local neighborhood search of KPS (with k > 1) and drops by an order of magnitude upon performing the local neighborhood search of KPS using parallel processing instead of serial processing. The computation time drops with the reduction in air traffic complexity of a scenario for a given number of flights, k (local neighborhood search), and rolling horizon window.

UTM↗