We present a methodology for computing the flexibility index when uncertainty is characterized using multivariate Gaussian random variables. Our approach computes the flexibility index by solving a mixed-integer conic program (MICP). This methodology directly characterizes ellipsoidal sets to capture correlations in contrast to previous methodologies that employ approximations. We also show that, under a Gaussian representation, the flexibility index can be used to obtain a lower bound for the so-called stochastic flexibility index (i.e., the probability of having feasible operation). Our results also show that the methodology can be generalized to capture different types of uncertainty sets.

This paper presents a novel method for UAV-based 3D modeling of large infrastructure objects, such as pipelines, canals and levees, that combines anomaly detection with automatic on-board 3D view planning. The study begins by assuming that anomaly detections are possible and focuses on quantifying the potential benefits of the combined method and the view planning algorithm. A simulated canal environment is constructed, and several simulated anomalies are created and marked. The algorithm is used to plan inspection flights for the anomaly locations, and simulated images from the flights are rendered and processed to construct 3D models of the locations of interest. The new flights are compared to traditional flights in terms of flight time, data collected and 3D model accuracy. When compared to a low speed, low elevation traditional flight, the proposed method is shown in simulation to decrease total flight time by up to 55%, while reducing the amount of image data to be processed by 89% and maintaining 3D model accuracy at areas of interest.

We present a computational framework for analyzing and quantifying system flexibility. Our framework incorporates new features that include: general uncertainty characterizations that are constructed using composition of sets, procedures for computing well-centered nominal points, and a procedure for identifying and ranking flexibility-limiting constraints and critical parameter values. These capabilities allow us to analyze the flexibility of complex systems such as distribution networks.

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We propose a computational framework to quantify (measure) and to optimize the reliability of complex systems. The approach uses a graph representation of the system that is subject to random failures of its components (nodes and edges). Under this setting, reliability is defined as the probability of finding a path between sources and sink nodes under random component failures and we show that this measure can be computed by solving a stochastic mixed-integer program. The stochastic programming setting allows us to account for system constraints and general probability distributions to characterize failures and allows us to derive optimization formulations that identify designs of maximum reliability. We also propose a strategy to approximately solve these problems in a scalable manner by using purely continuous formulations.

We study the problem of designing systems in order to minimize cost while meeting a given flexibility target. Flexibility is attained by enforcing a joint chance constraint, which ensures that the system will exhibit feasible operation with a given target probability level. Unfortunately, joint chance constraints are complicated mathematical objects that often need to be reformulated using mixed-integer programming (MIP) techniques. In this work, we cast the design problem as a conflict resolution problem that seeks to minimize cost while maximizing flexibility. We propose a purely continuous relaxation of this problem that provides a significantly more scalable approach relative to MIP methods and show that the formulation delivers solutions that closely approximate the Pareto set of the original joint chance-constrained problem.

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