Informs Annual Meeting Phoenix 2018

INFORMS Phoenix – 2018

MC06

3 - Non-convex Sparse Sample Average Approximations: Properties of D-stationary Solutions Miju Ahn, Southern Methodist University, Dallas, TX, United States In sparse learning, sample average approximation involving non-convex sparsity functions is a method that is widely used in practice. We introduce a unified difference-of-convex formulation and study properties of the directional stationary solutions. The solution kind is compared to a vector which is possibly the global optimum of an underlying expectation minimization problem. We provide a bound for the distance between the two solutions, a bound on the difference between their model outcomes, and a result showing inclusion relationships among their support sets. n MC06 North Bldg 122C Joint Session OPT/Practice Curated: Pyomo: Recent Developments and Applications Sponsored: Optimization/Computational Optimization and Software Sponsored Session Chair: John Siirola, Sandia National Laboratories, Albuquerque, NM, 87185, United States 1 - Pyomo.GDP: An Integrated Ecosystem for Generalized Disjunctive Programming Modeling and Optimization Qi Chen, Carnegie Mellon University, 5000 Forbes Avenue, Department of Chemical Engineering, Pittsburgh, PA, 15213, United States, David Bernal, John Siirola, Ignacio E. Grossmann In this work, we present new capabilities in Pyomo.GDP. Generalized Disjunctive Programs (GDPs) allow high-level description of optimization problems involving both discrete and continuous decision variables. For difficult problems, we must move beyond classical reformulation approaches. Pyomo.GDP offers automated application of advanced techniques such as disjunctive “basic steps and procedural reformulations. We also introduce a new direct solver for Pyomo.GDP models, GDPopt, which implements the logic-based outer approximation decomposition algorithm. We demonstrate the application of these tools on a set of GDP test problems. 2 - Pyomo.dae: A Framework for Modeling and Solving Dynamic Optimization Problems Bethany Nicholson, Sandia National Laboratories, P.O. Box 5800, MS 1326, Albuquerque, NM, 87185, United States, John Siirola Dynamic optimization problems include differential equations as constraints. These problems can be tough to implement and solve because they must be reformulated before being sent to standard optimization solvers. Pyomo.dae is a Pyomo extension for representing differential equations in an optimization modeling context. It includes implementations of several discretization schemes that will automatically convert differential equations to algebraic equations, making the model compatible with generic optimization solvers. In this talk we describe the capabilities of Pyomo.dae and demonstrate the concise model implementations of several complex dynamic optimization problems. 3 - The IDAES Framework: Process Modeling and Optimization in Pyomo John Siirola, Sandia National Laboratories, P.O. Box 5800, MS 1326, Albuquerque, NM, 87185, Qi Chen, Ignacio E. Grossmann A cornerstone of the Institute for the Design of Advanced Energy Systems (IDAES) is a modeling and algorithmic framework that addresses the capability gap between state-of-the-art process simulators and general-purpose algebraic modeling languages. The framework, built on Pyomo, provides an extensible process modeling environment that supports optimization-based synthesis, design, control, and uncertainty quantification. This presentation will show how Pyomo was extended into the PSE domain and highlight several case studies. 4 - Mixed-integer Nonlinear Decomposition Toolbox for Pyomo (MindtPy) David E. Bernal, Carnegie Mellon University, 5000 Forbes Ave., Pittsburgh, PA, 15213, United States, Felicity Gong, Qi Chen, Ignacio E. Grossmann This work describes a software toolbox developed in Pyomo, a modeling and optimization application in Python, where decomposition methods for solving mixed-integer nonlinear programs (MINLP) are implemented. Decomposition methods for MINLP rely on the iterative solution of mixed-integer linear programs and nonlinear programming; which have had a steady and considerable improvement in the last years. Several decomposition methods, together with recent algorithmic improvements such as primal heuristics and quadratic cuts, are available in MindtPy. We illustrate the application of this toolbox on a set of convex MINLP problems of varying sizes and degrees of difficulty.

n MC07 North Bldg 123 Modeling, Optimizing, and Controlling Interdependent Networks Sponsored: Optimization/Network Optimization Sponsored Session

Chair: Andres D. Gonzalez, PhD, University of Oklahoma, 202 Boyd St, Room 116b, Norman, OK, 73019, United States 1 - Bayesian Hierarchical Models for Decentralized Decision-making across Interdependent Network Restoration Hesam Talebiyan, Rice University, 6100 Main Street, MS-318, Houston, TX, 77005, United States, Leonardo Duenas-Osorio We propose tractable algorithms and models offering probabilistic decentralization for the realistic decision-making processes guiding the restoration of interdependent networks. We explore Bayesian Hierarchical (BH) models to embed the decision-makers’ judgment calls that guide a formal D-INDP formulation. We demonstrate our models with idealistic as well as real-world interdependent networks. 2 - A Probabilistic Network Flow Approach to the Resilience Analysis of Interdependent Infrastructure Systems Jin-Zhu Yu, Vanderbilt University, Nashville, TN, United States, Hiba Baroud Resilience models of interdependent infrastructure systems often consider static interdependent linkages across systems, ignoring their dynamic nature and corresponding uncertainty. This study proposes a probabilistic network flow-based approach to modelling the resilience of interdependent infrastructures systems under epistemic uncertainty due to the lack of data on historical events, systems properties, and social factors. The proposed approach is illustrated using a case study of the water and power distribution systems serving Shelby County in Tennessee. 3 - A Compositional Approach for Modeling and Control of Layered Networks Siavash Alemzadeh, University of Washington, Seattle, WA, United States, Mehran Mesbahi The analysis of large-scale networks often require the availability of models for the interactions amongst network agents. However, characterizing accurate real- world models of these interactions pose challenges due to inherent complexities. For certain classes of networks, the layering structure allows a compositional approach for modeling. We present a factorization methodology to find mathematical models and determine performance guarantees on layered networks with model uncertainties. This is viable either with the knowledge of the system parameters or through a data-driven process. Examples are provided to verify the presented methodology on modeling real-world problems. 4 - Optimum Evacuation Flows during Probabilistic Network Events Pitu B. Mirchandani, Arizona State University, Schol of Computing, Informatics and, Decision System, Tempe, AZ, 85287, Gita Ketut During catastrophic events, established infrastructures are often damaged and networks become decapitated temporally and spatially. The impacts of cascading disconnectivity, particularly in transportation network, affect the performance of the other connected networks as their operations rely upon the current state of the transportation network. We propose a network flow optimization model for a spatial-temporal damaged network to determine the optimal evacuation flow from multiple origins to multiple destinations competing over the same capacitated network.

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