2015 Informs Annual Meeting

MD13

INFORMS Philadelphia – 2015

MD13 13-Franklin 3, Marriott Stochastic Integer Programming Sponsor: Optimization/Optimization Under Uncertainty Sponsored Session

inhomogeneous tissue or irradiation with proton fields. We extend the model to account for tissue inhomogeneity, proton range errors, and organ motion. 2 - Robust Optimization Methods for Breast Cancer Radiation Therapy Houra Mahmoudzadeh, University of Toronto, Toronto ON, Canada,, houra@mie.utoronto.ca, Timothy Chan, Thomas Purdie We explore robust optimization methods for improving the quality of treatment in left-sided breast cancer radiation therapy. Our robust models take into account breathing uncertainty and minimize the dose to the organs at risk while meeting the clinical dose-volume limits on the cancerous target. We use clinical data from several breast cancer patients and compare the outcomes of our robust models with those of the current clinical methods. 3 - Chance-constrained Robust Optimization in Proton Therapy to Account for Beam Delivery Uncertainties Yu An, Mayo Clinic, 5777 East Mayo Blvd., Phoenix, AZ, 85054, United States of America, an.yu@mayo.edu, Jianming Liang, Wei Liu We propose a chance-constrained model in intensity-modulated proton therapy treatment planning by explicitly accounting for range and patient setup uncertainties in optimization algorithm. Decomposition methods are applied to render the large-scale optimization problems tractable and achieve the best trade- off between plan quality and robustness. The results are then checked by patient population study to demonstrate the statistically significant advantages of our planning method. 4 - Robust Spatiotemporally Integrated Fractionation in Radiotherapy Archis Ghate, University of Washington, Industrial & Systems Engineering, University of Washington Box 352650, Seattle, United States of America, archis@uw.edu, Ali Ajdari Feasibility of the fluence-maps in the spatiotemporally integrated fractionation problem crucially depends on the linear-quadratic dose-response parameters of the organs-at-risk. We present a robust formulation of this problem whereby the resulting dosing schedule remains feasible as long as the dose-response parameters vary within a known range. This robust model is non-convex and high-dimensional. We discuss approximate solution techniques rooted in convex programming. MD15 15-Franklin 5, Marriott Distributed Convex Optimization Sponsor: Optimization/Nonlinear Programming Sponsored Session Chair: Necdet Serhat Aybat, Assistant Professor, Industrial Engineering Dept., Penn State University, University Park, PA, United States of America, nsa10@engr.psu.edu 1 - A New Globally Convergent Incremental Newton Method Mert Gurbuzbalaban, Massachusetts Institute of Technology, 32 Vassar St, Cambridge, MA, United States of America, mertg@mit.edu, Asu Ozdaglar, Pablo Parrilo We develop and analyze a new globally convergent incremental Newton method for minimizing the sum of strongly convex functions, motivated by machine learning problems over large data sets and distributed optimization over networks. We discuss its convergence rate and prove its linear convergence under some assumptions. 2 - Multiagent Distributed Admm: Rate of Convergence Ali Makhdoumi, Massachusetts Institute of Technology, 32 Vassar St, Cambridge, MA, 02139, United States of America, makhdoum@mit.edu, Asu Ozdaglar We consider a multi agent optimization problem where a network of agents collectively solves a global optimization problem with the objective function given by the sum of locally known convex functions. This problem arises in many applications in large-scale distributed statistical estimation. We propose a fully distributed ADMM algorithm and characterize its rate of convergence as well as its dependence on the network structure. 3 - An Asynchronous Distributed Proximal Method for Composite Convex Optimization Zi Wang, Penn State University, 1400 Martin St, Apt. 2112, State College, PA, 16803, United States of America, zxw121@psu.edu, Necdet Serhat Aybat, Garud Iyengar We propose an asynchronous distributed first-order augmented Lagrangian (DFAL) algorithm to minimize sum of composite convex functions, where each term is a private function to one node, and only nodes connected by an edge can communicate. We show any limit point of iterates is optimal; an eps-optimal and eps-feasible solution can be computed with probability at least 1-p within O(1/eps log(1/p)) communications. We demonstrate the efficiency of DFAL on large scale sparse-group LASSO problems.

Chair: Kibaek Kim, Argonne National Laboratory, 9700 South Cass Avenue, Argonne, IL, 60439, United States of America, kimk@anl.gov 1 - A Scalable Approach to Solving Multi-stage Stochastic Integer Programs Osman Ozaltin, Assistant Professor, North Carolina State University, Raleigh, NC, United States of America, oyozalti@ncsu.edu, Burhaneddin Sandikci Despite being a flexible modeling framework, multi-stage SPs are not widely adopted in practice, mostly due to their unbearable size. Moreover, incorporating integer variables renders multi-stage SPs even less tractable. We propose a bounding-based solution approach, which does not assume convexity but it rather relies on scenario decomposition and is inherently parallelizable. Our results demonstrate that the proposed method scales nicely with problem size and produces high quality solutions. 2 - On Solving General Two-stage Stochastic Programs Manish Bansal, Postdoctoral Fellow, Department of Industrial Engineering and Management Science, Northwestern University, 2145 Sheridan Road, Evanston, IL, 60208, United States of America, manish.bansal@northwestern.edu, Sanjay Mehrotra We study general two-stage stochastic programs (TSSPs) and present conditions under which the second stage programs can be convexified. This generalizes the results of Bansal et al. (2015) for two-stage stochastic mixed integer programs. We present finitely convergent decomposition algorithms to solve many classes of TSSPs including TSSP with some non-convex program in the second stage. We computationally evaluate our convexification approach by solving two-stage stochastic lot-sizing problems. 3 - Algorithmic Innovations and Software for the Dual Decomposition Method Applied to SMIP Kibaek Kim, Argonne National Laboratory, 9700 South Cass Avenue, Argonne, IL, 60439, United States of America, kimk@anl.gov, Victor M. Zavala We develop algorithmic innovations for the dual decomposition method to address two-stage stochastic programs with mixed-integer recourse and provide a parallel software implementation. Our innovations include the derivation of valid inequalities that tighten Lagrangian subproblems and the stabilization of dual variables by solving the master problem with a primal-dual interior point method and provide termination criteria that guarantee finite termination of the algorithm. 4 - Updates to PIPS-SBB: A Parallel Distributed Memory Stochastic Mip Solver Geoff Oxberry, Lawrence Livermore National Laboratory, P.O. Box 808, L-792, Livermore, CA, United States of America, Deterministic equivalent formulations of stochastic MIPs from applications such as unit commitment (UC) can exceed available memory on a single workstation. To overcome this limitation, we have developed PIPS-SBB, a parallel distributed memory stochastic MIP solver based on the distributed memory stochastic LP solver PIPS-S. Here, we discuss ongoing work on PIPS-SBB, with a focus on parallel implementations of B&B techniques. We also present a path forward to solving large UC problem instances. MD14 14-Franklin 4, Marriott Robust Optimization in Radiation Therapy Planning Sponsor: Optimization/Optimization Under Uncertainty Sponsored Session Chair: Wei Liu, Assistant Professor, Mayo Clinic Arizona, 5777 E Mayo Blvd., Phoenix, AZ, 85054, United States of America, Liu.Wei@mayo.edu 1 - Scenario-based Radiotherapy Margins: Handling Tissue Inhomogeneity, Range Errors, and Organ Motion Rasmus Bokrantz, RaySearch Laboratories, Sveavägen 44, Stockholm, 111 34, Sweden, rasmus.bokrantz@raysearchlabs.com, Albin Fredriksson We consider a scenario-based optimization formulation to handle the effects of errors in radiotherapy planning. The formulation coincides with margin-based planning if the implicit assumptions made when the margins are delineated are valid, but also generalizes to more difficult situations such as irradiation of oxberry1@llnl.gov, Deepak Rajan, Thomas Edmunds, Pedro Sotorrio, Lluís Miquel Munguía, Cosmin Petra

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