Optym (United States)

In this article, we consider the misspecified optimization problem of minimizing a convex function <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$f(x;\theta ^*)$</tex-math></inline-formula> in <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$x$</tex-math></inline-formula> over a conic constraint set represented by <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$h(x;\theta ^*) \in \mathcal {K}$</tex-math></inline-formula> , where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\theta ^*$</tex-math></inline-formula> is an unknown (or misspecified) vector of parameters, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {K}$</tex-math></inline-formula> is a closed convex cone, and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$h$</tex-math></inline-formula> is affine in <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$x$</tex-math></inline-formula> . Suppose that <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\theta ^*$</tex-math></inline-formula> is unavailable but may be learnt by a separate process that generates a sequence of estimators <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\theta _k$</tex-math></inline-formula> , each of which is an increasingly accurate approximation of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\theta ^*$</tex-math></inline-formula> . We develop a first-order inexact augmented Lagrangian (AL) scheme for computing an optimal solution <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$x^*$</tex-math></inline-formula> corresponding to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\theta ^*$</tex-math></inline-formula> while simultaneously learning <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\theta ^*$</tex-math></inline-formula> . In particular, we derive rate statements for such schemes when the penalty parameter sequence is either constant or increasing and derive bounds on the overall complexity in terms of proximal gradient steps when AL subproblems are inexactly solved via an accelerated proximal gradient scheme. Numerical results for a portfolio optimization problem with a misspecified covariance matrix suggest that these schemes perform well in practice, while naive sequential schemes may perform poorly in comparison.

Overlooked for decades, the humoral alloimmune response is increasingly recognized as a leading cause of graft loss after transplantation. However, improvement in the diagnosis of antibody-mediated rejection has not yet translated into better outcomes for transplanted patients. After an update on B cell physiology and antibody generation, the 2015 Beaune Seminar in Transplant Research challenged the conventional view of antibody-mediated rejection pathophysiology and discussed the latest promising therapeutic approaches.

This article presents a reliability-based evacuation route planning model that seeks to find the relationship between the clearance time, number of evacuation paths, and congestion probability during an evacuation. Most of the existing models for network evacuation assume deterministic capacity estimates for road links without taking into account the uncertainty in capacities induced by myriad external conditions. Only a handful of models exist in the literature that account for capacity uncertainty of road links. A dynamic network–based evacuation model is extended by incorporating probabilistic arc capacity constraints and a minimum-cost network flow problem is formulated that finds a lower bound on the clearance time within the framework of a chance-constrained programming technique. Network breakdown minimization principles for traffic flow in evacuation planning problem are applied and a path-based evacuation routing and scheduling model is formulated. Given the horizon time for evacuation, the model selects the evacuation paths and finds flows on the selected paths that result in the minimum congestion in the network along with the reliability of the evacuation plan. Numerical examples are presented and the effectiveness of the stochastic models in evacuation planning is discussed. It is shown that the reliability-based evacuation plan is conservative compared with plans made using a deterministic model. Stochastic models guarantee that congestion can be avoided with a higher confidence level at the cost of an increased clearance time.

Clinicians face difficult treatment decisions in contexts that are not well addressed by available evidence as formulated based on research. The digitization of medicine provides an opportunity for clinicians to collaborate with researchers and data scientists on solutions to previously ambiguous and seemingly insolvable questions. But these groups tend to work in isolated environments, and do not communicate or interact effectively. Clinicians are typically buried in the weeds and exigencies of daily practice such that they do not recognize or act on ways to improve knowledge discovery. Researchers may not be able to identify the gaps in clinical knowledge. For data scientists, the main challenge is discerning what is relevant in a domain that is both unfamiliar and complex. Each type of domain expert can contribute skills unavailable to the other groups. “Health hackathons” and “data marathons”, in which diverse participants work together, can leverage the current ready availability of digital data to discover new knowledge. Utilizing the complementary skills and expertise of these talented, but functionally divided groups, innovations are formulated at the systems level. As a result, the knowledge discovery process is simultaneously democratized and improved, real problems are solved, cross-disciplinary collaboration is supported, and innovations are enabled.

Abstract The multicommodity flow problem is a generalization of the minimum cost network flow problem. In this problem, several commodities governed by their own network flow constraints share the same underlying network. Given the supplies and demands of the different commodities, the shared capacity of each arc in the network, and cost of flow of each commodity on each arc, the objective is to determine the flow that minimizes the total cost. The multicommodity flow problem has been extensively applied to solve problems in areas such as transportation, telecommunications, and scheduling. In this article, we introduce the multicommodity flow problem, outline some of its applications, and describe efficient methods to solve the problem.

In this paper, we study the curfew planning problem (CPP) encountered by railroads for the maintenance of their railway tracks. The CPP is to design an optimal annual timetable to complete a given set of repairs and replacement jobs (rail work and tie work) on the railway tracks for a set of crews specialized in rail work (rail crew) or tie work (tie crew). We develop the work schedule for each crew such that the disruptions in train routes because of subdivision curfews are minimized. A subdivision is said to be under curfew if any crew is working in it. The solution to the problem must also satisfy several operational and regulatory requirements such as the crew continuity, time windows, the maximum interproject distance travelled by crews, etc. Our paper presents four solution approaches for the CPP: (i) time-space network model (TSNM), (ii) duty-generation model (DGM), (iii) column-generation model (CGM), and (iv) decomposition-based heuristics. We solve each model using CPLEX and present the computational results based on real-life instances.

The intensity modulated radiation therapy (IMRT) treatment planning problem consists of several subproblems which are typically solved sequentially. We seek to combine two of the subproblems: the beam orientation optimization (BOO) problem and the fluence map optimization (FMO) problem. The BOO problem is the problem of selecting the beam orientations to deliver radiation to the patient. The FMO problem is the problem of determining the amount of radiation intensity, or fluence, of each beamlet in each beam. The solution to the FMO problem measures the quality of a beam set, but the majority of previous BOO studies rely on heuristics and approximations to gauge the quality of the beam set. In contrast with these studies, we use an exact measure of the treatment plan quality attainable using a given beam set, which ensures convergence to a global optimum in the case of our simulated annealing algorithm and a local optimum in the case of our local search algorithm. We have also developed a new neighborhood structure that allows for faster convergence using our simulated annealing and local search algorithms, thus reducing the amount of time required to obtain a good solution. Finally, we show empirically that we can generate clinically acceptable treatment plans that require fewer beams than in current practice. This may reduce the length of treatment time, which is an important clinical consideration in IMRT.

Abstract This paper develops a new model for allocating demand from retailers (or customers) to a set of production/storage facilities. A producer manufactures a product in multiple production facilities, and faces demand from a set of retailers. The objective is to decide which of the production facilities should satisfy each retailer's demand, in order minimize total production, inventory holding, and assignment costs (where the latter may include, for instance, variable production costs and transportation costs). Demand occurs continuously in time at a deterministic rate at each retailer, while each production facility faces fixed‐charge production costs and linear holding costs. We first consider an uncapacitated model, which we generalize to allow for production or storage capacities. We then explore situations with capacity expansion opportunities. Our solution approach employs a column generation procedure, as well as greedy and local improvement heuristic approaches. A broad class of randomly generated test problems demonstrates that these heuristics find high quality solutions for this large‐scale cross‐facility planning problem using a modest amount of computation time. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005.