A PARTAN-Accelerated Frank-Wolfe Algorithm for Large-Scale SVM Classification

Frank-Wolfe algorithms have recently regained the attention of the Machine Learning community. Their solid theoretical properties and sparsity guarantees make them a suitable choice for a wide range of problems in this field. In addition, several variants of the basic procedure exist that improve its theoretical properties and practical performance. In this paper, we investigate the application of some of these techniques to Machine Learning, focusing in particular on a Parallel Tangent (PARTAN) variant of the FW algorithm that has not been previously suggested or studied for this type of problems. We provide experiments both in a standard setting and using a stochastic speed-up technique, showing that the considered algorithms obtain promising results on several medium and large-scale benchmark datasets for SVM classification

Traffic Assignment Problem for Pedestrian Networks

The estimation of pedestrian traffic in urban areas is often performed with computationally intensive microscopic models that usually suffer from scalability issues in large-scale walking networks. In this study, we present a new macroscopic user equilibrium traffic assignment problem (UE-pTAP) framework for pedestrian networks while taking into account fundamental microscopic properties such as self-organization in bidirectional streams and stochastic walking travel times. We propose four different types of pedestrian volume-delay functions (pVDFs), calibrate them with empirical data, and discuss their implications on the existence and uniqueness of the assignment solution. We demonstrate the applicability of the developed UE-pTAP framework in a small network as well as a larger scale network of Sydney footpaths

System-Optimal Routing of Traffic Flows with User Constraints in Networks with Congestion

The design of route-guidance systems faces a well-known dilemma. The approach that theoretically yields the system-optimal traffic pattern may discriminate against some users, for the sake of favoring others. Proposed alternate models, however, do not directly address the system perspective and may result in inferior performance. We propose a novel model and corresponding algorithms to resolve this dilemma. We present computational results on real-world instances and compare the new approach with the well-established traffic assignment model. The quintessence is that system-optimal routing of traffic flow with explicit integration of user constraints leads to a better performance than the user equilibrium while simultaneously guaranteeing a superior fairness compared to the pure system optimum

Equilibrium-Based Workload Balancing for Robust Emergency Response Operations in Metropolitan Areas

This thesis presents an equilibrium-based modeling framework for emergency response (ER) workload balancing to achieve robust operation in large-scale metropolitan areas. The problem is formulated as a non-linear mathematical program (NLP), which determines the optimal workload cutoff for each ER station such that the weighted sum of the area-wide expected response time and its variation are minimized. The concept of Marginal Cost of Uncertainty (MCU) is introduced to measure the impact of a station’s workload increase on the area-wide service performance. The solution of the NLP is proved to be equivalent to a state of equilibrium in which all stations have a minimum MCU. An iterative solution methodology is developed, which adopts a modified version of the Frank-Wolfe decomposition algorithm for convex optimization. The workload is iteratively shifted among adjacent stations until the state of equilibrium is achieved. At equilibrium, no station can reduce its MCU value by unilaterally shifting a part of its workload to any other station(s) in the area. The developed framework is applied to determine the optimal workload balancing strategy for 58 fire stations serving the City of Dallas. The framework is shown to enhance the robustness of the ER service especially under operation scenarios with imbalanced workloads

A stochastic simulation model to support designs of experiments on transportation evacuation planning

This research presents a new discrete-event simulation model, the DOE_EVAC, that can (i) effectively simulate alternative modes of transportation during evacuations, (ii) support designs of experiments, thus, provide the users (e.g., emergency planners and traffic engineers) with means to investigate "what-if" scenarios with sound statistical analysis capabilities, and (iii) allow the users to build and execute these models without having to know complex simulation or coding languages.The contributions of this research are threefold. First, this research adopts designs of experiments to furnish users with statistical support to investigate "what-if" scenarios. Second, the DOE_EVAC model resolves existing issues of current simulation transportation evacuation modeling approaches by improving the initial system setup and supporting the stochastic traffic loading process. It allows users to implement and analyze various traffic management strategies, and is capable of rerouting traffic due to critical infrastructure failures during evacuation. DOE_EVAC also supports user-interruptions during simulation runs so that changes on the system can be executed. Finally, the DOE_EVAC model does not require the user to have any knowledge of specialized simulation or coding language as it relies only on four required (and one optional) data files supplied by the users to execute. A sample design of experiment is illustrated to show the multiple simulation run capabilities of the DOE_EVAC model and the ability of the DOE_EVAC to allow users to manipulate data that are typically inaccessible in existing evacuation models

Conditional Gradient Methods

The purpose of this survey is to serve both as a gentle introduction and a coherent overview of state-of-the-art Frank--Wolfe algorithms, also called conditional gradient algorithms, for function minimization. These algorithms are especially useful in convex optimization when linear optimization is cheaper than projections. The selection of the material has been guided by the principle of highlighting crucial ideas as well as presenting new approaches that we believe might become important in the future, with ample citations even of old works imperative in the development of newer methods. Yet, our selection is sometimes biased, and need not reflect consensus of the research community, and we have certainly missed recent important contributions. After all the research area of Frank--Wolfe is very active, making it a moving target. We apologize sincerely in advance for any such distortions and we fully acknowledge: We stand on the shoulder of giants.Comment: 238 pages with many figures. The FrankWolfe.jl Julia package (https://github.com/ZIB-IOL/FrankWolfe.jl) providces state-of-the-art implementations of many Frank--Wolfe method