Solving the Uncapacitated Single Allocation p-Hub Median Problem on GPU

A parallel genetic algorithm (GA) implemented on GPU clusters is proposed to solve the Uncapacitated Single Allocation p-Hub Median problem. The GA uses binary and integer encoding and genetic operators adapted to this problem. Our GA is improved by generated initial solution with hubs located at middle nodes. The obtained experimental results are compared with the best known solutions on all benchmarks on instances up to 1000 nodes. Furthermore, we solve our own randomly generated instances up to 6000 nodes. Our approach outperforms most well-known heuristics in terms of solution quality and time execution and it allows hitherto unsolved problems to be solved

Quadratically-Regularized Optimal Transport on Graphs

Optimal transportation provides a means of lifting distances between points on a geometric domain to distances between signals over the domain, expressed as probability distributions. On a graph, transportation problems can be used to express challenging tasks involving matching supply to demand with minimal shipment expense; in discrete language, these become minimum-cost network flow problems. Regularization typically is needed to ensure uniqueness for the linear ground distance case and to improve optimization convergence; state-of-the-art techniques employ entropic regularization on the transportation matrix. In this paper, we explore a quadratic alternative to entropic regularization for transport over a graph. We theoretically analyze the behavior of quadratically-regularized graph transport, characterizing how regularization affects the structure of flows in the regime of small but nonzero regularization. We further exploit elegant second-order structure in the dual of this problem to derive an easily-implemented Newton-type optimization algorithm.Comment: 27 page

Development of Eco-Friendly Ramp Control for Connected and Automated Electric Vehicles

With on-board sensors such as camera, radar, and Lidar, connected and automated vehicles (CAVs) can sense the surrounding environment and be driven autonomously and safely by themselves without colliding into other objects on the road. CAVs are also able to communicate with each other and roadside infrastructure via vehicle-to-vehicle and vehicle-to-infrastructure communications, respectively, sharing information on the vehicles’ states, signal phase and timing (SPaT) information, enabling CAVs to make decisions in a collaborative manner. As a typical scenario, ramp control attracts wide attention due to the concerns of safety and mobility in the merging area. In particular, if the line-of-the-sight is blocked (because of grade separation), then neither mainline vehicles nor on-ramp vehicles may well adapt their own dynamics to perform smoothed merging maneuvers. This may lead to speed fluctuations or even shockwave propagating upstream traffic along the corridor, thus potentially increasing the traffic delays and excessive energy consumption. In this project, the research team proposed a hierarchical ramp merging system that not only allowed microscopic cooperative maneuvers for connected and automated electric vehicles on the ramp to merge into mainline traffic flow, but also had controllability of ramp inflow rate, which enabled macroscopic traffic flow control. A centralized optimal control-based approach was proposed to both smooth the merging flow and improve the system-wide mobility of the network. Linear quadratic trackers in both finite horizon and receding horizon forms were developed to solve the optimization problem in terms of path planning and sequence determination, and a microscopic electric vehicle (EV) energy consumption model was applied to estimate the energy consumption. The simulation results confirmed that under the regulated inflow rate, the proposed system was able to avoid potential traffic congestion and improve the mobility (in terms of average speed) as much as 115%, compared to the conventional ramp metering and the ramp without any control approach. Interestingly, for EVs (connected and automated EVs in this study), the improved mobility may not necessarily result in the reduction of energy consumption. The “sweet spot” of average speed ranges from 27–34 mph for the EV models in this study.View the NCST Project Webpag

Dynamical Optimal Transport on Discrete Surfaces

We propose a technique for interpolating between probability distributions on discrete surfaces, based on the theory of optimal transport. Unlike previous attempts that use linear programming, our method is based on a dynamical formulation of quadratic optimal transport proposed for flat domains by Benamou and Brenier [2000], adapted to discrete surfaces. Our structure-preserving construction yields a Riemannian metric on the (finite-dimensional) space of probability distributions on a discrete surface, which translates the so-called Otto calculus to discrete language. From a practical perspective, our technique provides a smooth interpolation between distributions on discrete surfaces with less diffusion than state-of-the-art algorithms involving entropic regularization. Beyond interpolation, we show how our discrete notion of optimal transport extends to other tasks, such as distribution-valued Dirichlet problems and time integration of gradient flows