Related papers: Design of Transit Networks: Global Optimization of…
A general Continuum Approximation (CA) model is proposed for optimizing transit network designs (TND) in grid cities under spatially heterogeneous demand. While conventional studies often assume rigid geometric line configurations (e.g.,…
Continuum Approximation (CA) is an efficient and parsimonious technique for modeling complex logistics problems. In this paper,we review recent studies that develop CA models for transportation, distribution and logistics problems with the…
Motion planning for autonomous vehicles requires generating collision-free and dynamically feasible trajectories in complex environments under real-time constraints. While nonlinear optimal control formulations provide high-fidelity…
Optimization has been widely used to generate smooth trajectories for motion planning. However, existing trajectory optimization methods show weakness when dealing with large-scale long trajectories. Recent advances in parallel computing…
In this work, we construct a novel numerical method for solving the multi-marginal optimal transport problems with Coulomb cost. This type of optimal transport problems arises in quantum physics and plays an important role in understanding…
The complex spatial-temporal correlations in transportation networks make the traffic forecasting problem challenging. Since transportation system inherently possesses graph structures, many research efforts have been put with graph neural…
The Adaptive Cross Approximation (ACA) method is widely used to approximate admissible blocks of hierarchical matrices, or H-matrices, from discretized operators in the boundary integral method. These matrices are fully populated, making…
An approximate formulation of a robust geometric program (RGP) as a convex program is proposed. Interest in using geometric programs (GPs) to model complex engineering systems has been growing, and this has motivated explicitly modeling the…
In this paper the preliminary design of multiple gravity-assist trajectories is formulated as a global optimization problem. An analysis of the structure of the solution space reveals a strong multimodality, which is strictly dependent on…
In this paper, we present a generic framework to extend existing uniformly optimal convex programming algorithms to solve more general nonlinear, possibly nonconvex, optimization problems. The basic idea is to incorporate a local search…
Trajectory optimization offers mature tools for motion planning in high-dimensional spaces under dynamic constraints. However, when facing complex configuration spaces, cluttered with obstacles, roboticists typically fall back to…
Large optimal transport problems can be approached via domain decomposition, i.e. by iteratively solving small partial problems independently and in parallel. Convergence to the global minimizers under suitable assumptions has been shown in…
Faster pathfinding in time-dependent transport networks is an important and challenging problem in navigation systems. There are two main types of transport networks: road networks for car driving and public transport route network. The…
We introduce and study conic geometric programs (CGPs), which are convex optimization problems that unify geometric programs (GPs) and conic optimization problems such as semidefinite programs (SDPs). A CGP consists of a linear objective…
Trajectory optimization methods for motion planning attempt to generate trajectories that minimize a suitable objective function. Such methods efficiently find solutions even for high degree-of-freedom robots. However, a globally optimal…
In most cities, transit consists solely of fixed-route transportation, whence the inherent limited Quality of Service for travellers in suburban areas and during off-peak periods. On the other hand, completely replacing fixed-route (FR)…
In this work, we propose a generalized alternating nonlinear generalized minimal residual method (GA-NGMRES) to accelerate first-order optimization schemes for PDE-constrained optimization problems governed by transport equations. We apply…
Capacity expansions as well as its reduction have been widely anticipated as important countermeasures for traffic congestion. Although capacity expansion had been traditionally well noticed as a congestion mitigation measure, but it was…
Geometric programming (GP) provides a power tool for solving a variety of optimization problems. In the real world, many applications of geometric programming (GP) are engineering design problems in which some of the problem parameters are…
Spatiotemporal Graph Neural Networks (ST-GNNs) and Transformers have shown significant promise in traffic forecasting by effectively modeling temporal and spatial correlations. However, rapid urbanization in recent years has led to dynamic…