Optimization and Control (math.OC)

Abstract: The solution of the Multi-Depot Vehicle Scheduling Problem (MDVSP) can often be improved substantially by incorporating Trip Shifting (TS) as a model feature. By allowing departure times to deviate a few minutes from the original timetable, new combinations of trips may be carried out by the same vehicle, thus leading to more efficient scheduling. However, explicit modeling of each potential trip shift quickly causes the problem to get prohibitively large for current solvers, such that researchers and practitioners were obligated to resort to heuristic methods to solve large instances. In this paper, we develop a Dynamic Discretization Discovery algorithm that guarantees an optimal continuous-time solution to the MDVSP-TS without explicit consideration of all trip shifts. It does so by iteratively solving and refining the problem on a partially time-expanded network until the solution can be converted to a feasible vehicle schedule on the fully time-expanded network. Computational results demonstrate that this algorithm outperforms the explicit modeling approach by a wide margin and is able to solve the MDVSP-TS even when many departure time deviations are considered.

Abstract: An optimal control problem for longitudinal motions of a thin elastic rod is considered. We suppose that a normal force, which changes piecewise constantly along the rod's length, is applied to the cross-section so that the positions of force jumps are equidistantly placed along the length. Additionally, external loads act at the rod ends. These distributed force and boundary loads are considered as control functions of the dynamic system. Given initial and terminal states at fixed time instants, the problem is to minimize the mean mechanical energy stored in the rod during its motion. We replace the classical wave equation with a variational problem solved via traveling waves defined on a special time-space mesh. For a uniform rod, the shortest admissible time horizon is estimated exactly, and the exact optimal control law is symbolically found in a recurrent way.

Abstract: Localization is a fundamental enabler technology for many applications, like vehicular networks, IoT, and even medicine. While Global Navigation Satellite Systems solutions offer great performance, it is unavailable in scenarios like indoor or underwater environments, and, for large networks, the cost of instrumentation is prohibitive. We develop a localization algorithm from ranges and bearings, suitable for generic mobile networks of agents. Our algorithm is built on a tight convex relaxation of the Maximum Likelihood position estimator for a generic network. To serve positioning to mobile agents, a horizon-based version is developed accounting for velocity measurements at each agent. To solve the convex problem, a distributed gradient-based method is provided. This constitutes an advantage over other centralized approaches, which usually exhibit high latency for large networks and present a single point of failure. Additionally, the algorithm estimates all required parameters and effectively becomes parameter-free. Our solution to the dynamic network localization problem is theoretically well-founded and still easy to understand. We obtain a parameter-free, outlier-robust and trajectory-agnostic algorithm, with nearly constant positioning error regardless of the trajectories of agents and anchors, achieving better or comparable performance to state-of-the-art methods, as our simulations show. Furthermore, the method is distributed, convex and does not require any particular anchor configuration.