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In this paper we investigate real-time, dynamic traffic optimization in railway systems. In order to enable practical solution times, we operate the optimizer in a receding horizon fashion and with optimization horizons that are shorter than the full path to destinations, using a model predictive control (MPC) approach. We present new procedures to establish safe prediction horizons, providing formal guarantees that the system is operated in a way that satisfies hard safety constraints despite the fact that not all future train interactions are taken into account, by characterizing the minimal required optimization horizons. We also show that any feasible solution to our proposed models is sufficient to maintain a safe, automated operation of the railway system, providing an upper bound on the computations strictly required. Additionally, we show that these minimal optimization horizons also characterize an upper bound on computations required to construct a feasible solution for any arbitrary optimization horizon, paving the way for anytime algorithms. Finally, our results enable systematic solution reuse, when previous schedules are available. We test our approach on a detailed simulation environment of a real-world railway system used for freight transport.

This paper addresses the problem of planning time-optimal trajectories for multiple cooperative agents along specified paths through a static road network. Vehicle interactions at intersections create non-trivial decisions, with complex flow-on effects for subsequent interactions. A globally optimal, minimum time trajectory is found for all vehicles using Mixed Integer Linear Programming (MILP). Computational performance is improved by minimising binary variables using iteratively applied targeted collision constraints, and efficient goal constraints. Simulation results in an open-pit mining scenario compare the proposed method against a fast heuristic method and a reactive approach based on site practices. The heuristic is found to scale better with problem size while the MILP is able to avoid local minima., Comment: Submitted to ICRA 2019 on 16/9/2018

The weekly maintenance schedule specifies when maintenance activities should be performed on the equipment, taking into account the availability of workers and maintenance bays, and other operational constraints. The current approach to generating this schedule is labour intensive and requires coordination between the maintenance schedulers and operations staff to minimise its impact on the operation of the mine. This paper presents methods for automatically generating this schedule from the list of maintenance tasks to be performed, the availability roster of the maintenance staff, and time windows in which each piece of equipment is available for maintenance. Both Mixed-Integer Linear Programming (MILP) and genetic algorithms are evaluated, with the genetic algorithm shown to significantly outperform the MILP. Two fitness functions for the genetic algorithm are also examined, with a linear fitness function outperforming an inverse fitness function by up to 5% for the same calculation time. The genetic algorithm approach is computationally fast, allowing the schedule to be rapidly recalculated in response to unexpected delays and breakdowns.

Lagrangian duality in mixed integer optimization is a useful framework for problems decomposition and for producing tight lower bounds to the optimal objective, but in contrast to the convex counterpart, it is generally unable to produce optimal solutions directly. In fact, solutions recovered from the dual may be not only suboptimal, but even infeasible. In this paper we concentrate on large scale mixed--integer programs with a specific structure that is of practical interest, as it appears in a variety of application domains such as power systems or supply chain management. We propose a solution method for these structures, in which the primal problem is modified in a certain way, guaranteeing that the solutions produced by the corresponding dual are feasible for the original unmodified primal problem. The modification is simple to implement and the method is amenable to distributed computations. We also demonstrate that the quality of the solutions recovered using our procedure improves as the problem size increases, making it particularly useful for large scale instances for which commercial solvers are inadequate. We illustrate the efficacy of our method with extensive experimentations on a problem stemming from power systems., Comment: 23 pages, 9 figures