We develop a Model Predictive Control (MPC) approach for condition-based maintenance planning under uncertainty for railway infrastructure systems composed of multiple components. Piecewise-affine models with uncertain parameters are used to capture both the nonlinearity and uncertainties in the deterioration process. To keep a balance between robustness and optimality, we formulate the MPC optimization problem as a chance-constrained problem, which ensures that the constraints, e.g., bounds on the degradation level, are satisfied with a given probabilistic guarantee. Two distributed algorithms, one based on Dantzig-Wolfe decomposition and the other derived from a constraint-tightening technique, are proposed to improve the scalability of the MPC approach. Computational experiments show that the distributed method based on Dantzig-Wolfe decomposition performs the best in terms of computational time and convergence to global optimality. By comparing the chance-constrained MPC approaches with deterministic approach, and traditional time-based maintenance approach, we show that despite their high computational requirements, chance-constrained MPC approaches are cost-efficient and robust in the presence of uncertainties.

We develop a multi-level decision making approach for optimal condition-based maintenance planning of a railway network divided into a large number of sections with independent stochastic deterioration dynamics. At higher level, a chance-constrained Model Predictive Control (MPC) controller determines the long-term section-wise maintenance plan, minimizing condition deterioration and maintenance costs for a finite planning horizon, while ensuring that the deterioration level of each section stays below the maintenance threshold with a given probabilistic guarantee in the presence of parameter uncertainty. The resulting large MPC optimization problem containing both continuous and discrete decision variables is solved using Dantzig-Wolfe decomposition to improve the scalability of the proposed approach. At a lower level, the optimal short-term scheduling of the maintenance interventions suggested by the high-level controller and the optimal routing of the corresponding maintenance crew is formulated as a capacitated arc routing problem, which is solved exactly by transforming it into a node routing problem. The proposed approach is illustrated by a numerical case study on the optimal treatment of squats of a regional Dutch railway network. Simulation results show that the proposed approach is robust, non-conservative, and scalable.

In this paper, distributed optimization approaches are developed for the planning of maintenance operations of large-scale railway infrastructure formulated as a Mixed-Integer Linear Programming (MILP) problem. The proposed planning problem is solved using three different distributed optimization schemes: Parallel Augmented Lagrangian Relaxation (PALR), Alternating Direction Method of Multipliers (ADMM), and Distributed Robust Safe But Knowledgeable (DRSBK). The original distributed algorithms are modified to handle the non-convex nature of the optimization problem and to improve the solution quality. The results of large-scale test instances show that DRSBK can outperform the other distributed approaches, by providing the closest-to-optimum solution while requiring the lowest computation time.

We consider optimal scheduling of track maintenance activities for a railway network divided into sections. The goal is to find an optimal time schedule for the maintenance activities and optimal routes for the maintenance crew (including all necessary equipment and technicians) that minimize the total setup costs and the travel costs over the whole planning horizon. The maintenance time budget, which can be the same, different, or flexible for each period, and the minimum time to maintain a section are also taken into account. We recast the track maintenance scheduling problem with three different settings as three variants of the Capacitated Arc Routing Problem with Fixed cost (CARPF), which are solved by transforming them into three node routing problems. The proposed approach is demonstrated using a case study of a part of the Dutch regional network.

This paper develops a multi-level decision making approach for the optimal planning of maintenance operations of railway infrastructures, which are composed of multiple components divided into basic units for maintenance. Scenario-based chance-constrained Model Predictive Control (MPC) is used at the high level to determine an optimal long-term component-wise intervention plan for a railway infrastructure, and the Time Instant Optimization (TIO) approach is applied to transform the MPC optimization problem with both continuous and integer decision variables into a nonlinear continuous optimization problem. The middle-level problem determines the allocation of time slots for the maintenance interventions suggested at the high level to optimize the trade-off between traffic disruption and the setup cost of maintenance slots. Based on the high-level intervention plan, the low-level problem determines the optimal clustering of the basic units to be treated by a maintenance agent, subject to the time limit imposed by the maintenance slots. The proposed approach is applied to the optimal treatment of squats, with real data from the Eindhoven-Weert line in the Dutch railway network.

This paper develops a multilevel decision making approach based on model predictive control (MPC) for condition-based maintenance of rail. We address a typical railway surface defect called “squat”, in which three maintenance actions can be considered: no maintenance, grinding, and replacement. A scenario-based scheme is applied to address the uncertainty in the deterioration dynamics of the key performance indicator for each track section, and a piecewise-affine model is used to approximate the expected dynamics, which is to be optimized by a scenario-based MPC controller at the high level. A static optimization problem involving clustering and mixed integer linear programming is solved at the low level to produce an efficient grinding and replacing schedule. A case study using real measurements obtained from a Dutch railway line between Eindhoven and Weert is performed to demonstrate the merits of the proposed approach.