Recoverable Robustness by Column Generation

Real-life planning problems are often complicated by the occurrence of disturbances, which imply that the original plan cannot be followed anymore and some recovery action must be taken to cope with the disturbance. In such a situation it is worthwhile to arm yourself against common disturbances. Well-known approaches to create plans that take possible, common disturbances into account are robust optimization and stochastic programming. Recently, a new approach has been developed that combines the best of these two: recoverable robustness. In this paper, we apply the technique of column generation to find solutions to recoverable robustness problems. We consider two types of solution approaches: separate recovery and combined recovery. We show our approach on two example problems: the size robust knapsack problem, in which the knapsack size may get reduced, and the demand robust shortest path problem, in which the sink is uncertain and the cost of edges may increase

Algorithm Engineering in Robust Optimization

Robust optimization is a young and emerging field of research having received a considerable increase of interest over the last decade. In this paper, we argue that the the algorithm engineering methodology fits very well to the field of robust optimization and yields a rewarding new perspective on both the current state of research and open research directions. To this end we go through the algorithm engineering cycle of design and analysis of concepts, development and implementation of algorithms, and theoretical and experimental evaluation. We show that many ideas of algorithm engineering have already been applied in publications on robust optimization. Most work on robust optimization is devoted to analysis of the concepts and the development of algorithms, some papers deal with the evaluation of a particular concept in case studies, and work on comparison of concepts just starts. What is still a drawback in many papers on robustness is the missing link to include the results of the experiments again in the design

The Recoverable Robust Tail Assignment Problem

This is the author accepted manuscript. The final version is available from Institute for Operations Research and the Management Sciences (INFORMS) via the DOI in this record Schedule disruptions are commonplace in the airline industry with many flight-delaying events occurring each day. Recently there has been a focus on introducing robustness into airline planning stages to reduce the effect of these disruptions. We propose a recoverable robustness technique as an alternative to robust optimisation to reduce the effect of disruptions and the cost of recovery. We formulate the recoverable robust tail assignment problem (RRTAP) as a stochastic program, solved using column generation in the master and subproblems of the Benders decomposition. We implement a two-phase algorithm for the Benders decomposition incorporating the Magnanti-Wong [21] enhancement techniques. The RRTAP includes costs due to flight delays, cancellation, and passenger rerouting, and the recovery stage includes cancellation, delay, and swapping options. To highlight the benefits of simultaneously solving planning and recovery problems in the RRTAP we compare our tail assignment solution with the tail assignment generated using a connection cost function presented in Gr¨onkvist [15]. Using airline data we demonstrate that by developing a better tail assignment plan via the RRTAP framework, one can reduce recovery costs in the event of a disruption.Australian Research Council Centre of Excellence for MathematicsMASCOS

An Analysis of Source-Side Grammatical Errors in NMT

The quality of Neural Machine Translation (NMT) has been shown to significantly degrade when confronted with source-side noise. We present the first large-scale study of state-of-the-art English-to-German NMT on real grammatical noise, by evaluating on several Grammar Correction corpora. We present methods for evaluating NMT robustness without true references, and we use them for extensive analysis of the effects that different grammatical errors have on the NMT output. We also introduce a technique for visualizing the divergence distribution caused by a source-side error, which allows for additional insights.Comment: Accepted and to be presented at BlackboxNLP 201

A Quasi-Robust Optimization Approach for Resource Rescheduling

If a disruption takes place in a complex task-based system, where tasks are carried out by a number of resource units or servers, real-time disruption management usually has to deal with an uncertain duration of the disruption. In this paper we present a novel approach for rescheduling such systems, thereby taking into account the uncertain duration of the disruption. We assume that several possibilities for the duration of the disruption are given. We solve the rescheduling problem as a two-stage optimization problem. In the first stage, at the start of the disruption, we reschedule the plan based on the optimistic scenario for the duration of the disruption, while taking into account the possibility that another scenario will be realized. In fact, we require a prescribed number of the rescheduled resource duties to be recoverable. This means that they can be easily recovered if it turns out that another scenario than the optimistic one is realized. We demonstrate the effectiveness of our approach by an application in real-time railway crew rescheduling. This is an important subproblem in the disruption management process of a railway company with a lot of uncertainty about the duration of a disruption. We test our approach on a number of instances of Netherlands Railways (NS), the main operator of passenger trains in the Netherlands. The numerical experiments show that the approach indeed finds schedules which are easier to adjust if it turns out that another scenario than the optimistic one is realized

Recoverable robust single day aircraft maintenance routing problem

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record Aircraft maintenance planning is of critical importance to the safe and efficient operations of an airline. It is common to solve the aircraft routing and maintenance planning problems many months in advance, with the solution spanning multiple days. An unfortunate consequence of this approach is the possible infeasibility of the maintenance plan due to frequent perturbations occurring in operations. There is an emerging concept that focuses on the generation of aircraft routes for a single day to ensure maintenance coverage that night, alleviating the effects of schedule perturbations from preceding days. In this paper, we present a novel approach to ensure that a sufficient number of aircraft routes are provided each day so maintenance critical aircraft receive maintenance that night. By penalising the under supply of routes terminating at maintenance stations from each overnight airport, we construct a single day routing to provide the best possible maintenance plan. This single day aircraft maintenance routing problem (SDAMRP) is further protected from disruptions by applying the recoverable robustness framework. To efficiently solve the recoverable robust SDAMRP acceleration techniques, such as identifying Pareto-optimal cuts and a trust region approach, have been applied. The SDAMRP is evaluated against a set of flight schedules and the results demonstrate a significantly improved aircraft maintenance plan. Further, the results demonstrate the magnitude of recoverability improvement that is achieved by employing recoverable robustness to the SDAMRP.Australian Research Council Centre of Excellence for Mathematics and Statistics of Complex SystemsNatural Sciences and Engineering Research Council of Canada

Optimized shunting with mixed-usage tracks

We consider the planning of railway freight classification at hump yards, where the problem involves the formation of departing freight train blocks from arriving trains subject to scheduling and capacity constraints. The hump yard layout considered consists of arrival tracks of sufficient length at an arrival yard, a hump, classification tracks of non-uniform and possibly non-sufficient length at a classification yard, and departure tracks of sufficient length. To increase yard capacity, freight cars arriving early can be stored temporarily on specific mixed-usage tracks. The entire hump yard planning process is covered in this paper, and heuristics for arrival and departure track assignment, as well as hump scheduling, have been included to provide the neccessary input data. However, the central problem considered is the classification track allocation problem. This problem has previously been modeled using direct mixed integer programming models, but this approach did not yield lower bounds of sufficient quality to prove optimality. Later attempts focused on a column generation approach based on branch-and-price that could solve problem instances of industrial size. Building upon the column generation approach we introduce a direct arc-based integer programming model, where the arcs are precedence relations between blocks on the same classification track. Further, the most promising models are adapted for rolling-horizon planning. We evaluate the methods on historical data from the Hallsberg shunting yard in Sweden. The results show that the new arc-based model performs as well as the column generation approach. It returns an optimal schedule within the execution time limit for all instances but from one, and executes as fast as the column generation approach. Further, the short execution times of the column generation approach and the arc-indexed model make them suitable for rolling-horizon planning, while the direct mixed integer program proved to be too slow for this. Extended analysis of the results shows that mixing was only required if the maximum number of concurrent trains on the classification yard exceeds 29 (there are 32 available tracks), and that after this point the number of extra car roll-ins increases heavily

On the recoverable robust traveling salesman problem

We consider an uncertain traveling salesman problem, where distances between nodes are not known exactly, but may stem from an uncertainty set of possible scenarios. This uncertainty set is given as intervals with an additional bound on the number of distances that may deviate from their expected, nominal values. A recoverable robust model is proposed, that allows a tour to change a bounded number of edges once a scenario becomes known. As the model contains an exponential number of constraints and variables, an iterative algorithm is proposed, in which tours and scenarios are computed alternately. While this approach is able to find a provably optimal solution to the robust model, it also needs to solve increasingly complex subproblems. Therefore, we also consider heuristic solution procedures based on local search moves using a heuristic estimate of the actual objective function. In computational experiments, these approaches are compared