Scheduling problems are common in many applications that range from factories and transports to universities. Most times, these problems are optimization problems for which we want to find the best way to manage scarce resources. Reality is dynamic, and thus unexpected disruptions can make the original solution invalid. There are many methods to deal with disruptions well described in the literature. These methods can be divided into two main approaches: (i) create robust solutions for the most common disruptions, and (ii) solve the problem again from scratch extended with new constraints.
The goal of creating robust solutions is to ensure their validity even after the most common disruptions occur. For this reason, it requires a detailed study of the most likely disruptive scenarios. The main disadvantage of creating a robust solution is a possible reduction in the overall quality (e.g., financial cost, customer satisfaction) to support the most likely disruptive scenarios that may never occur. Regardless of the robustness of the solution, we may need to solve the problem again.
Most of the methods developed to recover solutions after disruptions occur consist of re-solving the problem from scratch with an additional cost function. This cost function ensures that the new solution is close to the original. In other words, the methods solve the Minimal Perturbation Problem (MPP). However, all these methods require more execution time than the original problem to find a new solution. This can be explained by the fact that we solve a different problem (with more optimization criteria). One can mitigate this problem by re-using the search. Moreover, they use generic cost functions (e.g., Hamming distance) that may have little significance in practice.
In this work, we propose novel algorithms to solve the MPP applied to two domains: university course timetabling and train scheduling. We tested our algorithms to solve university timetabling problems with data sets obtained from Instituto Superior Técnico and the 2019 International Timetabling Competition. One of these algorithms was ranked in the top 5 of the competition. When considering the train scheduling case study, we tested our algorithms with data from the Swiss Federal Railways and from PESPLib. The evaluation shows that the new algorithms are more efficient than the ones described in the literature.
Summing up, the proposed algorithms show a significant improvement on the state-of-the-art to re-solve scheduling problems under disruptions.