The reoptimization version of an optimization problem deals with the following scenario: Given an input instance together with an optimal solution for it, the objective is to find a high-quality solution for a locally modified instance. In this paper, we investigate several reoptimization variants of the traveling salesman problem with deadlines in metric graphs (Δ-DlTSP). The objective in the Δ-DlTSP is to find a minimum-cost Hamiltonian cycle in a complete undirected graph with a metric edge cost function which visits some of its vertices before some prespecified deadlines. As types of local modifications, we consider insertions and deletions of a vertex as well as of a deadline. We prove the hardness of all of these reoptimization variants and give lower and upper bounds on the achievable approximation ratio which are tight in most cases. © 2009 Elsevier B.V. All rights reserved.
Böckenhauer, H. J., & Komm, D. (2010). Reoptimization of the metric deadline TSP. Journal of Discrete Algorithms, 8(1), 87–100. https://doi.org/10.1016/j.jda.2009.04.001