Reoptimizing the rural postman problem

doi:10.1016/j.cor.2012.12.010

2013-05-01

PRE

Claudia Archetti

Gianfranco Guastaroba *

M. Grazia Speranza

DOI：10.1016/j.cor.2012.12.010

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摘要

En 中文

Given an instance of the Rural Postman Problem (RPP) together with its optimal solution, we study the problem of finding a good feasible solution after a perturbation of the instance has occurred. We refer to this problem as the reoptimization of the RPP. We first consider the case where a new required edge is added. Second, we address the case where an edge (required or not) is removed. We show that the reoptimization problems are NP-hard. We consider a heuristic for the case where a new required edge is added which is a modification of the cheapest insertion algorithm for the traveling salesman problem and show that it has a worst-case ratio equal to 2. Moreover, we show that simple algorithms to remove an edge from an optimal RPP tour guarantee a tight ratio equal to 3/2. Computational tests are made to compare the performance of these algorithms with respect to the Frederickson algorithm running from scratch. (C) 2012 Elsevier Ltd. All rights reserved.

Keyword:

Reoptimization

Rural postman problem

Heuristic algorithms

Worst-case analysis