New heuristic algorithms for the windy rural postman problem

Abstract

In this paper we deal with the Windy Rural Postman Problem. This problem generalizes several important Arc Routing Problems and has interesting real-life applications. Here, we present several heuristics whose study has lead to the design of a Scatter Search algorithm for the Windy Rural Postman Problem. Extensive computational experiments over different sets of instances, with sizes up to 988 nodes and 3952 edges, are also presented.

A New View on Rural Postman Based on Eulerian Extension and Matching

“…Consider a solution E to I EEA that also contains the arcs (1, 3), (3,5) to E, and add arcs from all remaining sources to their corresponding targets that reside in the same component to obtain a solution to I EE . Also, every solution to I EE has to connect the connected component W 1 1 to the rest of the graph.…”

“…Subsequent to RP's introduction [13,28] it has been shown NP-complete [23]. Heuristics and approximation algorithms have been presented [3,17,18,20,32] as well as exact exponential-time algorithms based on integer linear programs [7,8,19,25]. See also overview articles by Eiselt et al [14], by Assad and Golden [1] and the book edited by Dror [12].…”

“…Given a directed, arc-weighted graph G and a subset R of its arcs (called "required arcs"), the task is to find a minimum-cost closed walk in G that visits all arcs of R. The practical applications of RP include snow plowing, garbage collection, and mail delivery [1,3,5,12,14,30]. Recently, it has been observed that RP is closely related (more precisely, "parameterized equivalent") to the arc addition problem Eulerian Extension (EE) [10].…”

A branch-and-price algorithm for the windy rural postman problem

“…The RPP is an arc routing problem that arises when a subset of the arcs must be visited. It is a general case of the Chinese Postman Problem (CPP) in which a circuit that visits all the arcs at least once must be found [2,14]. In the WRPP, the cost of traversing an edge depends on the traveling direction.…”

“…The WRPP is an asymmetric variant of the Rural Postman Problem (RPP) [2]. The RPP is an arc routing problem that arises when a subset of the arcs must be visited.…”