A parameterized approximation algorithm for the mixed and windy capacitated arc routing problem: Theory and experiments

We prove that any polynomial‐time α ( n ) ‐approximation algorithm for the n‐vertex metric asymmetric Traveling Salesperson Problem yields a polynomial‐time O ( α ( C ) ) ‐approximation algorithm for the mixed and windy Capacitated Arc Routing Problem, where C is the number of weakly connected compo...

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Bibliographic Details
Published in:Networks Vol. 70; no. 3; pp. 262 - 278
Main Authors: van Bevern, René, Komusiewicz, Christian, Sorge, Manuel
Format: Journal Article
Language:English
Published: New York Wiley Subscription Services, Inc 01.10.2017
Subjects:
Algorithms
Approximation
Benchmarks
Chinese Postman
combinatorial optimization
Computer simulation
fixed‐parameter algorithm
Mathematical analysis
NP‐hard problem
Polynomials
Production scheduling
Rural Postman
transportation
vehicle routing
ISSN:0028-3045, 1097-0037
Online Access:Get full text
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Summary:We prove that any polynomial‐time α ( n ) ‐approximation algorithm for the n‐vertex metric asymmetric Traveling Salesperson Problem yields a polynomial‐time O ( α ( C ) ) ‐approximation algorithm for the mixed and windy Capacitated Arc Routing Problem, where C is the number of weakly connected components in the subgraph induced by the positive‐demand arcs—a small number in many applications. In conjunction with known results, we obtain constant‐factor approximations for C ∈ O ( log n ) and O ( log C / log log C ) ‐approximations in general. Experiments show that our algorithm, together with several heuristic enhancements, outperforms many previous polynomial‐time heuristics. Finally, since the solution quality achievable in polynomial time appears to mainly depend on C and since C = 1 in almost all benchmark instances, we propose the Ob benchmark set, simulating cities that are divided into several components by a river. © 2017 Wiley Periodicals, Inc. NETWORKS, Vol. 70(3), 262–278 2017
Bibliography:This version describes several algorithmic enhancements, contains an experimental evaluation of our algorithm, and provides a new benchmark data set.
A preliminary version of this article appeared in the Proceedings of the 15th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems (ATMOS’15)
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ISSN:0028-3045
1097-0037
DOI:10.1002/net.21742