The Capacitated Arc Routing Problem: Lower bounds

1997 ii ACKNOWLEDGEMENTS We would like mostly to thank Mr. Peter Keenan, who was as much a partner as a supervisor, for his invaluable time and erudite guidance during the summer. We must also pay tribute to our parents for their encouragement and support, not only for the duration of this dissertation, but throughout the year. ABSTRACT The Capacitated Arc Routing Problem is a NP-hard arc routing problem in which a fleet of vehicles, based on a specific vertex (the depot) and with a known capacity, must service the arcs of a graph on which demand exists, with minimal total cost and such that the capacity of the vehicles is not exceeded. In 1992, three Japanese researchers devised the first exact algorithm to solve the Capacitated Arc Routing Problem optimally. In 1994, in an MMS dissertation, Montwill and Naughton implemented and improved this algorithm. Despite their success they found that the algorithm did not perform well when solving large problems, since it used too much computer memory and took too long. The aim of our dissertation was to combat this problem. To this end our first objective was to implement recent developments in the field of lower bound heuristics for the Capacitated Arc Routing Problem. We concluded that lower bounds devised by three Spanish researchers were, as claimed, the tightest lower bounds to date. Our second objective was to modify and improve these lower bound heuristics. This second objective was indeed successfully achieved and our new lower bound heuristic returns the best results to date. iv SUMMARY Chapter 1 of our dissertation is an introductory chapter where we introduce the Chinese Postman Problem, on which the Capacitated Arc Routing Problem is based. We then explain the Capacitated Arc Routing Problem itself and outline the purpose of our dissertation. Chapter 2 describes our main solution technique for solving the Capacitated Arc Routing Problem i.e. the Tour Construction algorithm as devised by Hirabayashi et al. and implemented and improved by Montwill and Naughton. With an understanding of the operation of the algorithm borne in mind, the motivation for our study of lower bound heuristics for the Capacitated Arc