This volume contains the papers selected for presentationat IPCO VI, the Sixth InternationalConferenceonInteger ProgrammingandCombinatorialOptimi- tion,held inHouston,Texas,USA, June22{24,1998.TheIPCOseriesofconf- ences highlights recent developments in theory, computation, and applications of integer programming and combinatorial optimization. These conferences are sponsoredby the Mathematical ProgrammingSociety, and are held in the years in which no International Symosium on Mathema- cal Programming takes place. Earlier IPCO conferences were held in Waterloo (Canada) in May 1990; Pittsburgh (USA) in May 1992; Erice (Italy) in April 1993; Copenhagen (Denmark) in May 1995; and Vancouver (Canada) in June 1996. The proceedings of IPCO IV (edited by Egon Balas and Jens Clausen in 1995) and IPCO V (edited by William Cunningham, Thomas McCormick, and Maurice Queyranne in 1996), were published by Springer-Verlag in the series Lecture Notes in Computer Science as Volumes 920 and 1084, respectively. The proceedings of the rst three IPCO conferences were published by organizing institutions. A total of77 extended abstracts,mostly of an excellentquality, wereinitially submitted. Following the IPCO policy of having only one stream of sessions over a three day span, the ProgramCommittee selected 32 papers. As a result, many outstanding papers could not be selected. The papers included in this volume have not been refereed. It is expected that revised versions of these works will appear in scienti c journals. The Program Committee thanks all the authors of submitted extended - stracts and papers for their support of the IPCO conferences.

This book presents the latest findings on one of the most intensely investigated subjects in computational mathematics--the traveling salesman problem. It sounds simple enough: given a set of cities and the cost of travel between each pair of them, the problem challenges you to find the cheapest route by which to visit all the cities and return home to where you began. Though seemingly modest, this exercise has inspired studies by mathematicians, chemists, and physicists. Teachers use it in the classroom. It has practical applications in genetics, telecommunications, and neuroscience.

The authors of this book are the same pioneers who for nearly two decades have led the investigation into the traveling salesman problem. They have derived solutions to almost eighty-six thousand cities, yet a general solution to the problem has yet to be discovered. Here they describe the method and computer code they used to solve a broad range of large-scale problems, and along the way they demonstrate the interplay of applied mathematics with increasingly powerful computing platforms. They also give the fascinating history of the problem--how it developed, and why it continues to intrigue us.