CNF Encodings for the Min-Max Multiple Traveling Salesmen Problem

Aolong Zha, Rongxuan Gao, Qiong Chang, Miyuki Koshimura, Itsuki Noda

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In this study, we consider the multiple traveling salesmen problem (mTSP) with the min-max objective of minimizing the longest tour length. We begin by reviewing an existing integer programming (IP) formulation of this problem. Then, we present several novel conjunctive normal form (CNF) encodings and an approach based on modifying a maximum satisfiability (MaxSAT) algorithm for the min-max mTSP. The correctness and the space complexity of each encoding are analyzed. In our experiments, we compare the performance of solving the TSP benchmark instances using an existing encoding and our new encodings comparing the results achieved using an implemented group MaxSAT solver to those achieved using the IP method. The results show that for the same problem, the new encodings significantly reduce the number of generated clauses over the existing CNF encoding. Although the proposals are still not competitive compared to the IP method, one of them may be more effective on relatively large-scale problems, and it has an advantage over the IP method in solving an instance with a small ratio of the number of cities to the number of salesmen.

Original languageEnglish
Title of host publicationProceedings - IEEE 32nd International Conference on Tools with Artificial Intelligence, ICTAI 2020
EditorsMiltos Alamaniotis, Shimei Pan
PublisherIEEE Computer Society
Pages285-292
Number of pages8
ISBN (Electronic)9781728192284
DOIs
Publication statusPublished - Nov 2020
Externally publishedYes
Event32nd IEEE International Conference on Tools with Artificial Intelligence, ICTAI 2020 - Virtual, Baltimore, United States
Duration: Nov 9 2020Nov 11 2020

Publication series

NameProceedings - International Conference on Tools with Artificial Intelligence, ICTAI
Volume2020-November
ISSN (Print)1082-3409

Conference

Conference32nd IEEE International Conference on Tools with Artificial Intelligence, ICTAI 2020
CountryUnited States
CityVirtual, Baltimore
Period11/9/2011/11/20

All Science Journal Classification (ASJC) codes

  • Software
  • Artificial Intelligence
  • Computer Science Applications

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