TY - GEN
T1 - CNF Encodings for the Min-Max Multiple Traveling Salesmen Problem
AU - Zha, Aolong
AU - Gao, Rongxuan
AU - Chang, Qiong
AU - Koshimura, Miyuki
AU - Noda, Itsuki
N1 - Funding Information:
This paper is based on results obtained from a project commissioned by the New Energy and industrial technology Development Organization (NEDO). This work was also partially supported by JSPS KAKENHI Grant Number JP19H04175.
Publisher Copyright:
© 2020 IEEE.
PY - 2020/11
Y1 - 2020/11
N2 - 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.
AB - 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.
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U2 - 10.1109/ICTAI50040.2020.00053
DO - 10.1109/ICTAI50040.2020.00053
M3 - Conference contribution
AN - SCOPUS:85098790618
T3 - Proceedings - International Conference on Tools with Artificial Intelligence, ICTAI
SP - 285
EP - 292
BT - Proceedings - IEEE 32nd International Conference on Tools with Artificial Intelligence, ICTAI 2020
A2 - Alamaniotis, Miltos
A2 - Pan, Shimei
PB - IEEE Computer Society
T2 - 32nd IEEE International Conference on Tools with Artificial Intelligence, ICTAI 2020
Y2 - 9 November 2020 through 11 November 2020
ER -