Delaunay-Triangulation-Based Variable Neighborhood Search to Solve Large-Scale General Colored Traveling Salesman Problems

Document Type

Article

Publication Date

3-1-2021

Abstract

A colored traveling salesman problem (CTSP) is a generalization of the well-known multiple traveling salesman problem. It utilizes colors to differentiate the accessibility of its cities to its salesmen. In our prior work, CTSPs are formulated over graphs associated with a city-color matrix. This work redefines a general colored traveling salesman problem (GCTSP) in the framework of hypergraphs and reveals several important properties of GCTSP. In GCTSP, the setting of city colors is richer than that in CTSPs. As results, it can be used to model and address various complex scheduling problems. Then, a Delaunay-triangulation-based Variable Neighborhood Search (DVNS) algorithm is developed to solve large-scale GCTSPs. At the beginning stage of DVNS, a divide and conquer algorithm is exploited to prepare a Delaunay candidate set for lean insertion. Next, the incumbent solution is perturbed by utilizing greedy multi-insertion and exchange mutation to obtain a variety of neighborhoods. Subsequently, 2-opt and 3-opt are used for local search in turn. Extensive experiments are conducted for many large scale GCTSP cases among which two maximal ones are up to 33000+ cities for 4 salesmen and 240 salesmen given 11000+ cities, respectively. The results show that the proposed method outperforms the existing four genetic algorithms and two VNS methods in terms of search ability and convergence rate.

Identifier

85102335362 (Scopus)

Publication Title

IEEE Transactions on Intelligent Transportation Systems

External Full Text Location

https://doi.org/10.1109/TITS.2020.2972389

e-ISSN

15580016

ISSN

15249050

First Page

1583

Last Page

1593

Issue

3

Volume

22

Grant

61374069

Fund Ref

National Natural Science Foundation of China

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