Title: A modified ant colony optimisation based approach to solve sub-tour constant travelling salesman problem

Authors: Chiranjit Changdar; G.S. Mahapatra; Rajat Kumar Pal

Addresses: Department of Computer Science, Raja N.L. Khan Women's College, Midnapore, West Bengal, 721102, India ' Department of Mathematics, National Institute of Technology Puducherry, Karaikal-609605, India ' Department of Computer Science and Engineering, University of Calcutta, Calcutta-700 098, West Bengal, India

Abstract: This paper presents an advanced ant colony optimisation approach to solve sub-tour constant travelling salesman problem (SCTSP) with time limit in fuzzy environment. In SCTSP, there is a set of sub-tours (two cities for each sub-tour). A traveller must complete his/her tour with predetermined sequence of distinct sub-tours. In this proposed model, the total time of travel must not exceed a predetermined time limit, i.e., the salesman should maintain a maximum time limit to complete his/her tour. In this paper, we present a modified form of the basic ACO algorithm, obtained by introducing a new operation known as restoring operation for solving the problem. In restoring operation, the low-quality path/solution given by any ant is replaced by a nearest better solution. The proposed problem is solved by considering fuzzy travel costs and time. Fuzzy credibility measure and graded mean integration method are used to obtain optimal decision. Computational results with different datasets are presented for illustration.

Keywords: ant colony optimisation; ACO; genetic algorithm; graded mean integration; travelling salesman problem; credibility measure.

DOI: 10.1504/IJMOR.2017.087204

International Journal of Mathematics in Operational Research, 2017 Vol.11 No.3, pp.310 - 331

Available online: 19 Sep 2017 *

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