Abstract
In this paper, a genetic-ant colony optimization algorithm has been presented to solve a solid multiple Travelling Salesmen Problem (mTSP) in fuzzy rough environment. In solid mTSP, a set of nodes (locations/cities) are given, and each of the cities must be visited exactly once by the salesmen such that all of them start and finish at a depot using different conveyance facility. A solid mTSP is an extension of mTSP where the travellers use different conveyance facilities for travelling from one city to another. To solve an mTSP, a hybrid algorithm has been developed based on the concept of two algorithms, namely genetic algorithm (GA) and ant colony optimization (ACO) based algorithm. Each salesman selects his/her route using ACO and the routes of different salesmen (to construct a complete solution) are controlled by the GA. Here, a set of simple ACO characteristics have further been modified by incorporating a special feature namely ‘refinement’. In this paper, we have utilized cyclic crossover and two-point’s mutation in the proposed algorithm to solve the problem. The travelling cost is considered as imprecise in nature (fuzzy-rough) and is reduced to its approximate crisp using fuzzy-rough expectation. Computational results with different data sets are presented and some sensitivity analysis has also been made.
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Appendix
In Table 5, each fuzzy-rough travel cost has six components; the first and the last components are L and R, respectively as described in Lemma 2. The second, third, fourth, and fifth components are a, b, c, and d, respectively (rough number components), that have also been described in Lemma 2. Here 1stvh, 2ndvh, and 3rdvh indicate cost of travel using the first, second, and third type vehicle, respectively.
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Changdar, C., Pal, R.K. & Mahapatra, G.S. A genetic ant colony optimization based algorithm for solid multiple travelling salesmen problem in fuzzy rough environment. Soft Comput 21, 4661–4675 (2017). https://doi.org/10.1007/s00500-016-2075-4
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DOI: https://doi.org/10.1007/s00500-016-2075-4