Granular Computing

, Volume 4, Issue 1, pp 125–142 | Cite as

A rough multi-objective genetic algorithm for uncertain constrained multi-objective solid travelling salesman problem

  • Samir MaityEmail author
  • Arindam Roy
  • Manoanjan Maiti
Original Paper


This paper addresses a rough multi-objective genetic algorithm (R-MOGA) to solve constrained multi-objective solid travelling salesman problems (CMOSTSPs) in rough, fuzzy rough and random rough environments. In the proposed R-MOGA, “3- and 5-level linguistic-based rough age oriented selection” and “adaptive crossover” are used along with a new generation-dependent mutation. In the present study, the age of each chromosome is termed as 3-level by young, middle and old and 5-level by very young, young, middle, old and very old. Here, we model the CMOSTSP with travelling costs and times as two objectives and a constraint for route risk/discomfort factors. The costs, times and risk/discomfort are rough, fuzzy rough and random rough in nature. To test the efficiency, combining same size single objective problems from standard TSPLIB, the results of such multi-objective problems are obtained by the proposed algorithm, simple MOGA and NSGA-II are compared. Moreover, a statistical analysis (analysis of variance) is carried out to show the supremacy of the proposed algorithm.


CMOSTSP Rough set-based selection Adaptive crossover Generation-dependent mutation R-MOGA 



This research article is supported by University Grant Commission of India by Grant number PSW-150/14-15(ERO).

Supplementary material

41066_2018_94_MOESM1_ESM.pdf (69 kb)
Supplementary material 1 (pdf 68 KB)


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Operations Management GroupIndian Institute of Management CalcuttaCalcuttaIndia
  2. 2.Contai P. K. CollegePurba MedinipurIndia
  3. 3.Applied Mathematics with Oceanology and Computer ProgrammingVidyasagar UniversityMidnapurIndia

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