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

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.