An imprecise Multi-Objective Genetic Algorithm for uncertain Constrained Multi-Objective Solid Travelling Salesman Problem

•New imprecise Multi-Objective Genetic Algorithm (iMOGA) uses fuzzy-age selection.•Also adaptive crossover and generation dependent mutation are used in iMOGA.•Fuzzy-extended age based selection is also used in place of fuzzy-age based selection.•Constrained Solid TSPs are solved with random, fuzzy-random, random-fuzzy and bi-random data.•iMOGA is tested with TSPLIB data and its supremacy also proved by ANOVA test.

In this paper, an imprecise Multi-Objective Genetic Algorithm (iMOGA) is developed to solve Constrained Multi-Objective Solid Travelling Salesman Problems (CMOSTSPs) in crisp, random, random-fuzzy, fuzzy-random and bi-random environments. In the proposed iMOGA, ‘3- and 5-level linguistic based age oriented selection’, ‘probabilistic selection’ and an ‘adaptive crossover’ are used along with a new generation dependent mutation. In each environment, some sensitivity studies due to different risk/discomfort factors and other system parameters are presented. 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 (Roulette wheel selection, cyclic crossover and random mutation), NSGA-II, MOEA-D/ACO and compared. Moreover, a statistical analysis (Analysis of Variance) is carried out to show the supremacy of the proposed algorithm.