Constrained covering solid travelling salesman problems in uncertain environment

Abstract

In this paper, we introduce some constrained covering solid travelling salesman problems (CCSTSPs). In CCSTSPs, a salesman begins from an initial city, visits a subset of cities exactly once using any one of available vehicles at each step on the tour such that all other cities are covered within an imprecise predetermined distance and comes back to the initial city within a restricted time. Here, the travelling costs between the cities are considered as rough variables where the covering distance is taken as fuzzy and rough variable separately. A travel time constraint has been imposed where the time variable may be represented as rough variable. We develop an RID-MGA heuristics to solve the proposed model in trust measure and justify its performance by comparing some best known result of some benchmark problems and then solve experiment with some randomly generated data. Sensitivity analyses on RID-MGA are also performed with respect to different population size and number of generations. Finally, following the proposed model, some near optimal paths which could have been implemented for humanitarian delivery service due to the earthquake of Nepal ($25{\text {th}}$ April, 2015) is obtained by RID-MGA.