Constrained solid travelling salesman problem solving by rough GA under bi-fuzzy coefficients

Abstract

In this paper, a Rough Genetic Algorithm (RGA) is proposed to solve constrained solid travelling salesman problems (CSTSPs) in crisp and bi-fuzzy coefficients. In the proposed RGA, we developed a ‘rough set based selection’ (7-point scale) technique and ‘comparison crossover’ with new generation dependent mutation. A solid travelling salesman problem (STSP) is a tavelling salesman problem (TSP) in which, at each station, there are a number of conveyances available to travel to another station. The costs and risk/discomforts factors are in the form of crisp, bifuzzy in nature. In this paper, CSTSPs are illustrated numerically by some standard test data from TSPLIB using RGA. In each environment, some statistical significance studies due to different risk/discomfort factors and other system parameters are presented.