An intelligent hybrid algorithm for 4- dimensional TSP

In this paper, a hybridized algorithmic approach to solve 4- dimensional Travelling Salesman Problem (4DTSP) where different paths with various number of conveyances are available to travel between two cities. The algorithm is a hybridization of rough set based ant colony optimization (rACO) with genetic algorithm (GA). The initial solutions are produced by ACO which act as a selection operation of GA and then GA is developed with a virgin extended rough set based selection (7-point scale), comparison crossover and generation dependent mutation. The said hybrid algorithm rough set based Ant Colony Optimization (rACO) with Genetic Algorithm (rACO-GA) is tested against some test functions and efficiency of the proposed algorithm is established. The 4DTSPs are formulated with crisp and bi-fuzzy costs. In each environment, some statistical significant studies due to different time constraint values and other system parameters are presented. The models are illustrated with some numerical data. The proposed algorithm or its modified form can be easily adapted for applications in real life industrial information gathering. Proposed hybrid algorithm can be apply for industrial enterprise such as airline and supply chain, etc.