Coordination of Cyclic crossover and Bat Algorithm for the Travelling Salesman Problems in Different Environments: A Simulation Approach

In this study, the features of cyclic crossover process and K-opt are incorporated in the bat algorithm (BA) to solve the Travelling Salesman Problems (TSP) in different environments. Swap operation and swap sequence are applied for the modification of the different operations of the BA to solve the TSPs. The cyclic crossover operation is applied in a regular interval of iterations on the best found solution and each solution of the final population of BA for the enhancement of the exploration as well as exploitation of the search process. K-Opt operation is applied on the population in each iteration of the BA with some probability for the exploitation. The algorithm is tested with a set of benchmark test instances of the TSPLIB. The algorithm produces exact results for a set of significantly large size problems. For the TSPs in fuzzy environment, a fuzzy simulation approach is proposed to deal with the fuzzy data having linear as well as non-linear membership functions. Also, a rough simulation process is proposed to deal with the TSPs in the rough environment where rough estimation can be done following any type of rough measure. The performance of the algorithm is compared with the state-of-the-art algorithms for the TSPs with crisp cost matrices using different statistical tools.