Solving a new application of asymmetric TSP by modified migrating birds optimization algorithm

In this study, we first introduce a new application of the asymmetric traveling salesman problem (ATSP) which is about a small restaurant with one cook and a single stove. Once a meal has started cooking on the stove, the cook prepares the next meal on the table where the preparation time is dependent on the previous meal prepared. For the solution of this problem, besides several simple construction algorithms and a new version of the simulated annealing algorithm, we focus on enhanced versions of the recently introduced migrating birds optimization (MBO) algorithm. The original MBO algorithm might suffer from early convergence. Here we introduce several different ways of handling this problem. The extensive numerical experimentation conducted shows the superiority of the enhanced MBO over the original MBO (about 2.62 per cent) and over the simulated annealing algorithm (about 1.05 per cent).