One of the most important decisions in any manufacturing company is how to schedule the operations on the available machines. In several industries, the nature of the job imposes certain constraints to operations scheduling. In a no-wait flow shop, once a job starts on the first machine, it has to continue being processed on the next ones, without any interruptions. As an extension of the flow shop scheduling, the no-wait version is also very difficult to be solved to optimality within a reasonable time, and many heuristics have been proposed for this problem. This work aims to classify existing solution algorithms proposed to solve the no-wait flow shop scheduling problem with setup times and some of its variants. We show how combining a heuristic to generate a good initial solution, local search procedures, insertion and swapping of job positions and techniques developed originally to solve transportation problems are among the popular and efficient techniques for the problem at hand. We also propose a new solution method based on the well-known Adaptive Large Neighborhood Search (ALNS) algorithm from transportation science. The use of this algorithm aims to minimize the total flow time as a performance measure. As this is a problem with high complexity, to achieve high solution quality in a reasonable time, an acceleration method was also adapted and applied into local search procedures with swapping operations. The results of the new method were compared to the best results in the literature for widespread instances, validating the quality of the method.