Searching for the Shortest Path Through Group Processing for TSP

Thanks to its complexity, Traveling Salesman Problem (TSP) has been one of the most intensively studied problems in computational mathematics. Although many solutions have been offered so far, all of them have yielded some disadvantages and none has been able to claim for the best solution. We believe that better solution could be obtained through iterative evaluations, until a certain number of islands are reached, if we could develop an algorithm which grows geometrically. Some algorithms have suggested random solutions and many suggested using the closest neighbors. In many cases islands exist in groups or chains in any length. Therefore they can be connected to any other island rather than the closest one. This can be better identified when we spot out the patterns and island chains. In this paper, we have searched for the identification of patterns and chains. We propose an iterative Group Processing (GP) approach which finds better paths in the 90% of the cases overall as we compare it to Random Logic (RL) programs and most up-to-date Artificial Neural Network based TSP programs.