Reducing The Order Of The Travelling SalesmanProblems By Minimin Optimization Theory AndToStudyBy DAS Technique

The purpose of this article is to propose a new approach for finding the guaranteed solution set of minimizedassignment problems and maximized assignment problems. Firstly the existence of the minimin and maximaxoptimization problems are studied with the help of newly defined weakly φ-convex function in φ-convex set. Next the assignment problems and traveling problems are converted to a complete bipartite graph in a unifiedapproach. The concept dominated assignment simulation (DAS) technique based on the theory of miniminandmaximax optimization problems. Later a pair of traveling salesman problems are studied using the DAS technique and complete bipartite graphas an application of minimin optimization problem. Finally, a pair of comparison studies are discussed to showequality of solutions and the number of steps in between Hungarian method and DAS technique