The　greedy　randomized　adaptive　search　procedure　and　the　dynamic　convexized　method　are　two　state-of-the-art　methods　for　the　traveling　salesman　problem,　which　are　tour　improvement　methods.　For　comparing　the　performances　of　the　two　methods,　we　give　the　implementation　details,　and　test　the　two　methods　on　the　TSPLIB　standard　test　instances.　Experimental　results　show　that　the　dynamic　convexized　method　outperforms　the　greedy　randomized　adaptive　search　procedure　for　the　traveling　salesman　problem.