Visiting the holy shrines is of great importance to Muslims in Islamic countries in general and to Muslims in Iraq in particular. Visitors usually try to visit as many holy shrines as possible in a single visit at the lowest possible cost. In this research, visiting the Iraqi Holy Shrines Problem (IHSP) was considered, which is in fact, a practical application of the symmetrical traveling salesman problem (TSP). The summary of this problem is that a visitor wants to visit all (or most) of the (14) holy shrines in Iraq. This visitor lives in a city that includes one of these shrines and wants to find the appropriate route to visit all of them at the lowest cost (cost here means distance and/or time and/or financial cost) and then return to the same city from which he started without repeating the route between any two shrines. One of the most important results of this research is that the optimal (shortest) distance path was found to help the visitor achieve the minimum financial cost of fuel consumption using more than one accurate or approximate method to solve this problem