1. In an optimum route determination apparatus which, according to a destination set by a vehicle operator, reads road map data of an area containing a departure point and that destination out of a road map memory for a road map and which determined an optimum route leading from the departure point to the destination based on the road map data, selection means exterior to said optimum route determination apparatus having previously selected a plurality of specific points, calculation means exterior to said optimum route determination apparatus having previously calculated a plurality of optimum routes which lead from said plurality of specific points to a plurality of destinations, respectively, passing in sequence through specific points and each specific point representing at least one departure point in a respective optimum route, said optimum route determination apparatus comprising: a route memory having stored therein a route table containing data of said specific points, data of said destinations and data of a plurality of initial routes, one of said initial routes leading from one of said specific points to at least the next specific point in said sequence positioned on one of said optimum routes leading from said one of said specific points to one of said destinations, and not including all specific points comprising the optimum route to a respective destination, wherein said data of said data of said specific points, said data of said destinations and said data of said initial routes are contained in said route table in such a manner that the data of said one of said initial routes is acquired by searching said route table for said one of said specific points and one of said destinations; initialization means for setting one of said destinations and one of said specific points near to a current location of a vehicle; and initial route acquisition means for searching said route table for the specific point and the destination set by said initialization means to acquire said data of said initial route, said initialization means then replacing said one of said specific points with the next specific point, said initial route acquisition means and said initialization means then repeating the searching and replacing operations until one of said optimum routes is constituted by the repeatedly acquired initial route data.