Nearest Route Problem1

In this paper we propose a new class of optimization problems on oriented graphs with weight, which are called nearest route problems. A nearest problem has a target value, which generates an error function in a sense. Which route is nearest to the designated value? The nearest route problem includes both the shortest route problem and longest one. We give an invariant imbedding solution through both forward-backward and backward-forward approaches. A typical nearest problem is solved by both approaches