Uniform Path Cost Search - artificial intelligence:

A breadth first search will find the solution with the shortest path length from the initial state to the goal state. In fact, this may not be the least expensive solution in terms of the path cost. A uniform path cost search chooses that node to expand by looking at the path cost for each node: the node that as cost least to get to is expanded first. Hence, if, as is usually the case, the path cost of a node increases with the path length, then this search is fully guaranteed to find the least expensive solution. It is therefore an optimal search strategy. Unfortunately, the searching of strategy can be much inefficient.