(14th-April-2020)
When a non-unit cost is associated with arcs, we often want to find the solution that minimizes the total cost of the path.
For example, for a delivery robot, costs may be distances and we may want a solution that gives the minimum total distance. Costs for a delivery robot may be resources required by the robot to carry out the action represented by the arc. The cost for a tutoring system may be the time and effort required by the students. In each of these cases, the searcher should try to minimize the total cost of the path found to reach the goal.
The search algorithms considered thus far are not guaranteed to find the minimum-cost paths; they have not used the arc cost information at all. Breadth-first search finds a solution with the fewest arcs first, but the distribution of arc costs may be such that a path of fewest arcs is not one of minimal cost.
The simplest search method that is guaranteed to find a minimum cost path is similar to breadth-first search; however, instead of expanding a path with the fewest number of arcs, it selects a path with the minimum cost. This is implemented by treating the frontier as a priority queue ordered by the cost function.
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