(algorithm) A graph search algorithm where the current path is extended with a successor node which is closer to the solution than the end of the current path.
In simple hill climbing, the first closer node is chosen whereas in steepest ascent hill climbing all successors are compared and the closest to the solution is chosen. Both forms fail if there is no closer node. This may happen if there are local maxima in the search space which are not solutions. Steepest ascent hill climbing is similar to best first search but the latter tries all possible extensions of the current path in order whereas steepest ascent only tries one.