Classifications of Different Trends ( Extended

The most famous, and simple suboptimal search algorithm is Weighted A∗ (WA∗) (Pohl 1970). Similar to A∗, WA∗ uses two data structures: OPEN and CLOSED. Initially, OPEN contains only the start state and CLOSED is empty. At every iteration, the algorithm chooses the state in OPEN that minimizes the cost function f(n) = g(n)+W ·h(n), where g(n) is the cost of the lowest cost path found so far, from the start state to n, h(n) is an admissible heuristic estimate of the cost of reaching the goal from n, and W is a parameter. It is well-known that A∗ with a consistent heuristic (and thus the f -cost is monotonically increasing) expands a state only after the lowest cost path to it was found. This is not the case for non-monotonic f -functions such as the one used by WA∗. In this case, a state n may be generated with a smaller g-value, after it has been already expanded. At this point, it can be removed from CLOSED and put back in OPEN – an action called reopening. Reopening is optional; for every closed state which is seen with a smaller g-value, a decision needs to be made whether to reopen it or not. In the case of not reopening, the newly seen state is not placed back in OPEN but remains in CLOSED. However, it is a common practice to update its g-value as well as its parent pointer. In this paper we focus on the two extreme reopening polices: always reopen (AR) and never reopen (NR).