Admissible heuristic

About: Admissible heuristic is a(n) research topic. Over the lifetime, 197 publication(s) have been published within this topic receiving 15329 citation(s). The topic is also known as: admissible heuristics.

A Formal Basis for the Heuristic Determination of Minimum Cost Paths

Abstract: Although the problem of determining the minimum cost path through a graph arises naturally in a number of interesting applications, there has been no underlying theory to guide the development of efficient search procedures. Moreover, there is no adequate conceptual framework within which the various ad hoc search strategies proposed to date can be compared. This paper describes how heuristic information from the problem domain can be incorporated into a formal mathematical theory of graph searching and demonstrates an optimality property of a class of search strategies.

Depth-first iterative-deepening: an optimal admissible tree search

Abstract: The complexities of various search algorithms are considered in terms of time, space, and cost of solution path. It is known that breadth-first search requires too much space and depth-first search can use too much time and doesn't always find a cheapest path. A depth-first iterative-deepening algorithm is shown to be asymptotically optimal along all three dimensions for exponential tree searches. The algorithm has been used successfully in chess programs, has been effectively combined with bi-directional search, and has been applied to best-first heuristic search as well. This heuristic depth-first iterative-deepening algorithm is the only known algorithm that is capable of finding optimal solutions to randomly generated instances of the Fifteen Puzzle within practical resource limits.

Admissible heuristics for optimal planning

Abstract: HSP and HSPr are two recent planners that search the state-space using an heuristic function extracted from Strips encodings. HSP does a forward search from the initial state recomputing the heuristic in every state, while HSPr does a regression search from the goal computing a suitable representation of the heuristic only once. Both planners have shown good performance, often producing solutions that are competitive in time and number of actions with the solutions found by Graphplan and SAT planners. HSP and HSPr. however, are not optimal planners. This is because the heuristic function is not admissible and the search algorithms are not optimal. In this paper we address this problem. We formulate a new admissible heuristic for planning, use it to guide an IDA* search, and empirically evaluate the resulting optimal planner over a number of domains. The main contribution is the idea underlying the heuristic that yields not one but a whole family of polynomial and admissible heuristics that trade accuracy for efficiency. The formulation is general and sheds some light on the heuristics used in HSP and Graphplan, and their relation. It exploits the factored (Strips) representation of planning problems, mapping shortest-path problems in state-space into suitably defined shortest-path problems in atom-space. The formulation applies with little variation to sequential and parallel planning, and problems with different action costs.

Landmarks, critical paths and abstractions: what's the difference anyway?

Abstract: Current heuristic estimators for classical domain-independent planning are usually based on one of four ideas: delete relaxations, critical paths, abstractions, and, most recently, landmarks. Previously, these different ideas for deriving heuristic functions were largely unconnected. We prove that admissible heuristics based on these ideas are in fact very closely related. Exploiting this relationship, we introduce a new admissible heuristic called the landmark cut heuristic, which compares favourably with the state of the art in terms of heuristic accuracy and overall performance.

Finding optimal solutions to Rubik's cube using pattern databases

Abstract: We have found the first optimal solutions to random instances of Rubik's Cube. The median optimal solution length appears to be 18 moves. The algorithm used is iterative-deepening-A* (IDA*), with a lower-bound heuristic function based on large memory-based lookup tables, or "pattern databases" (Culberson and Schaeffer 1996). These tables store the exact number of moves required to solve various subgoals of the problem, in this case subsets of the individual movable cubies. We characterize the effectiveness of an admissible heuristic function by its expected value, and hypothesize that the overall performance of the program obeys a relation in which the product of the time and space used equals the size of the state space. Thus, the speed of the program increases linearly with the amount of memory available. As computer memories become larger and cheaper, we believe that this approach will become increasingly cost-effective.