Showing papers on "Incremental heuristic search published in 1985"

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 iteratiw-deepening algorithm is shown to be asymptotically optimal along all three dimensions for exponential pee searches. The algorithm has been used successfully in chess programs, has been eflectiuely combined with bi-directional search, and has been applied to best-first heuristic search as well. This heuristic depth-first iteratiw-deepening algorithm is the only known algorithm that is capable of finding optimal solutions to randomly generated instances of the Fifeen Puzzle within practical resource limits.

Searching with probabilities

Abstract: : In this thesis we investigate two issues relating to heuristic search algorithms. The first and most important issue addressed is the technique used to represent knowledge within a search tree. Previous techniques have used either single values or ranges. We demonstrate that probability distributions, using a modified B*-type search algorithm, can successfully be used as a knowledge representation technique. Furthermore we show that the use of probability distributions is superior to the use of either of the previous techniques. The former conclusion is based on experiments that show that the probability-based algorithm is able to solve a wide variety of tactical chess problems. The latter conclusion is based on both analytical examples as well as experimental results. In analyzing search algorithms that use single-valued or range-based state descriptions, several important problems arise. For each problem we show how it is solved by the use of probability-based state descriptions. Experimentally we show that the probability-based algorithm solves over one-third more problems than the comparable range-based algorithm and expands approximately one-tenth the nodes on problems that both algorithms solve. Keywords: Reports, Military publications, Periodicals.

Stochastic Modeling of Branch-and-Bound Algorithms with Best-First Search

Abstract: Branch-and-bound algorithms are organized and intelligently structured searches of solutions in a combinatorially large problem space. In this paper, we propose an approximate stochastic model of branch-and-bound algorithms with a best-first search. We have estimated the average memory space required and have predicted the average number of subproblems expanded before the process terminates. Both measures are exponentials of sublinear exponent. In addition, we have also compared the number of subproblems expanded in a best-first search to that expanded in a depth-first search. Depth-first search has been found to have computational complexity comparable to best-first search when the lower-bound function is very accurate or very inaccurate; otherwise, best-fit search is usually better. The results obtained are useful in studying the efficient evaluation of branch-and-bound algorithms in a virtual memory environment. They also confirm that approximations are very effective in reducing the total number of iterations.

The complexity of backtrack searches

Abstract: In this paper, we study the complexity of finding an efficient search for combinatorial problems which are commonly solved by backtracking. First, a formalism is introduced. Backtrack searches are ordinarily thought of as following a tree pattern. Our model is considerably more general, and there are problems where this allows much shorter searches.Next, we look at the complexity of search strategies (probabilistic decision trees) that can solve any problem in a collection of problems. Let C be the collection of problems that can be solved by a (possibly lucky) search involving K or fewer queries. We prove a nonpolynomial lower bound (in terms of K) on any search strategy for C. We conjecture that a matching upper bound exists.Finally, a few heuristics are presented that give the flavor of an interesting line of research: to test the effectiveness of a heuristic that should work on any problem, try it out on a few specific problems of known complexity. On some simple problems, our heuristics allow polynomial-time searches.

A new algorithm for heuristic search which uses hints

Abstract: In computer aided decision making an algorithm to determine the next step (i.e. the decision) must be formulated. However, often we are not able to express our knowledge of the problem algorithmically and the decision making is based on heuristic search, which is usually guided by some cost evaluation function — heuristic function. But quite often even this heuristic function cannot be formulated ideally (due to the lack of our knowledge of the problem). When such a function is used by the “classical” A ∗ algorithm [Nilsson, 1971], whole subspaces not containing the solution path can be searched in vain. We propose a new search guiding algorithm which allows one to specify also other forms of heuristic knowledge to reduce the search. We analyze the new algorithm, state and prove its basic properties and compare it with known algorithms.