Iterative-deepening searches mimic a breadth-first node expansion with a series of depth-first searches that operate with successively extended search horizons. They have been proposed as a simple way to reduce the space complexity of best-first searches like A* from exponential to linear in the search depth.

Abstract. The efficiency of A * searching depends on the quality of the lower bound estimates of the solution cost. Pattern databases enumerate all possible subgoals required by any solution, subject to constraints on the subgoal size. Each subgoal in the database provides a tight lower bound on the cost of achieving it. For a given state in the search space, all possible subgoals are looked up, with the maximum cost over all lookups being the lower bound. For sliding tile puzzles, the database enumerates all possible patterns containing N tiles and, for each one, contains a lower bound on the distance to correctly move all N tiles into their correct final location. For the 15-Puzzle, iterative~deepening A * with pattern databases (N=8) reduces the total number of nodes searched on a standard problem set of 100 positions by over 1000-fold. 1

Many search domains are non-deterministic. Although real-time search methods have traditionally been studied in deterministic domains, they are well suited for searching nondeterministic domains since they do not have to plan for every contingency { they can react to the actual outcomes of actions. In this paper, we introduce the min-max LRTA * algorithm, a simple extension of Korf's Learning Real-Time A * algorithm (LRTA*) to non-deterministic domains. We describe which non-deterministic domains min-max LRTA * can solve, and analyze its performance for these domains. We also give tight bounds on its worst-case performance and show how this performance depends on properties of both the domains and the heuristic functions used to encode prior information about the domains. 1

study on realization of generalized quantum

The A* algorithm for single-agent search has attracted considerable attention in recent years due to Korf's iterative deepening improvement (IDA*). The algorithm's efficiency depends on the quality of the lower bound estimates of the solution cost. For sliding tile puzzles, reduction databases are introduced as a means of improving the lower bound. The database contains all solutions to the subproblem of correctly placing N tiles. For the 15-Puzzle, IDA* with reduction databases (N=8) are shown to reduce the total number of nodes searched on a standard problem set of 100 positions by over 1000-fold. With the addition of transposition tables and endgame databases, an improvement of over 1700-fold is seen. 1 Introduction In recent years, the A* algorithm for single-agent search has attracted considerable attention. Korf pioneered the use of iterative deepening with depthfirst A* (IDA*), eliminating many of the difficulties of the basic A* algorithm [4]. Even with this enhancement, the s...

Gridworlds are popular testbeds for planning with incomplete information but not much is known about their properties. We study a fundamental planning problem, localization, to investigate whether gridworlds make good testbeds for planning with incomplete information. We find empirically that greedy planning methods that interleave planning and plan execution can localize robots very quickly on random gridworlds or mazes. Thus, they may not provide adequately challenging testbeds. On the other hand, we show that finding localization plans that are within a log factor of optimal is NP-hard. Thus there are instances of gridworlds on which all greedy planning methods perform very poorly, and we show how to construct them. These theoretical results help empirical researchers to select appropriate planning methods for planning with incomplete information as well as testbeds to demonstrate them. Introduction Testbeds (prototypical test domains) are planning domains that allo...

This paper reports about research projects of the University of Paderborn in the field of distributed combinatorial optimization. We give an introduction into combinatorial optimization and a brief definition of some important applications. As a first exact solution method we describe branch & bound and present the results of our work on its distributed implementation. Results of our distributed implementation of iterative deepening conclude the first part about exact methods. In the second part we give an introduction into simulated annealing as a heuristic method and present results of its parallel implementation. This part is concluded with a brief description of genetic algorithms and some other heuristic methods together with some results of their distributed implementation.

Admissible and consistent heuristic functions are usually preferred in single-agent heuristic search as they guarantee optimal solutions with complete search methods such as A * and IDA*. Larger problems, however, frequently make a complete search intractable due to space and/or time limitations. In particular, a path-planning agent in a realtime strategy game may need to take an action before its complete search has the time to finish. In such cases, incomplete search techniques (such as RTA*, SRTA*, RTDP, DTA*) can be used. Such algorithms conduct a limited ply lookahead and then evaluate the states envisioned using a heuristic function. The action selected on the basis of such evaluations can be suboptimal due to the incompleteness of search and inaccuracies in the heuristic. It is usually believed that deeper lookahead increases the chances of taking the optimal action. In this paper, we demonstrate that this is not necessarily the case, even when admissible and consistent heuristic functions are used. 1 Lookahead Pathologies in Real-time Single-agent Search Complete search methods such as A * [Hart et al, 1968] and IDA * [Korf, 1985] produce optimal solutions when based on an admissible and monotonic heuristic function. The primary drawbacks are the exponential running time and the necessity to wait until the search completes before the first action can be taken [Korf, 1990], This limits the applicability of complete search in practice as the deliberation time per action can be severely limited [Higgins, 2002], the domain model can be expensive [Bulitko and Wilkins, 2002], the goal states can be difficult to recognize [Levner et al, 2002]. Consequently, despite numerous advances in improving heuristic functions [Korf and Taylor, 1996; Culberson and Schaeffer, 1994; Reinefeld, 1993; Korf, 1997], incomplete real-time/on-line search methods remain the practical choice for complex reallife problems. Various incomplete search methods have been proposed

Abstract Automated image interpretation is an important task innumerous applications ranging from security systems to natural resource inventorization based on remote-sensing.Recently, a second generation of adaptive machine-learned image interpretation system (ADORE) has shown expert-level performance in several challenging domains. Its extension, MR ADORE, aims at removing the last vestiges ofhuman intervention still present in the original design of ADORE. Both systems treat the image interpretation pro-cess as a sequential decision making process guided by a machine-learned heuristic value function. This paper em-ploys a new leveraging algorithm for regression (R ESLEV)to improve the learnability of the heuristics in MR ADORE. Experiments show that RESLEV improves the system's per-formance if the base learners are weak. Further analysis discovers the difference between regression and decision-making problems, and suggests an interesting research direction. Keywords: adaptive image interpretation system, leverag-ing for regression, boosting, sequential decision making. 1.

Planning problems are often formulated as heuristic search. The choice of the heuristic function plays a significant role in the performance of planning systems, but a good heuristic is not always available. We propose a new approach to learning heuristic functions from previously solved problem instances in a given domain. Our approach is based on approximate linear programming, commonly used in reinforcement learning. We show that our approach can be used effectively to learn admissible heuristic estimates and provide an analysis of the accuracy of the heuristic. When applied to common heuristic search problems, this approach reliably produces good heuristic functions.