Showing papers on "Admissible heuristic published in 2005"

Finding optimal solutions to the graph partitioning problem with heuristic search

Abstract: As search spaces become larger and as problems scale up, an efficient way to speed up the search is to use a more accurate heuristic function. A better heuristic function might be obtained by the following general idea. Many problems can be divided into a set of subproblems and subgoals that should be achieved. Interactions and conflicts between unsolved subgoals of the problem might provide useful knowledge which could be used to construct an informed heuristic function. In this paper we demonstrate this idea on the graph partitioning problem (GPP). We first show how to format GPP as a search problem and then introduce a sequence of admissible heuristic functions estimating the size of the optimal partition by looking into different interactions between vertices of the graph. We then optimally solve GPP with these heuristics. Experimental results show that our advanced heuristics achieve a speedup of up to a number of orders of magnitude. Finally, we experimentally compare our approach to other states of the art graph partitioning optimal solvers on a number of classes of graphs. The results obtained show that our algorithm outperforms them in many cases.

External-memory pattern databases using structured duplicate detection

Abstract: A pattern database is a lookup table that stores an exact evaluation function for a relaxed search problem, which provides an admissible heuristic for the original search problem. In general, the larger the pattern database, the more accurate the heuristic function. We consider how to build large pattern databases that are stored in external memory, such as disk, and how to use an external-memory pattern database efficiently in heuristic search. To limit the number of slow disk I/O operations needed to construct and query an external-memory pattern data-base, we adapt an approach to external-memory graph search called structured duplicate detection that localizes memory references by leveraging an abstraction of the state space. We present results that show this approach increases the scalability of heuristic search by allowing larger and more accurate pattern database heuristics.

A heuristic search algorithm for solving first-order MDPs

Abstract: We present a heuristic search algorithm for solving first-order MDPs (FOMDPs). Our approach combines first-order state abstraction that avoids evaluating states individually, and heuristic search that avoids evaluating all states. Firstly, we apply state abstraction directly on the FOMDP avoiding propositionalization. Such kind of abstraction is referred to as first-order state abstraction. Secondly, guided by an admissible heuristic, the search is restricted only to those states that are reachable from the initial state. We demonstrate the usefullness of the above techniques for solving FOMDPs on a system, referred to as FC-Planner, that entered the probabilistic track of the International Planning Competition (IPC'2004).

Integrating learning from examples into the search for diagnostic policies

Abstract: This paper studies the problem of learning diagnostic policies from training examples. A diagnostic policy is a complete description of the decision-making actions of a diagnostician (i.e., tests followed by a diagnostic decision) for all possible combinations of test results. An optimal diagnostic policy is one that minimizes the expected total cost, which is the sum of measurement costs and misdiagnosis costs. In most diagnostic settings, there is a tradeoff between these two kinds of costs. This paper formalizes diagnostic decision making as a Markov Decision Process (MDP). The paper introduces a new family of systematic search algorithms based on the AO* algorithm to solve this MDP. To make AO* efficient, the paper describes an admissible heuristic that enables AO* to prune large parts of the search space. The paper also introduces several greedy algorithms including some improvements over previously-published methods. The paper then addresses the question of learning diagnostic policies from examples. When the probabilities of diseases and test results are computed from training data, there is a great danger of overfitting. To reduce overfitting, regularizers are integrated into the search algorithms. Finally, the paper compares the proposed methods on five benchmark diagnostic data sets. The studies show that in most cases the systematic search methods produce better diagnostic policies than the greedy methods. In addition, the studies show that for training sets of realistic size, the systematic search algorithms are practical on today's desktop computers.

Improved methods for scheduling flexible manufacturing systems based on Petri nets and heuristic search

Abstract: This paper proposes and evaluates two improved Petri net (PN)-based hybrid search strategies and their applications to flexible manufacturing system (FMS) scheduling. The algorithms proposed in some previous papers, which combine PN simulation capabilities with A * heuristic search within the PN reachability graph, may not find an optimum solution even with an admissible heuristic function. To remedy the defects an improved heuristic search strategy is proposed, which adopts a different method for selecting the promising markings and reserves the admissibility of the algorithm. To speed up the search process, another algorithm is also proposed which invokes faster termination conditions and still guarantees that the solution found is optimum. The scheduling results are compared through a simple FMS between our algorithms and the previous methods. They are also applied and evaluated in a set of randomly-generated FMSs with such characteristics as multiple resources and alternative routes.

An efficient LP-based admissible heuristic for cost-based abduction

Abstract: Cost-based abduction (CBA) is an important problem in reasoning under uncertainty. The CBA problem is NP-hard, and existing techniques have exponential worst-case complexity. This paper presents an admissible heuristic for CBA based on the use of linear programming to obtain an optimistic estimate of the cost-to-goal. The article then presents empirical results that indicate that the authors' method is efficient in comparison to Santos‘ integer linear programming method.

Generating admissible heuristics by abstraction for search in stochastic domains

Abstract: Search in abstract spaces has been shown to produce useful admissible heuristic estimates in deterministic domains. We show in this paper how to generalize these results to search in stochastic domains. Solving stochastic optimization problems is significantly harder than solving their deterministic counterparts. Designing admissible heuristics for stochastic domains is also much harder. Therefore, deriving such heuristics automatically using abstraction is particularly beneficial. We analyze this approach both theoretically and empirically and show that it produces significant computational savings when used in conjunction with the heuristic search algorithm LAO*.