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Anytime Heuristic Search (1110.2737v1)

Published 12 Oct 2011 in cs.AI

Abstract: We describe how to convert the heuristic search algorithm A* into an anytime algorithm that finds a sequence of improved solutions and eventually converges to an optimal solution. The approach we adopt uses weighted heuristic search to find an approximate solution quickly, and then continues the weighted search to find improved solutions as well as to improve a bound on the suboptimality of the current solution. When the time available to solve a search problem is limited or uncertain, this creates an anytime heuristic search algorithm that allows a flexible tradeoff between search time and solution quality. We analyze the properties of the resulting Anytime A* algorithm, and consider its performance in three domains; sliding-tile puzzles, STRIPS planning, and multiple sequence alignment. To illustrate the generality of this approach, we also describe how to transform the memory-efficient search algorithm Recursive Best-First Search (RBFS) into an anytime algorithm.

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Authors (2)
  1. E. A. Hansen (1 paper)
  2. R. Zhou (160 papers)
Citations (284)

Summary

Anytime Heuristic Search: An Expert Analysis

The paper "Anytime Heuristic Search" by Eric A. Hansen and Rong Zhou presents a novel approach for converting the traditional A* heuristic search algorithm into an anytime algorithm. The central idea is to create algorithms capable of delivering preliminary solutions quickly while subsequently improving upon them as computational resources permit. This characteristic is crucial in domains where time constraints are variable or uncertain.

The authors propose a transformation of the A* algorithm by incorporating a weighted heuristic function, effectively creating the "Anytime A*" algorithm. This adaptation allows the algorithm to first find a potentially suboptimal solution rapidly and then iteratively refine this solution toward optimality. The weighted heuristic is achieved by modifying the node evaluation function with an adjustable weight parameter, w, which influences the balance between speed and accuracy. The weighted evaluation function is defined as:

fw(n)=g(n)+w×h(n)f_w(n) = g(n) + w \times h(n)

Here, g(n)g(n) represents the cost from the start node to the current node, and h(n)h(n) is the heuristic estimate from the current node to the goal node. The introduction of weights enables the algorithm to adopt a more depth-first search strategy, implicitly prioritizing solution discovery over strict optimality during initial search phases.

Theoretical and Empirical Insights

The authors rigorously analyze the theoretical properties of the Anytime A* algorithm, proving its convergence to an optimal solution and bounding the suboptimality of intermediate solutions. This theoretical groundwork ensures that the algorithm not only functions as intended but also provides measurable reliability in its performance within different domains.

Empirical evaluations across domains such as sliding-tile puzzles, STRIPS planning, and multiple sequence alignment demonstrate the practical utility and flexibility of the Anytime A* algorithm. Notable findings include a significant reduction in memory usage without a substantial increase in the time required to find optimal solutions, challenging prevailing assumptions regarding the inefficiency of node reexpansions in weighted heuristic searches.

Especially within the domain of STRIPS planning, Anytime A* consistently produced optimal solutions while utilizing memory resources more efficiently than traditional A* approaches. These results convey that the use of weighted heuristics does not invariably lead to inefficiencies in node expansions, a hypothesis previously unexplored with such depth.

Implications and Future Directions

The paper's contributions extend beyond specific applications, offering insights into broader heuristic search methodologies and enhancing their usability across varied computational problems. In particular, the adaptability of Anytime A* to achieve optimal solutions more efficiently offers a compelling advantage in environments where solution quality is paramount but computational time is constrained.

The methodology presented suggests several areas for future research. The exploration of using non-admissible heuristics combined with admissible lower bounds to further optimize the performance of anytime algorithms stands out as a promising avenue. Additionally, the integration of weighting techniques and memory-efficient search algorithms such as Recursive Best-First Search (RBFS) into the anytime heuristic framework could yield further advancements.

Ultimately, the Anytime A* algorithm proposed by Hansen and Zhou embodies a significant methodological advancement, offering both theoretical assurance and practical effectiveness. This work paves the way for enhanced heuristic search strategies that are more attuned to the demands of diverse AI problem domains.