A New Result on the Complexity of Heuristic Estimates for the A* Algorithm

Relaxed models are abstract problem descriptions generated by ignoring constraints that are present in base-level problems. They play an important role in planning and search algorithms, as it has been shown that the length of an optimal solution to a relaxed model yields a monotone heuristic for an A? search of a base-level problem. Optimal solutions to a relaxed model may be computed algorithmically or by search in a further relaxed model, leading to a search that explores a hierarchy of relaxed models. In this paper, we review the traditional definition of problem relaxation and show that searching in the abstraction hierarchy created by problem relaxation will not reduce the computational effort required to find optimal solutions to the base- level problem, unless the relaxed problem found in the hierarchy can be transformed by some optimization (e.g., subproblem factoring). Specifically, we prove that any A* search of the base-level using a heuristic h2 will largely dominate an A* search of the base-level using a heuristic h1, if h1 must be computed by an A* search of the relaxed model using h2.

The Optimality of Satisficing Solutions

This paper addresses a prevailing assumption in single-agent heuristic search theory- that problem-solving algorithms should guarantee shortest-path solutions, which are typically called optimal. Optimality implies a metric for judging solution quality, where the optimal solution is the solution with the highest quality. When path-length is the metric, we will distinguish such solutions as p-optimal.

Heuristic Search as Evidential Reasoning

BPS, the Bayesian Problem Solver, applies probabilistic inference and decision-theoretic control to flexible, resource-constrained problem-solving. This paper focuses on the Bayesian inference mechanism in BPS, and contrasts it with those of traditional heuristic search techniques. By performing sound inference, BPS can outperform traditional techniques with significantly less computational effort. Empirical tests on the Eight Puzzle show that after only a few hundred node expansions, BPS makes better decisions than does the best existing algorithm after several million node expansions