Topic
Admissible heuristic
About: Admissible heuristic is a research topic. Over the lifetime, 197 publications have been published within this topic receiving 15329 citations. The topic is also known as: admissible heuristics.
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TL;DR: An alternative approach is suggested: to model the accuracy of admissible heuristic functions as the probability of the heuristic hill-climbing search algorithm to find the goal state in a number of steps that equals theHeuristic value of an arbitrary node.
Abstract: Comparing heuristics has been a major issue from the early days of heuristic search. From the very beginning, measures of the accuracy of heuristic functions were strongly based on the number of nodes generated, and they are often still based on it. In this work, an alternative approach is suggested: to model the accuracy of admissible heuristic functions as the probability of the heuristic hill-climbing search algorithm to find the goal state in a number of steps that equals the heuristic value of an arbitrary node. The resulting method serves to assess on the accuracy of both consistent and inconsistent heuristic functions. Comparisons with different sizes of the sliding-tile puzzle show that the model suggested predicts the accuracy of the heuristic function with a good precision. The resulting procedure is used to derive figures on the accuracy of a large number of heuristics for the 15-Puzzle with different variants of the search algorithm IDA?.
2 citations
01 Sep 2021
TL;DR: This article looks at two-player zero-sum stochastic games with a discounted criterion with a view to proposing zsSG-HSVI, an algorithm based on heuristic search value iteration (HSVI), and which thus relies on generating trajectories.
Abstract: In sequential decision making, heuristic search algorithms allow exploiting both the initial situation and an admissible heuristic to efficiently search for an optimal solution, often for planning purposes Such algorithms exist for problems with uncertain dynamics, partial observability, multiple criteria, or multiple collaborating agents In this article, we look at two-player zero-sum stochastic games (zsSGs) with a discounted criterion, in a view to propose a solution tailored to the fully observable case, while solutions have been proposed for particular, though still more general, partially observable cases This setting induces reasoning on both a lower and an upper bound of the value function, which leads us to proposing zsSG-HSVI, an algorithm based on heuristic search value iteration (HSVI), and which thus relies on generating trajectories We demonstrate that, each player acting optimistically, and employing simple heuristic initializations, HSVI's convergence in finite time to an $\epsilon$ -optimal solution is preserved An empirical study of the resulting approach is conducted on benchmark problems of various sizes
2 citations
01 Jan 2018
TL;DR: A new family of admissible heuristics for classical planning, based on Cartesian abstractions, is introduced, which is derived by counterexample-guided abstraction refinement and it is shown that saturated cost partitioning outperforms the previous state of the art in optimal classical planning.
Abstract: Heuristic search with an admissible heuristic is one of the most prominent approaches to solving classical planning tasks optimally. In the first part of this thesis, we introduce a new family of admissible heuristics for classical planning, based on Cartesian abstractions, which we derive by counterexample-guided abstraction refinement. Since one abstraction usually is not informative enough for challenging planning tasks, we present several ways of creating diverse abstractions. To combine them admissibly, we introduce a new cost partitioning algorithm, which we call saturated cost partitioning. It considers the heuristics sequentially and uses the minimum amount of costs that preserves all heuristic estimates for the current heuristic before passing the remaining costs to subsequent heuristics until all heuristics have been served this way.
In the second part, we show that saturated cost partitioning is strongly influenced by the order in which it considers the heuristics. To find good orders, we present a greedy algorithm for creating an initial order and a hill-climbing search for optimizing a given order. Both algorithms make the resulting heuristics significantly more accurate. However, we obtain the strongest heuristics by maximizing over saturated cost partitioning heuristics computed for multiple orders, especially if we actively search for diverse orders.
The third part provides a theoretical and experimental comparison of saturated cost partitioning and other cost partitioning algorithms. Theoretically, we show that saturated cost partitioning dominates greedy zero-one cost partitioning. The difference between the two algorithms is that saturated cost partitioning opportunistically reuses unconsumed costs for subsequent heuristics. By applying this idea to uniform cost partitioning we obtain an opportunistic variant that dominates the original. We also prove that the maximum over suitable greedy zero-one cost partitioning heuristics dominates the canonical heuristic and show several non-dominance results for cost partitioning algorithms. The experimental analysis shows that saturated cost partitioning is the cost partitioning algorithm of choice in all evaluated settings and it even outperforms the previous state of the art in optimal classical planning.
2 citations
05 Mar 2021
TL;DR: In this paper, the authors proposed an algorithm that would more efficiently operate the search while on the same time not lower the quality of path, which includes two phase of search, the first phase is to fasten the process of path finding, while the second phase are to guarantee the quality.
Abstract: Traditional optimal path finding algorithms are usually too complex for real world problems, motivating the need to find path with sub-optimality. Typically suboptimal algorithms use a single admissible heuristic value to decide how to find a path and bound the cost. Algorithms like Weighted A*(WA*), Convex upward parabola(XUP) and Convex downward parabola(XDP) have overcome the node re-expansion problem during search. However, this re-incur a balance between the quality of path and the speed of search. In this paper, we research the process of extending and put forward an algorithm that would more efficiently operate the search while on the same time not lower the quality of path. This algorithm includes two phase of search, the first phase is to fasten the process of path finding, while the second phase is to guarantee the quality of path. In most maps we choose from Dragon Age Origins(DAO), our algorithm performs better than WA*.
2 citations
12 Nov 2002
TL;DR: The pomset-based model presented in this paper takes into account the precedence constraints in order to obtain a better estimation for the second heuristic function, so that the performance of the algorithm could be improved.
Abstract: This paper presents a model based on pomsets (partially ordered multisets) for estimating the minimum number of setups in the workcells in Assembly Sequence Planning. This problem is focused through the minimization of the makespan (total assembly time) in a multirobot system. The planning model considers, apart from the durations and resources needed for the assembly tasks, the delays due to the setups in the workcells. An A* algorithm is used to meet the optimal solution. It uses the And/Or graph for the product to assemble, that corresponds to a compressed representation of all feasible assembly plans. Two basic admissible heuristic functions can be defined from relaxed models of the problem, considering the precedence constraints and the use of resources separately. The pomset-based model presented in this paper takes into account the precedence constraints in order to obtain a better estimation for the second heuristic function, so that the performance of the algorithm could be improved.
2 citations