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.

Top-Down Search with Bottom-Up Evidence for Recognizing Handwritten Mathematical Expressions

Abstract: In handwritten mathematical expressions (ME), understanding the general structure of an ME is often easier than resolving local ambiguities. For instance, identifying a key operator in terms of its spatial relationship with its subordinates is relatively easier than resolving the ambiguities of single symbol identity and local spatial relationships. In addition, decisions related to key operators often occur close to the top (root) of the parse tree, while local decisions take place at the bottom of it. Based on these observations, we propose an incremental search framework in which a parse tree is expanded by tentatively selecting the key operators of an expression. The goodness of the selection is defined by the likelihood of key symbol, the goodness of the sub expressions, and their spatial relationships. In this framework, ambiguous local parts are processed after tentative decisions have been made at the global level. To handle explosiveness of key operator selection, an admissible heuristic function is defined based on the direct relationship of the key operator with the symbols at the bottom level. An experimental evaluation shows that our system is promising. Using it a robust interpretation can be made by utilizing global information and an interpretation can be reached quickly by the admissible heuristic function.

Solving Planning Under Uncertainty: Quantitative and Qualitative Approach

Abstract: Classical decision-theoretic planning methods assume that the probabilistic model of the domain is always accurate. We present two algorithms rLAO* and qLAO* in this paper. rLAO* and qLAO* can solve uncertainty Markov decision problems and qualitative Markov decision problems respectively. We prove that given an admissible heuristic function, both rLAO* and qLAO* can find an optimal solution. Experimental results also show that rLAO* and qLAO* inherit the merits of excellent performance of LAO* for solving uncertainty problems.

Robot Path Planning for Multiple Target Regions

Abstract: Optimal path planning to point goals is a well-researched problem. However, in the context of mobile robotics, it is often desirable to generate plans which visit a sequence of regions, rather than point goals. In this paper, we investigate methods for planning paths which visit multiple regions in a specified order, whilst minimising total path cost. We propose Multi-Region A*, an extension to the A* algorithm with an admissible heuristic for traversing multiple target regions. The heuristic is used to trim sub-optimal paths from the search, thereby reducing the computation time required to find the optimal solution. Additionally, we extend this method to create the Windowed Multi-Region A* which plans through overlapping sequences of regions. This provides a mechanism to trade-off optimality against computation time. We evaluate the performance of the proposed methods against point-to-point A* planning methods using a simulation of a wheeled office robot. The evaluation shows that Multi-Region A* with search pruning produces an optimal path, and the Windowed Multi-Region A* with a small window size gives a good approximate solution without compromising the total navigation time, in addition to providing robustness to dynamic obstacles.

A heuristic in A* for inference in nonlinear Probabilistic Classifier Chains

Abstract: Probabilistic Classifier Chains (PCC) is a very interesting method to cope with multi-label classification, since it is able to obtain the entire joint probability distribution of the labels. However, such probability distribution is obtained at the expense of a high computational cost. Several efforts have been made to overcome this pitfall, proposing different inference methods for estimating the probability distribution. Beam search and the - approximate algorithms are two methods of this kind. A more recently approach is based on the A* algorithm with an admissible heuristic, but it is limited to be used just for linear classifiers as base methods for PCC. This paper goes in that direction presenting an alternative admissible heuristic for the A* algorithm with two promising advantages in comparison to the above-mentioned heuristic, namely, i) it is more dominant for the same depth and, hence, it explores fewer nodes and ii) it is suitable for nonlinear classifiers. Additionally, the paper proposes an efficient implementation for the computation of the heuristic that reduces the number of models that must be evaluated by half. The experiments show, as theoretically expected, that this new algorithm reaches Bayes-optimal predictions in terms of subset 0/1 loss and explores fewer nodes than other state-of-the-art methods that also provide optimal predictions. In spite of exploring fewer nodes, this new algorithm is not as fast as the -approximate algorithm with =0 when the search for an optimal solution is highly directed. However, it shows its strengths when the datasets present more uncertainty, making faster predictions than other state-of-the-art approaches.

FluCaP: A Heuristic Search Planner for First-Order MDPs

Abstract: We present a heuristic search algorithm for solving first-order Markov Decision Processes (FOMDPs). Our approach combines first-order state abstraction that avoids evaluating states individually, and heuristic search that avoids evaluating all states. Firstly, in contrast to existing systems, which start with propositionalizing the FOMDP and then perform state abstraction on its propositionalized version we apply state abstraction directly on the FOMDP avoiding propositionalization. This kind of abstraction is referred to as first-order state abstraction. Secondly, guided by an admissible heuristic, the search is restricted to those states that are reachable from the initial state. We demonstrate the usefulness of the above techniques for solving FOMDPs with a system, referred to as FluCaP (formerly, FCPlanner), that entered the probabilistic track of the 2004 International Planning Competition (IPC2004) and demonstrated an advantage over other planners on the problems represented in first-order terms.