Heuristic functions play an important role in drastically improving performance of satisficing planners based on greedy best-first search (GBFS). While automatic generation of heuristic functions (e.g., (Hoffmann and Nebel 2001; Helmert 2006)) enables state-of-the-art satisficing planners to solve very complicated planning problems including benchmarks in the International Planning Competitions, accurate evaluations of nodes still remain as a challenging task. Although GBFS is fundamental and powerful in planning, it has an essential drawback when heuristic functions return inaccurate estimates. Assume that a heuristic function underestimates the difficulties of unpromising nodes. Then, since GBFS must expand nodes with small heuristic values first, it spends most of time in searching only unpromising areas and delays moving to the promising part. Previous work tackles this issue by adding a diversity to search, which is an ability in simultaneously exploring different parts of the search space to bypass large errors in heuristic functions. Several algorithms combined with diversity (e.g., K-best-first search (KBFS) in (Felner, Kraus, and Korf 2003)) are empirically shown to be superior to naive best-first search algorithms. However, they still have limited diversity, since they do not immediately expand nodes mistakenly evaluated as very unpromising ones. This paper presents a new technique called diverse best-first search (DBFS) , which incorporates a diversity into search in a different way than previous search-based approaches. We show empirical results clearly showing that DBFS is effective in satisficing planning.

Real-time search is a well known approach to solving search problems under tight time constraints. Recently, it has been shown that LSS-LRTA∗ , a well-known real-time search algorithm, can be improved when search is actively guided away of depressions. In this paper we investigate whether or not RTAA∗ can be improved in the same manner. We propose aRTAA∗ and daRTAA∗ , two algorithms based on RTAA∗ that avoid heuristic depressions. Both algorithms outperform RTAA∗ on standard path-finding tasks, obtaining better-quality solutions when the same time deadline is imposed on the duration of the planning episode. We prove, in addition, that both algorithms have good theoretical properties.

Herein, we employ a genetic algorithm (GA) to obtaining solvers for both the difficult FreeCell puzzle and the slidingtile Discrete puzzles, also known as single-player games, are puzzle. Note that although from a computationalcomplexity an excellent problem domain for artificial intelligence research, point of view the Rush Hour puzzle is harder because they can be parsimoniously described yet (unless NP PSPACE), search spaces induced by typical instances are often hard to solve (Pearl 1984). A well-known, highly of FreeCell tend to be substantially larger than those popular example within the domain of discrete puzzles is the of Rush Hour, and thus far more difficult to solve. This is card game of FreeCell. Another highly popular game is the evidenced by the failure of standard search methods to solve sliding-tile puzzle, the traditional versions of which are the FreeCell, as opposed to their success in solving all 6x6 Rush 15-puzzle (4X4) and the 24-puzzle (5X5). State-of-the-art Hour problems without requiring any heuristics (Hauptman heuristics allow for fast solutions of arbitrary instances of et al. 2009).

In many domains, different actions have different costs. In this paper, we show that various kinds of best-first search algorithms are sensitive to the ratio between the lowest and highest operator costs. First, we take common benchmark domains and show that when we increase the ratio of operator costs, the number of node expansions required to find a solution increases. Second, we provide a theoretical analysis showing one reason this phenomenon occurs. We also discuss additional domain features that can cause this increased difficulty. Third, we show that searching using distance-to-go estimates can significantly ameliorate this problem. Our analysis takes an important step toward understanding algorithm performance in the presence of differing costs. This research direction will likely only grow in importance as heuristic search is deployed to solve real-world problems.

The Pancake problem has become a classical combinatorial problem. Different attempts have been made to optimally solve it and/or to derive tighter bounds on the diameter of its state space for a different number of discs. Until very recently, the most successful technique for solving different instances optimally was based on Pattern Databases. Although different approaches have been tried, solutions with Pattern Databases on Pancakes with more than 19 discs have never been reported. In this work, a new technique is introduced which allows the definition of Additive Pattern Databases for solving Pancakes of an arbitrary length. As a result, this technique solves Pancake problems with twice as many discs as the largest ones solved nowadays with other techniques based on Pattern Databases saving up to two orders of magnitude of space.

A* is a best-first search algorithm that returns an optimal solution. w-admissible algorithms guarantee that the returned solution is no larger than w times the optimal solution. In this paper we introduce a generalization of the w-admissibility concept that we call PAC search, which is inspired by the PAC learning framework in Machine Learning. The task of a PAC search algorithm is to find a solution that is w-admissible with high probability. In this paper we formally define PAC search, and present a framework for PAC search algorithms that can work on top of any search algorithm that produces a sequence of solutions. Experimental results on the 15-puzzle demonstrate that our framework activated on top of Anytime Weighted A* (AWA*) expands significantly less nodes than regular AWA* while returning solutions that have almost the same quality.

We address the problem of optimal path finding for multiple agents where agents must not collide and their total travel cost should be minimized. Previous work used traditional single-agent search variants of the A* algorithm. In Sharon et. al. (2011), we introduced a novel two-level search algorithm framework for this problem. The high-level searches a novel search tree called increasing cost tree (ICT). The low-level performs a goal test on each ICT node. The new framework, called ICT search (ICTS), showed to run faster than the previous state-of-the-art A* approach by up to three orders of magnitude in many cases. In this paper we focus on the low-level of ICTS which performs the goal test. We introduce a number of optional pruning techniques that can significantly speed up the goal test. We discuss these pruning techniques and provide supporting experimental results.

In this paper we describe novel representations for precomputed heuristics based on Level-Ordered Edge Sequence (LOES) encodings. We introduce compressed LOES, an extension to LOES that enables more aggressive compression of the state-set representation. We evaluate the novel repre- sentations against the respective perfect-hash and binary decision diagram (BDD) representations of pattern databases in a variety of STRIPS domains.

Tree search is a common technique for solving constraint satisfaction and combinatorial optimization problems. The most popular strategies are depth-first search and limited discrepancy search. Aside from pruning or ordering the children of each node, these algorithms do not adapt their search order to take advantage of information that becomes available during search, such as heuristic scores or leaf costs. We present a framework called best-leaf-first search (BLFS) that uses this additional information to estimate the cost of taking discrepancies in the search tree and then attempts to visit leaves in a best-first order. In this way, BLFS brings the idea of best-first search from shortest path problems to the areas of constraint satisfaction and combinatorial optimization. Empirical results demonstrate that this new dynamic approach results in better search performance than previous static search strategies on two very different domains: structured CSPs and the traveling salesman problem.

State-set search is state space search when the states being manipulated by the search algorithm are sets of states from some underlying state space. State-set search arises commonly in planning and abstraction systems, but this paper provides the first formal, general analysis of state-set search. We show that the state-set distance computed by planning systems is different than that computed by abstraction systems and introduce a distance in between the two, dww, the maximum admissible distance. We introduce the concept of a multi-abstraction, which maps a state to more than one abstract state in the same abstract space, describe the first implementation of a multi-abstraction system that computes dww, and give initial experimental evidence that it can be superior to domain abstraction.