A ubiquitous feature of planning problems — problems involving the automatic generation of action sequences for attaining a given goal — is the need to economize limited resources such as fuel or money. While heuristic search, mostly based on standard algorithms such as A*, is currently the superior method for most varieties of planning, its ability to solve critically resource-constrained problems is limited: current planning heuristics are bad at dealing with this kind of structure. To address this, one can try to devise better heuristics. An alternative approach is to change the nature of the search instead. Local search has received some attention in planning, but not with a specific focus on how to deal with limited resources. We herein begin to fill this gap. We highlight the limitations of previous methods, and we devise a new improvement (smart restarts) to the local search method of a previously proposed planner (Arvand). Systematic experiments show how performance depends on problem structure and search parameters. In particular, we show that our new method can outperform previous planners by a large margin.

In this paper we propose a new algorithm for solving general two-player turn-taking games that performs symbolic search utilizing binary decision diagrams (BDDs). It consists of two stages: First, it determines all breadth-first search (BFS) layers using forward search and omitting duplicate detection, next, the solving process operates in backward direction only within these BFS layers thereby partitioning all BDDs according to the layers the states reside in. We provide experimental results for selected games and compare to a previous approach. This comparison shows that in most cases the new algorithm outperforms the existing one in terms of runtime and used memory so that it can solve games that could not be solved before with a general approach.

The number partitioning problem is to divide a set of integers into a collection of subsets, so that the sum of the numbers in each subset are as nearly equal as possible. There are at least three natural objective functions for number partitioning. One is to minimize the largest subset sum, another is to maximize the smallest subset sum, and the third is to minimize the difference between the largest and smallest subset sums. I show that contrary to my previous claims, no two of these objective functions are equivalent for partitioning numbers three or more ways. Minimizing the largest subset sum or maximizing the smallest subset sum correspond to different practical applications of number partitioning, and both allow a recursive strategy for finding optimal solutions that is very effective in practice. Finally, a completely new version of this recursive strategy appears to reduce the asymptotic complexity of the algorithm, and results in orders of magnitude improvement over the best previous results for multi-way partitioning.

One of the latest prominent results was by Schaeffer In recent years general game playing has received an increasing et al. (2007), who were able to solve American Checkers after amount of attention, especially due to the annual more than ten years of computation and proved that the general game playing competition (Genesereth, Love, and optimal outcome is a draw. Of course, due to the domain Pell 2005) that is held at AAAI or IJCAI since 2005. In independent scenario, we cannot expect to come up with solutions general game playing the agents are provided a description for such complex games in general game playing. of a game according to certain rules and need to play it. In explicit representation, many general games are too In case of multi-player games the agents often play against complex to fit into RAM or even on a hard disk. So, to solve each other, while in case of single-player games the agent them we perform symbolic search, which utilizes binary decision tries to find a sequence of moves to reach a terminal state diagrams (BDDs) (Bryant 1986) as they decrease the where it can achieve the best reward possible. The authors memory consumption, if a good variable ordering is found. of the agents do not know which games will be played, so In this paper we will present a new approach to solve general no domain specific knowledge can be inserted.

HDA* is a simple, parallelization of A* where work is asynchronously distributed among the nodes by a global hash function. Using up to 1024 cores on a large distributed memory cluster, we evaluate HDA* for a domain-independent planner as well an application-specific 24-puzzle solver. We show that HDA* scales fairly well on a large cluster using up to 1024 cores. Our analysis of the scaling behavior shows that on a cluster of multicore nodes, using only a subset of the available cores and leaving some cores idle can, surprisingly, lead to better results.

search algorithms such as IDA* or heuristic-search planners. Our method aims to generate a strong heuristic from a given weak heuristic h 0 through bootstrapping. The "easy" problem instances that can be solved using h 0 provide training examples for a learning algorithm that produces a heuristic h 1 that is expected to be stronger than h 0 . If h 0 is too weak to solve any of the given instances we use a random walk technique to create a sequence of successively more difficult instances starting with ones that are solvable by h 0 . The bootstrap process is then repeated using h i in lieu of h i –1 until a sufficiently strong heuristic is produced. We test our method on the 15- and 24-sliding tile puzzles, the 17- and 24-pancake puzzles, and the 15- and 20-blocks world. In every case our method produces a heuristic that allows IDA* to solve randomly generated problem instances extremely quickly with solutions very close to optimal.

This paper examines the following statements about heuristic search, which are commonly held to be true: More accurate heuristics result in fewer node expansions by A* and IDA*. A* does fewer node expansions than any other equally informed algorithm that finds optimal solutions.  Any admissible heuristic can be turned into a consistent heuristic by a simple technique called pathmax. In search spaces whose operators all have the same cost A* with the heuristic function h(s)=0 for all states, s, is the same as breadth-first search. Bidirectional A* stops when the forward and backward search frontiers meet. The paper demonstrates that all these statements are false and provides alternative statements that are true.

True distance memory-based heuristics (TDHs) were recently introduced as a way to obtain admissible heuristics for explicit state spaces. In this paper, we introduce a new TDH, the portal-based heuristic. The domain is partitioned into regions and portals between regions are identified. True distances between all pairs of portals are stored and used to obtain admissible heuristics throughout the search. We introduce an A*-based algorithm that takes advantage of the special properties of the new heuristic. We study the advantages and limitations of the new heuristic. Our experimental results show large performance improvements over previously-reported TDHs for commonly used classes of maps.

We present a new heuristic point-to-point shortest path algorithm based on contraction hierarchies (CH). Given an epsilon >= 0, we can prove that the length of the path computed by our algorithm is at most (1 + ε) times the length of the optimal (shortest) path. Exact CH is based on node contraction: removing nodes from a network and adding shortcuts to preserve shortest path distances. Our heuristic CH tries to avoid adding shortcuts even when a replacement path is (1+epsilon) times longer. However, we cannot avoid all such shortcuts, as we need to ensure that errors do not stack. Combinations with goal-directed techniques bring further speed-ups.

In this paper we improve solving two-player games by computing the game-theoretical value of every reachable state. A graphics processing unit located on the graphics card is used as a co-processor to accelerate the solution process. We exploit perfect hash functions to store the game states efficiently in memory and to transfer their ordinal representation between the host and the graphics card. As an application we validate Gasser's results that Nine-Men-Morris is a draw on a personal computer. Moreover, our solution is strong, while for the opening phase Gasser only provided a weak solution.