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Optimizing Selective Search in Chess

arXiv.org Artificial Intelligence

In this paper we introduce a novel method for automatically tuning the search parameters of a chess program using genetic algorithms. Our results show that a large set of parameter values can be learned automatically, such that the resulting performance is comparable with that of manually tuned parameters of top tournament-playing chess programs.


Solving the Resource Constrained Project Scheduling Problem with Generalized Precedences by Lazy Clause Generation

arXiv.org Artificial Intelligence

The technical report presents a generic exact solution approach for minimizing the project duration of the resource-constrained project scheduling problem with generalized precedences (Rcpsp/max). The approach uses lazy clause generation, i.e., a hybrid of finite domain and Boolean satisfiability solving, in order to apply nogood learning and conflict-driven search on the solution generation. Our experiments show the benefit of lazy clause generation for finding an optimal solutions and proving its optimality in comparison to other state-of-the-art exact and non-exact methods. The method is highly robust: it matched or bettered the best known results on all of the 2340 instances we examined except 3, according to the currently available data on the PSPLib. Of the 631 open instances in this set it closed 573 and improved the bounds of 51 of the remaining 58 instances.


Entropy-Based Search Algorithm for Experimental Design

arXiv.org Machine Learning

The scientific method relies on the iterated processes of inference and inquiry. The inference phase consists of selecting the most probable models based on the available data; whereas the inquiry phase consists of using what is known about the models to select the most relevant experiment. Optimizing inquiry involves searching the parameterized space of experiments to select the experiment that promises, on average, to be maximally informative. In the case where it is important to learn about each of the model parameters, the relevance of an experiment is quantified by Shannon entropy of the distribution of experimental outcomes predicted by a probable set of models. If the set of potential experiments is described by many parameters, we must search this high-dimensional entropy space. Brute force search methods will be slow and computationally expensive. We present an entropy-based search algorithm, called nested entropy sampling, to select the most informative experiment for efficient experimental design. This algorithm is inspired by Skilling's nested sampling algorithm used in inference and borrows the concept of a rising threshold while a set of experiment samples are maintained. We demonstrate that this algorithm not only selects highly relevant experiments, but also is more efficient than brute force search. Such entropic search techniques promise to greatly benefit autonomous experimental design.


GPU Exploration of Two-Player Games with Perfect Hash Functions

AAAI Conferences

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.


Anytime Heuristic Search: Frameworks and Algorithms

AAAI Conferences

Anytime search is a pragmatic approach for trading solution cost and solving time. It can also be used for solving problems within a time bound. Three frameworks for constructing anytime algorithms from bounded suboptimal search have been proposed: continuing search, repairing search, and restarting search, but what combination of suboptimal search and anytime framework performs best? An extensive empirical evaluation results in several novel algorithms and reveals that the relative performance of frameworks is essentially fixed, with the repairing framework having the strongest overall performance. As part of our study, we present two enhancements to Anytime Window A* that allow it to solve a wider range of problems and hastens its convergance on optimal solutions.


Directed Plateau Search for MAX-k-SAT

AAAI Conferences

Local search algorithms for MAX-k-SAT must often explore large regions of mutually connected equal moves, or plateaus, typically by taking random walks through the region. In this paper, we develop a surrogate plateau "gradient" function using a Walsh transform of the objective function. This function gives the mean value of the objective function over localized volumes of the search space.  This information can be used to direct search through plateaus more quickly. The focus of this paper is on demonstrating that formal analysis of search space structure can direct existing algorithms in a more principled manner than random walks.  We show that embedding the gradient computation into a hill-climbing local search for MAX-k-SAT improves its convergence profile.


Search Space Reduction Using Swamp Hierarchies

AAAI Conferences

In various domains, such as computer games, robotics, and transportation networks, shortest paths may need to be found quickly. Search time can be significantly reduced if it is known which parts of the graph include "swamps" - areas that cannot lie on the only available shortest path, and can thus safely be pruned during search. We introduce an algorithm for detecting hierarchies of swamps, and exploiting them. Experiments support our claims of improved efficiency, showing significant reduction in search time.


Common Misconceptions Concerning Heuristic Search

AAAI Conferences

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.


Improving Local Search for Resource-Constrained Planning

AAAI Conferences

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.


Real-Time Search in Dynamic Worlds

AAAI Conferences

Our approach is conceptually simple: we perform a the search algorithm. In video game pathfinding and robot standard dynamic search but interrupt it periodically to move motion planning, the search is often required to be real-time, the agent according to a real-time search. In this paper, we that is, return the next move for the agent within a strict time use D* Lite (Koenig and Likhachev 2002) or Anytime D* bound, so that the agent can continue acting in the world. To (Likhachev et al. 2005) as the dynamic search algorithm and accommodate this constraint, real-time search algorithms interleave LRTA* (Korf 1990) or LSS-LRTA* (Koenig and Sun 2009) planning and moving. Because the agent must make as the real-time search algorithm. D* Lite and Anytime D* a choice of which move to execute next before finding a perform a global search backwards from the goal, trying to complete path to a goal, real-time search algorithms achieve reach the agent's current location. LRTA* and LSS-LRTA* fast response times at the cost of sub-optimality of the resulting perform a local search forward from the agent's current location, trajectories. There has been much research on real-time trying to reach the goal. Therefore, RTD* is a form of search algorithms, starting with LRTA* (Korf 1990).