Best-first Search Algorithm Research Articles

The More, the Merrier: Combining Heuristic Estimators for Satisficing Planning

We empirically examine several ways of exploiting the information of multiple heuristics in a satisficing best-first search algorithm, comparing their performance in terms of coverage, plan quality, speed, and search guidance. Our results indicate that using multiple heuristics for satisficing search is indeed useful. Among the combination methods we consider, the best results are obtained by the alternation method of the "Fast Diagonally Downward" planner.

Flexible protein‐protein docking based on Best‐First search algorithm

We developed a new high resolution protein-protein docking method based on Best-First search algorithm that loosely imitates protein-protein associations. The method operates in two stages: first, we perform a rigid search on the unbound proteins. Second, we search alternately on rigid and flexible degrees of freedom starting from multiple configurations from the rigid search. Both stages use heuristics added to the energy function, which causes the proteins to rapidly approach each other and remain adjacent, while optimizing on the energy. The method deals with backbone flexibility explicitly by searching over ensembles of conformations generated before docking. We ran the rigid docking stage on 66 complexes and grouped the results into four classes according to evaluation criteria used in Critical Assessment of Predicted Interactions (CAPRI; "high," "medium," "acceptable," and "incorrect"). Our method found medium binding conformations for 26% of the complexes and acceptable for additional 44% among the top 10 configurations. Considering all the configurations, we found medium binding conformations for 55% of the complexes and acceptable for additional 39% of the complexes. Introducing side-chains flexibility in the second stage improves the best found binding conformation but harms the ranking. However, introducing side-chains and backbone flexibility improve both the best found binding conformation and the best found conformation in the top 10. Our approach is a basis for incorporating multiple flexible motions into protein-protein docking and is of interest even with the current use of a simple energy function.

Memory intensive AND/OR search for combinatorial optimization in graphical models

In this paper we explore the impact of caching during search in the context of the recent framework of AND/OR search in graphical models. Specifically, we extend the depth-first AND/OR Branch-and-Bound tree search algorithm to explore an AND/OR search graph by equipping it with an adaptive caching scheme similar to good and no-good recording. Furthermore, we present best-first search algorithms for traversing the same underlying AND/OR search graph and compare both algorithms empirically. We focus on two common optimization problems in graphical models: finding the Most Probable Explanation (MPE) in belief networks and solving Weighted CSPs (WCSP). In an extensive empirical evaluation we demonstrate conclusively the superiority of the memory intensive AND/OR search algorithms on a variety of benchmarks.

A performance comparison of distance-based query algorithms using R-trees in spatial databases

Efficient processing of distance-based queries (DBQs) is of great importance in spatial databases due to the wide area of applications that may address such queries. The most representative and known DBQs are the K Nearest Neighbors Query (KNNQ), ρ Distance Range Query ( ρDRQ), K Closest Pairs Query (KCPQ) and ρ Distance Join Query ( ρDJQ). In this paper, we propose new pruning mechanism to apply them in the design of new Recursive Best-First Search (RBFS) algorithms for DBQs between spatial objects indexed in R-trees. RBFS is a general search algorithm that runs in linear space and expands nodes in best-first order, but it can suffer from node re-expansion overhead (i.e. to expand nodes in best-first order, some nodes can be considered more than once). The R-tree and its variations are commonly cited spatial access methods that can be used for answering such spatial queries. Moreover, an exhaustive experimental study was also included using R-trees, which resulted to several conclusions about the efficiency of proposed RBFS algorithm and its comparison with respect to other search algorithms (Best-First Search (BFS) and Depth-First Branch-and-Bound (DFBnB)), in terms of disk accesses, response time and main memory requirements, taking into account several important parameters as maximum branching factor ( Cmax), cardinality of the final query result ( K), distance threshold ( ρ) and size of a global LRU buffer ( B). In general RBFS is competitive for KNNQ and KCPQ where the maximum branching factor ( Cmax) is large enough (even better than DFBnB and very close to BFS), and it is a good alternative when we have main memory limitations in our computer due to high process overload in our system, since it is linear space consuming with respect to the height of the R-trees. Nevertheless, RBFS is the worst alternative for ρDRQ and ρDJQ. DFBnB is also a linear space algorithm and it obtains the same behavior as BFS for ρDRQ and ρDJQ; and it is the best when an LRU buffer was included. Finally, we have been able to check experimentally that BFS is the best for all DBQs, but it can consume many main memory resources to perform spatial queries.

Searching for close alternative plans

Consider the situation where an intelligent agent accepts as input a complete plan, i.e., a sequence of states (or operators) that should be followed in order to achieve a goal. For some reason, the given plan cannot be implemented by the agent, who then goes about trying to find an alternative plan that is as close as possible to the original. To achieve this, a search algorithm that will find similar alternative plans is required, as well as some sort of comparison function that will determine which alternative plan is closest to the original. In this paper, we define a number of distance metrics between plans, and characterize these functions and their respective attributes and advantages. We then develop a general algorithm based on best-first search that helps an agent efficiently find the most suitable alternative plan. We also propose a number of heuristics for the cost function of this best-first search algorithm. To explore the generality of our idea, we provide three different problem domains where our approach is applicable: physical roadmap path finding, the blocks world, and task scheduling. Experimental results on these various domains support the efficiency of our algorithm for finding close alternative plans.

The Fast Downward Planning System

Fast Downward is a classical planning system based on heuristic search. It can deal with general deterministic planning problems encoded in the propositional fragment of PDDL2.2, including advanced features like ADL conditions and effects and derived predicates (axioms). Like other well-known planners such as HSP and FF, Fast Downward is a progression planner, searching the space of world states of a planning task in the forward direction. However, unlike other PDDL planning systems, Fast Downward does not use the propositional PDDL representation of a planning task directly. Instead, the input is first translated into an alternative representation called multi-valued planning tasks, which makes many of the implicit constraints of a propositional planning task explicit. Exploiting this alternative representation, Fast Downward uses hierarchical decompositions of planning tasks for computing its heuristic function, called the causal graph heuristic, which is very different from traditional HSP-like heuristics based on ignoring negative interactions of operators. In this article, we give a full account of Fast Downward's approach to solving multi-valued planning tasks. We extend our earlier discussion of the causal graph heuristic to tasks involving axioms and conditional effects and present some novel techniques for search control that are used within Fast Downward's best-first search algorithm: preferred operators transfer the idea of helpful actions from local search to global best-first search, deferred evaluation of heuristic functions mitigates the negative effect of large branching factors on search performance, and multi-heuristic best-first search combines several heuristic evaluation functions within a single search algorithm in an orthogonal way. We also describe efficient data structures for fast state expansion (successor generators and axiom evaluators) and present a new non-heuristic search algorithm called focused iterative-broadening search, which utilizes the information encoded in causal graphs in a novel way. Fast Downward has proven remarkably successful: It won the "classical'' (i.e., propositional, non-optimising) track of the 4th International Planning Competition at ICAPS 2004, following in the footsteps of planners such as FF and LPG. Our experiments show that it also performs very well on the benchmarks of the earlier planning competitions and provide some insights about the usefulness of the new search enhancements.

Frontier search

The critical resource that limits the application of best-first search is memory. We present a new class of best-first search algorithms that reduce the space complexity. The key idea is to store only the Open list of generated nodes, but not the Closed list of expanded nodes. The solution path can be recovered by a divide-and-conquer technique, either as a bidirectional or unidirectional search. For many problems, frontier search dramatically reduces the memory required by best-first search. We apply frontier search to breadth-first search of sliding-tile puzzles and the 4-peg Towers of Hanoi problem, Dijkstra's algorithm on a grid with random edge costs, and the A* algorithm on the Fifteen Puzzle, the four-peg Towers of Hanoi Problem, and optimal sequence alignment in computational biology.

Heuristic allocation based on a dynamic programming state-space representation

In this paper, we focus on the lower level allocation problem of a hierarchical time-constrained product development situation. Commonly found in the industrial practice, the type of product development process we consider is the radical/experiential model of product development of Eisenhardt and Tabrizi, (Administr. Sci. Q. 40 (1995) 84). The description of the main characteristics of the process follows the line of the recent research of Bowers et al. (in: M.T. Brannick, E. Salas, C. Prince (Eds.), Team Performance Assessment and Measurement: Theory, Research, and Applications, Lawrence Erlbaum Associates, Inc., Publishers, New Jersey, 1997, pp. 85–108) and Oorschot (Analysing Radical NPD Projects from an Operational Control Perspective, Ph.D. Thesis, Eindhoven University of Technology, The Netherlands, 2001). Starting from the dynamic programming techniques, we propose a solution to this optimization problem by employing an A ∗ monotonic heuristic evaluation function for best-search algorithms. This function is based on aggregate information on the design task set. We discuss the efficiency of the general best-first search algorithm using an A ∗ evaluation function, and of an RBFS variant of it, which also searches in best-first order, using the same A ∗ evaluation function. We prove that the algorithms find an optimal feasible allocation, provided that there exists a feasible allocation. We conclude by commenting upon some experimental results.

The [formula omitted]-search algorithm: Application to tsume-shogi

This paper proposes a new search algorithm, denoted PN ∗ , for AND/OR tree search. The algorithm is based on proof-number (PN) search, a best-first search algorithm, proposed by Allis et al. [Artificial Intelligence 66 (1) (1994) 91–124], and on Korf's RBFS algorithm [Artificial Intelligence 62 (1) (1993) 41–78]. PN ∗ combines several existing ideas. It transforms a best-first PN-search algorithm into an iterative-deepening depth-first approach. Moreover, it is enhanced by methods such as recursive iterative deepening, dynamic evaluation, efficient successor ordering, and pruning by dependency relations. The resulting algorithm turns out to be highly efficient as witnessed by the experimental results. The PN ∗ algorithm is implemented in a tsume-shogi (Japanese-chess mating-problem) program, and evaluated by testing it on 295 notoriously difficult tsume-shogi problems (one problem has a depth of search of over 1500 plies). The experimental results are compared with those of other programs. The PN ∗ program shows by far the best results, solving all problems but one. Needless to say, it outperforms the best human tsume-shogi problem solvers by far.

Planning as heuristic search

In the AIPS98 Planning Contest, the hsp planner showed that heuristic search planners can be competitive with state-of-the-art Graphplan and sat planners. Heuristic search planners like hsp transform planning problems into problems of heuristic search by automatically extracting heuristics from Strips encodings. They differ from specialized problem solvers such as those developed for the 24-Puzzle and Rubik's Cube in that they use a general declarative language for stating problems and a general mechanism for extracting heuristics from these representations. In this paper, we study a family of heuristic search planners that are based on a simple and general heuristic that assumes that action preconditions are independent. The heuristic is then used in the context of best-first and hill-climbing search algorithms, and is tested over a large collection of domains. We then consider variations and extensions such as reversing the direction of the search for speeding node evaluation, and extracting information about propositional invariants for avoiding dead-ends. We analyze the resulting planners, evaluate their performance, and explain when they do best. We also compare the performance of these planners with two state-of-the-art planners, and show that the simplest planner based on a pure best-first search yields the most solid performance over a large set of problems. We also discuss the strengths and limitations of this approach, establish a correspondence between heuristic search planning and Graphplan, and briefly survey recent ideas that can reduce the current gap in performance between general heuristic search planners and specialized solvers.

Facial modeling from an uncalibrated face image using flexible generic parameterized facial models

The paper presents an optimization approach for facial modeling from an uncalibrated face image using flexible generic parameterized facial models (FGPFMs). An FGPFM consists of a topological structure and geometric knowledge of human faces. The topological description consists of a set of well-designed triangular polygons with a multilayered elastic structure in which the microstructural information can be expressed without complicated facial features. All the geometric values are obtained from a set of training facial models using statistical approaches and genetic algorithms. FGPFM can be easily modified using facial features as FGPFMs parameters to create an accurate specific three-dimensional (3D) facial model from only a photograph of an individual with a yawed face. In addition, the facial modeling problem is formulated as a parameter optimization problem. A hybrid optimization approach based on the Taguchi method and a best-first search algorithm is used to accelerate the search for a near optimal solution. Furthermore, sensitivity analysis and experimental results with texture mapping demonstrate the effectiveness of the proposed approach.

Searching networks with unrestricted edge costs

Best-first and depth-first heuristic search algorithms often assume underlying search graphs with only nonnegative edge costs and attempt to optimize simple objective functions. Applicability of these algorithms to graphs with both positive and negative edge costs is not completely studied. In the paper, two new problems are identified: one in computational geometry and the other in the layout design of very large scale integrated (VLSI) circuits. The former problem relates to a weight-balanced bipartitioning of a given set of points in a plane. The goal of the second problem is to find an area-balanced staircase path in a VLSI floorplan. Formulations of these problems lead to an interesting directed acyclic search graph with positive, zero and negative edge costs and an objective function of general nature. These problems are NP-hard. To solve such general problems optimally, search schemes are proposed. Experimental results reveal the efficacy and versatility of the proposed schemes, the depth-first scheme being the better choice. It is shown that the classical number-partitioning problem can also be formulated in this framework.

A solution to the GHI problem for best-first search

Best-first search algorithms usually amalgamate identical nodes for optimization reasons, meanwhile transforming the search tree into a search graph. However, identical nodes may represent different search states, e.g., due to a difference of history. So, in a search graph a node's value may be dependent on the path leading to it. This implies that different paths may result in different values. Therefore, it is difficult to determine the value of any node unambiguously. The problem is known as the graph–history-interaction (GHI) problem. This paper provides a solution for best-first search. First, we give a precise formulation of the problem. Then, for best-first search and for other searches, we review earlier proposals to overcome the problem. Next, our solution is given in detail. Here we introduce the notion of twin nodes, enabling a distinction of nodes according to their history. The implementation, called base-twin algorithm (BTA), is performed for pn search, a best-first search algorithm. It is generally applicable to other best-first search algorithms. Experimental results in the field of computer chess confirm the claim that the GHI problem has been solved for best-first search.

Deterministic approximation of marginal probabilities in Bayes nets

Computation of marginal probabilities in Bayes nets is central to numerous reasoning and automatic decision-making systems. This paper presents a deterministic approximation scheme for this hard problem that supplies provably correct bounds by aggregating probability mass in independence-based (IB) assignments. It refines belief updating methods. It approximates posterior probabilities by finding a small number of the highest probability complete (or evidentially supported) assignments. Under certain assumptions, the probability mass in the union of these assignments is sufficient to obtain a good approximation. Such methods are especially useful for highly connected networks. Since IB assignments contain fewer assigned variables, the probability mass in each assignment is greater than in the respective complete assignment. Thus, fewer assignments are sufficient, and a good approximation can be obtained efficiently. Two classes of algorithms for finding high-probability assignments are suggested: best-first heuristic search and a special integer linear program (ILP). Since IB assignments may be overlapping events in probability space, accumulating the mass in a set of assignments may be hard. In the ILP variant, it is easy to avoid the problem by adding equations that prohibit overlap. In the best-first search algorithm, other schemes are necessary, but experimental results suggest that using inclusion-exclusion (potentially exponential-time in the worst case) in the overlap cases is not too expensive for most problem instances.

Applications of Non-Order-Preserving Path Selection of Hazmat Routing

In this paper, we consider the problem of determining a path that maximizes a multi-attribute, non-order-preserving value function. The motivating application is the determination of a most preferred path for transporting hazardous materials based on transportation cost and risk to population. A sub-path of an optimal path may not be optimal for a non-order-preserving value function, implying that a traditional application of dynamic programming may intentionally or unintentionally produce sub-optimal paths. We consider two approximation procedures for two general cases, the q = 0 case and the q > 0 case, where q is the number of required intermediate stops between origin and destination. The first approximation procedure involves applying dynamic programming as if a sub-path of an optimal path were always optimal. The second approximation procedure involves determining a linear order-preserving criterion that approximates the non-order-preserving value function and then applying dynamic programming. We use the best-first search algorithm BU* to determine optimal routes for both the q = 0 and q < 0 cases. We examine the frequency and magnitude of the resulting sub-optimalities for a multi-attribute value model based on a six-county road network that includes Cleveland, Ohio. Numerical results show that if one of the two approximations is used, significant sub-optimalities can occur over a wide range of decision maker preferences. Both approximations can produce sub-optimality error magnitudes of over 50%.

Best-first fixed-depth minimax algorithms

This article has three main contributions to our understanding of minimax search: First, a new formulation for Stockman's SSS ∗ algorithm, based on Alpha-Beta, is presented. It solves all the perceived drawbacks of SSS ∗, finally transforming it into a practical algorithm. In effect, we show that SSS ∗ = Alpha-Beta + transposition tables. The crucial step is the realization that transposition tables contain so-called solution trees, structures that are used in best-first search algorithms like SSS ∗. Having created a practical version, we present performance measurements with tournament game-playing programs for three different minimax games, yielding results that contradict a number of publications. Second, based on the insights gained in our attempts at understanding SSS ∗, we present a framework that facilitates the construction of several best-first fixed-depth game-tree search algorithms, known and new. The framework is based on depth-first null-window Alpha-Beta search, enhanced with storage to allow for the refining of previous search results. It focuses attention on the essential differences between algorithms. Third, a new instance of this framework is presented. It performs better than algorithms that are currently used in most state-of-the-art game-playing programs. We provide experimental evidence to explain why this new algorithm, MTD( f), performs better than other fixed-depth minimax algorithms.

Design and evaluation of data allocation algorithms for distributed multimedia database systems

A major cost in retrieving multimedia data from multiple sites is the cost incurred in transferring multimedia data objects (MDOs) from different sites to the site where the query is initiated. The objective of a data allocation algorithm is to locate the MDOs at different sites so as to minimize the total data transfer cost incurred in executing a given set of queries. The optimal allocation of MDOs depends on the query execution strategy employed by a distributed multimedia system while the query execution strategy optimizes a query based on this allocation. We fix the query execution strategy and develop a site-independent MDO dependency graph representation to model the dependencies among the MDOs accessed by a query. Given the MDO dependency graphs as well as the set of multimedia database sites, data transfer costs between the sites, the allocation limit on the number of MDOs that can be allocated at a site, and the query execution frequencies from the sites, an allocation scheme is generated. We formulate the data allocation problem as an optimization problem. We solve this problem with a number of techniques that broadly belong to three classes: max-flow min-cut, state-space search, and graph partitioning heuristics. The max-flow min-cut technique formulates the data allocation problem as a network-flow problem, and uses a hill-climbing approach to try to find the optimal solution. For the state-space search approach, the problem is solved using a best-first search algorithm. The graph partitioning approach uses two clustering heuristics, the agglomerative clustering and divisive clustering. We evaluate and compare these approaches, and assess their cost-performance trade-offs. All algorithms are also compared with optimal solutions obtained through exhaustive search. Conclusions are also made on the suitability of these approaches to different scenarios.

A best-first search algorithm guided by a set-valued heuristic

Presents an algorithm, called A/sup G/, for finding the least-cost path from start node to goal node set in an OR-graph, where arc costs are scalar-valued and the cost of each path is the sum of the concomitant arc costs. Search is guided by a set, H, of real-valued functions on the node set. Such a heuristic set can be a useful representation of knowledge acquired from human knowledge sources. If H.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Reliability and wirability optimizations for module placement on a convectively cooled printed wiring board

Traditionally, printed wiring board (PWB) placement techniques have been focused on improving wirability. However, with the increasing demand for highly reliable densely packaged electronic equipment, considerable attention has been focused on the methods which can improve reliability at higher packaging levels. This paper considers both reliability and wirability together for arranging electronic modules on a convectively cooled printed wiring board. An ordered best-first search algorithm is presented for the two-objective optimization problem. The algorithm always examines the “successors” of the “most promising” node in the search tree. The results show that the system failure rate can be greatly reduced without deteriorating the wirability. Furthermore, the first obtained solution which satisfies the bound on wirability was demonstrated to have very high quality in system failure rate. Thus, the method can be used for large-sized problems if the solutions needed are only nearly optimum. On the other hand, for small-sized problems, the Pareto optimal solutions can be obtained by the method.

Cost-based abduction and MAP explanation

Cost-based abduction attempts to find the best explanation for a set of facts by finding a minimal cost proof for the facts. The costs are computed by summing the costs of the assumptions necessary for the proof plus the cost of the rules. We examine existing methods for constructing explanations (proofs), as a minimization problem on a DAG (directed acyclic graph). We then define a probabilistic semantics for the costs, and prove the equivalence of the cost minimization problem to the Bayesian network MAP (maximum a posteriori probability) solution of the system. A simple best-first algorithm for finding least-cost proofs is presented, and possible improvements are suggested. The semantics of cost-based abduction for complete models are then generalized to handle negation. This, in turn, allows us to apply the best-first search algorithm as a novel way of computing MAP assignments to belief networks that can enumerate assignments in order of decreasing probability. An important point is that improvement results for the best-first search algorithm carry over to the computation of MAPs.