Bidirectional Heuristic Search Algorithm Research Articles

On Bidirectional Heuristic Search in Classical Planning: An Analysis of BAE*

Heuristic search is a successful approach to cost-optimal planning. Bidirectional heuristic search algorithms have been around for a long time, but only recent advances have led to algorithms like BAE* that have the potential to outperform unidirectional heuristic search algorithms like A* in practice. In this work, we analyze BAE* for classical planning and the challenges associated with the underlying assumption of an explicit state representation. We show that it is crucial to use mutexes and reachability analysis to reduce the potentially exponential number of goal states, which makes it possible to create an explicit representation of a reversed planning task that can be used for the backward search of BAE*. Our empirical evaluation shows that BAE* solves more instances than A* in multiple domains with significantly fewer node expansions, demonstrating the usefulness of BAE* in planning.

A dynamic bidirectional heuristic trust path search algorithm

Online social networks greatly promote peoples' online interaction, where trust plays a crucial role. Trust prediction with trust path search is widely used to help users find the trusted friends and obtain valid information. However, the shortcomings of accuracy and time still exist in some famous algorithms. Therefore, the dynamic bidirectional heuristic search (DBHS) algorithm is proposed in this paper to find the reliable trust path by studying the heuristic search. First, the trust value and path length are comprehensively considered to find the most trusted user. Specially, it constrains the traversal depth based on the ‘small world’ theory and obtains the acceptable path set by using the relaxation coefficient λ to relax the depth of the shortest path. By this way, some longer path with the higher trust can be considered to improve the precision of algorithm. Then, an adjustment factor is designed based on the meet in the middle (MM) algorithm to assign search weights to two directions based on the size of the search tree expanded, so as to improve the problem of no priori when fixed parameters are used. Besides, the complexity of unidirectional trust path search can also be reduced by searching from two directions, which can reduce the depth and improve the efficiency of search. Finally, the predictive trust degree is outputted by the trust propagation function. Two public datasets are used to generate experimental results, which show that DBHS can quickly search and form reliable trust relationship, and it partly improves other algorithms.

GBFHS: A Generalized Breadth-First Heuristic Search Algorithm

Recently there has been renewed interest in bidirectional heuristic search. New algorithms, e.g., MM, MMe, and NBS, have been introduced which seem much closer to refuting the accepted wisdom that "any front-to-end bidirectional heuristic search algorithm will likely be dominated by unidirectional heuristic search or bidirectional brute-force search". However, MM and MMe can still be dominated by their bidirectional brute-force versions, i.e., they can show a "hump-in-the-middle". We introduce a novel general breadth-first heuristic search algorithm, GBFHS, that unifies both unidirectional and bidirectional search into a single algorithm. It uses knowledge of the edge cost in unit cost domains to stop on first-collision in unidirectional search and in bidirectional search, unlike MM, MMe, and NBS. With no heuristic it expands fewer nodes bidirectionally than Nicholson's blind bidirectional search algorithm. GBFHS expands substantially fewer nodes than MM0, MM, MMe, and NBS. Additionally, GBFHS does not show a "hump-in-the-middle". GBFHS run bidirectionally is not dominated by bidirectional brute-force search, likewise, GBFHS run unidirectionally is not dominated by A*.

An Improved Meet in the Middle Algorithm for Graphs with Unit Costs

This paper proves several new properties of the Meet in the Middle (MMe) bidirectional heuristic search algorithm when applied to graphs with unit edge costs. Primarily, it is shown that the length of the first path discovered by MMe never exceeds the optimal length by more than one and that if the length of the first path found is odd, then it must be optimal. These properties suggest that the search strategy should emphasize finding a complete path as soon as possible. Computational experiments demonstrate that fully exploiting these new properties can decrease the number of nodes expanded by anywhere from twofold to over tenfold.

Extended Abstract: An Improved Priority Function for Bidirectional Heuristic Search

Bidirectional search algorithms interleave a search forward from the start state (start ) and a search backward (i.e. using reverse operators) from the goal state (goal). We say that the two searches “meet in the middle” if neither search expands a node whose g-value (in the given direction) exceeds C*/2 , where C* is the cost of an optimal solution. The only bidirectional heuristic search algorithm that is guaranteed to meet in the middle under all circumstances is the recently introduced MM algorithm (Holte et al. 2016). The feature of MM that provides this guarantee is its unique priority functions for nodes on its open lists. In this short note we present MMe, which enhances MM’s priority function and is expected to expand fewer nodes than MM under most circumstances. We sketch a proof of MMe’s correctness, describe conditions under which MMe will expand fewer nodes than MM and vice versa, and experimentally compare MMe and MM on the 10-Pancake problem.

On the Differences and Similarities of fMM and GBFHS

fMM and GBFSH are two prominent bidirectional heuristic search algorithms. Over the past few years, there has been a great deal of theoretical and empirical work on both of these algorithms. As part of the research conducted on these algorithms, some interesting theoretical properties were proven for fMM and not for GBFSH and vice versa. In addition, both of them are used as benchmarks for evaluation bidirectional heuristic search algorithms. In this paper we show that fMM infused by a lower-bound propagation and GBFSH are equivalent. In essence, every instance of fMM can be mapped to an instance of GBFSH that expands the exact sequence of nodes and vice versa. This equivalence indicates that all theoretical properties proven for one algorithm hold for both algorithm, and that future analyses and benchmarks can consider only one of these algorithms.

Improving Bidirectional Heuristic Search by Bounds Propagation

Recent work in bidirectional heuristic search characterize pairs of nodes from which at least one node must be expanded in order to ensure optimality of solutions. We use these findings to propose a method for improving existing heuristics by propagating lower bounds between the forward and backward frontiers. We then define a number of desirable properties for bidirectional heuristic search algorithms, and show that applying the bound propagations adds these properties to many existing algorithms (e.g. to the MM family of algorithms). Finally, experimental results show that applying these propagations significantly reduce the running time of various algorithms.

Iterative-Deepening Bidirectional Heuristic Search with Restricted Memory

This extended abstract presents a bidirectional heuristic search algorithm called IDBiHS that operates under restricted memory. Several variants of this algorithm are introduced for different types of memory restrictions, and are compared against existing algorithms with similar restrictions.

Iterative-deepening Bidirectional Heuristic Search with Restricted Memory

The field of bidirectional heuristic search has recently seen great advances. However, the subject of memory-restricted bidirectional search has not received recent attention. In this paper we introduce a general iterative deepening bidirectional heuristic search algorithm (IDBiHS) that searches simultaneously in both directions while controlling the meeting point of the search frontiers. First, we present the basic variant of IDBiHS, whose memory is linear in the search depth. We then add improvements that exploit consistency and front-to-front heuristics. Next, we move to the case where a fixed amount of memory is available to store nodes during the search and develop two variants of IDBiHS: (1) A*+IDBiHS, that starts with A* and moves to IDBiHS as soon as memory is exhausted. (2) A variant that stores partial forward frontiers until memory is exhausted and then tries to match each of them from the backward side. Finally, we experimentally compare the new algorithms to existing unidirectional and bidirectional ones. In many cases our new algorithms outperform previous ones in both node expansions and time.

Bidirectional heuristic search to find the optimal Bayesian network structure

Bayesian networks have many applications. Learning the optimal structure of a Bayesian network has always been important in this respect. In this paper, a bidirectional heuristic search algorithm is proposed for the order graph space commonly used in a Bayesian network. At the same time, heuristic functions that are admissible and consistent in terms of both forward and backward search are proposed to ensure convergence of the algorithm to the optimal solution. The experimental results show that, compared with traditional unidirectional heuristic search, in most cases, the bidirectional heuristic search proposed in this paper needs to expand fewer states, the convergence efficiency is higher, and less running time is needed.

A Unifying View on Individual Bounds and Heuristic Inaccuracies in Bidirectional Search

In the past few years, new very successful bidirectional heuristic search algorithms have been proposed. Their key novelty is a lower bound on the cost of a solution that includes information from the g values in both directions. Kaindl and Kainz (1997) proposed measuring how inaccurate a heuristic is while expanding nodes in the opposite direction, and using this information to raise the f value of the evaluated nodes. However, this comes with a set of disadvantages and remains yet to be exploited to its full potential. Additionally, Sadhukhan (2013) presented BAE∗, a bidirectional best-first search algorithm based on the accumulated heuristic inaccuracy along a path. However, no complete comparison in regards to other bidirectional algorithms has yet been done, neither theoretical nor empirical. In this paper we define individual bounds within the lower-bound framework and show how both Kaindl and Kainz's and Sadhukhan's methods can be generalized thus creating new bounds. This overcomes previous shortcomings and allows newer algorithms to benefit from these techniques as well. Experimental results show a substantial improvement, up to an order of magnitude in the number of necessarily-expanded nodes compared to state-of-the-art near-optimal algorithms in common benchmarks.

MM: A bidirectional search algorithm that is guaranteed to meet in the middle

Bidirectional search algorithms interleave two separate searches, a normal search forward from the start state, and a search backward from the goal. It is well known that adding a heuristic to unidirectional search dramatically reduces the search effort. By contrast, despite decades of research, bidirectional heuristic search has not yet had a major impact. Additionally, no comprehensive theory was ever devised to understand the nature of bidirectional heuristic search. In this paper we aim to close this gap. We first present MM, a novel bidirectional heuristic search algorithm. Unlike previous bidirectional heuristic search algorithms, MM's forward and backward searches are guaranteed to “meet in the middle”, i.e. never expand a node beyond the solution midpoint. Based on this unique attribute we present a novel framework for comparing MM, A*, and their brute-force variants. We do this by dividing the entire state space into disjoint regions based on their distance from the start and goal. This allows us to perform a comparison of these algorithms on a per region basis and identify conditions favoring each algorithm. Finally, we present experimental results that support our theoretical analysis.

Bidirectional Search That Is Guaranteed to Meet in the Middle

We present MM, the first bidirectional heuristic search algorithm whose forward and backward searches are guaranteed to ''meet in the middle'', i.e. never expand a node beyond the solution midpoint. We also present a novel framework for comparing MM, A*, and brute-force search, and identify conditions favoring each algorithm. Finally, we present experimental results that support our theoretical analysis.

Incorporating Bidirectional Heuristic Search and Improved ACO in Route Planning

A multi-objective multi-node dynamic route planning system for a vehicle is presented in this paper. In this system, a bidirectional heuristic search algorithm is designed to perform path planning between two nodes in a topological map created by OpenStreetMap for urban scenarios. And then an improved multi-objective Ant Colony Optimization (ACO) algorithm considering the timeliness of goal nodes is proposed to generate the node sequence. Experimental results validated the proposed approach.

Limitations of Front-To-End Bidirectional Heuristic Search

We present an intuitive explanation for the limited effectiveness of front-to-end bidirectional heuristic search, supported with extensive evidence from many commonly-studied domains. While previous work has proved the limitations of specific algorithms, we show that any front-to-end bidirectional heuristic search algorithm will likely be dominated by unidirectional heuristic search or bidirectional brute-force search. We also demonstrate a pathological case where bidirectional heuristic search is the dominant algorithm, so a stronger claim cannot be made. Finally, we show that on the four-peg Towers Of Hanoi with arbitrary start and goal states, bidirectional brute-force search outperforms unidirectional heuristic search using pattern-database heuristics.

BIDA ∗: an improved perimeter search algorithm

In this paper we present a new bidirectional heuristic search algorithm. Our algorithm can be viewed as a perimeter search algorithm, and it uses a new technique for reducing the number of heuristic evaluations. We also prove some general results on the behavior of iterative deepening perimeter search algorithms, and we discuss some new ‘lazy evaluation’ techniques for improving their performance. The theoretical and experimental results show that perimeter search algorithms outperform the other bidirectional algorithms, and we believe it is worthwhile to give them a deep look in subsequent research.

Bidirectional heuristic search with limited resources

Heuristic search strategies have useful applicable problem solving in AI. It has been observed that bidirectional heuristic search algorithms can be potentially than their unidirectional counterparts. However, the problem with bidirectional search in practice is to make the two search fronts (forward and backward) meet in the middle. De Champeaux suggested a front-to-front algorithm [3] that overcomes this problem. But the disadvantage of that algorithm is that it is computationally very expensive. In this paper, we suggest a new front-to-front algorithm that is computationally much less expensive. Our algorithm does not guarantee optimality always, but its solution quality and execution time can be controlled by some external parameters. Finally, we present some experimental results on a generic state space problem, viz. 15-puzzle, showing the effectiveness of our algorithm.

BS ∗: An admissible bidirectional staged heuristic search algorithm

In order to reap the potential advantage of less extensive searching which bidirectional heuristic search algorithms offer, strategies are needed to influence the two search wavefronts to meet such that early termination will occur. The principled search control strategy aims to achieve this without trading running time, but can be found wanting still. An improved algorithm BS∗ is described which expands significantly less nodes on average than any other algorithm in the same class of non-wave-shaping admissible bidirectional algorithms. When pitted against BHPA, the only other heuristically guided member in this class, BS∗'s average search efficiency in time and space is about 30% better. BS∗'s superior performance stems from the use of all opportunities to achieve early termination and the elimination of unfruitful avenues by search reduction operations: nipping, pruning, trimming and screening. Such operations exploit information gathered during search and have several spin-offs: more accurate guidance of search control, early exposure of nonpromising nodes and reduced bookkeeping overheads, all of which further enhance BS∗'s performance. A further noteworthy feature of BS∗ is that it is the first staged search algorithm which preserves admissibility.

An Improved Bidirectional Heuristic Search Algorithm

A modification of Pohl's bidirectional heuristic search algorithm is described together with a simplified implementation. Theorems are proved about conditions yielding shortest paths. The results are given of a worst-case analysis of different algorithms, suggesting a rank order of their quality. Results that Pohl had obtained with a unidirectional heuristic search algorithm on the 15-puzzle are compared with the results obtained with the new — simplified — algorithm.

An optimality theorem for a bi-directional heuristic search algorithm

An optimality theorem for a bi-directional heuristic search algorithm