Anytime heuristic search algorithms try to find a (potentially suboptimal) solution as quickly as possible and then work to find better and better solutions until an optimal solution is obtained or time is exhausted. The most widely-known anytime search algorithms are based on best-first search. In this paper, we propose a new algorithm, rectangle search, that is instead based on beam search, a variant of breadth-first search. It repeatedly explores alternatives at all depth levels and is thus best-suited to problems featuring deep local minima. Experiments using a variety of popular search benchmarks suggest that rectangle search is competitive with fixed-width beam search and often performs better than the previous best anytime search algorithms.

Beam search is a popular satisficing approach to heuristic search problems that allows one to trade increased computation time for lower solution cost by increasing the beam width parameter. We make two contributions to the study of beam search. First, we show how to make beam search monotonic; that is, we provide a new variant that guarantees nonincreasing solution cost as the beam width is increased. This makes setting the beam parameter much easier. Second, we show how using distance-to-go estimates can allow beam search to find better solutions more quickly in domains with non-uniform costs. Together, these results improve the practical effectiveness of beam search.

This paper studies the equivalence problem for relational pattern languages, where a relation imposes dependencies between the two strings with which two variables in a pattern can be replaced simultaneously. Our focus is on the question whether the non-equivalence of two relational patterns is witnessed by short strings, namely those generated by replacing variables in the patterns by strings of length bounded by some (small) number z. After establishing a close connection between this problem and the study of the notions of teaching dimension and no-clash teaching dimension, we investigate specific classes of relational pattern languages. We show that the smallest number z that serves as a bound for testing equivalence is 2 when the relation between variable substitutions is that of equal string length, and the alphabet size it at least 3. This has interesting implications on the size and form of non-clashing teaching sets for the corresponding languages. By contrast, not even z = 3 is sufficient when the constraints require two substituted strings to be the reversal of one another, for alphabets of size 2. We conclude with a negative result on erasing pattern languages.

In multi-agent systems, agents often have to rely on interactions with other agents in order to accomplish a given task. They hence need to assess the trustworthiness of other agents, which is particularly difficult if the latter change their behavior dynamically. The two common techniques to solve this problem are Hidden Markov Models (HMMs) and standard Beta Reputation Systems (BRS) equipped with a simple decay mechanism to discount older interactions. We propose instead to use \emph{Page-Hinkley} statistics in BRS to detect and dismiss an agent whose behavior worsens. Our experimental study demonstrates that our method outperforms HMMs and, in the vast majority of tested settings, either outperforms or is on par with other typically used BRS-type methods.

Multi-agent pathfinding, where multiple agents must travel to their goal locations without getting stuck, has been studied in both theoretical and practical contexts, with a variety of both optimal and sub-optimal algorithms proposed for solving problems. Recent work has shown that there is a linear-time check for whether a multi-agent pathfinding problem can be solved in a tree, however this was not used to actually produce solutions. In this paper we provide a constructive proof of how to solve multi-agent pathfinding problems in a tree that culminates in a novel approach that we call the tree-based agent swapping strategy (TASS). Experimental results showed that TASS can find solutions to the multi-agent pathfinding problem on a highly crowded tree with 1000 nodes and 996 agents in less than 8 seconds. These results are far more efficient and general than existing work, suggesting that TASS is a productive line of study for multi-agent pathfinding.

To assess the trustworthiness of an agent in a multiagent system, one often combines two types of trust information: direct trust information derived from one’s own interactions with that agent, and indirect trust information based on advice from other agents. This paper provides the first systematic study on when it is beneficial to combine these two types of trust as opposed to relying on only one of them. Our large-scale experimental study shows that strong methods for computing indirect trust make direct trust redundant in a surprisingly wide variety of scenarios. Further, a new method for the combination of the two trust types is proposed that, in the remaining scenarios, outperforms the ones known from the literature.

Weighted A* (wA*) is a widely used algorithm for rapidly, but suboptimally, solving planning and search problems. The cost of the solution it produces is guaranteed to be at most W times the optimal solution cost, where W is the weight wA* uses in prioritizing open nodes. W is therefore a suboptimality bound for the solution produced by wA*. There is broad consensus that this bound is not very accurate, that the actual suboptimality of wA*'s solution is often much less than W times optimal. However, there is very little published evidence supporting that view, and no existing explanation of why W is a poor bound. This paper fills in these gaps in the literature. We begin with a large-scale experiment demonstrating that, across a wide variety of domains and heuristics for those domains, W is indeed very often far from the true suboptimality of wA*'s solution. We then analytically identify the potential sources of error. Finally, we present a practical method for correcting for two of these sources of error and experimentally show that the corrections frequently eliminate much of the error.

Edelkamp et al. (2005) proved that A*, given an admissible heuristic, is guaranteed to return an optimal solution in any cost algebra, not just in the traditional shortest path setting. In this paper, we investigate cost-algebraic A*'s optimal efficiency: in the cost-algebraic setting, under what conditions is A* guaranteed to expand the fewest possible states? In the traditional setting, this question was examined in detail by Dechter & Pearl (1985). They identified five different situations in which A* was optimally efficient. We show that three of them continue to hold in the cost-algebraic setting, but that one does not. We also show that one of them is false, it does not hold even in the traditional setting. We introduce an alternative that does hold in the cost-algebraic setting. Finally, we show that a well-known result due to Nilsson does not hold in the general cost-algebraic setting but does hold in a slightly less general setting.

Merge-and-shrink is a general framework for creating abstraction heuristics. In this paper we present two new variations of merge-and-shrink: MS-lite and DM-HQ. MS-lite is an extremely fast merge-and-shrink that maintains only the smallest abstractions that preserve local heuristic information. MS-lite has complementary strength over other merge-and-shrink methods due to its efficiency. In addition, we show that MS-lite has little dependence on merging strategies and its eager shrinking strategy can lead to better heuristics for some planning tasks. DM-HQ features a merging criterion that utilizes information about heuristic quality to make the merging decisions. Our experiments show that combining DM-HQ and MS-lite dramatically outperforms the current state-of-the-art merge-and-shrink method by solving 75 more tasks on an International Planning Competition (IPC) benchmark set of 1499 tasks.

In this paper we study bidirectional state space search with consistent heuristics, with a focus on obtaining sufficient conditions for node expansion, that is, conditions characterizing nodes that must be expanded by any admissible bidirectional search algorithm. We provide such conditions for front-to-front and front-to-end bidirectional search. The sufficient conditions are used to prove that the front-to-front bidirectional search algorithm BDS1 is optimally efficient, in terms of node expansion, among a broad class of bidirectional search algorithms, for a specific class of problem instances. Dechter and Pearl's well-known result on sufficient conditions for node expansion by unidirectional algorithms such as A* is shown to be a special case of our results.

In many planning applications, actions can have highly diverse costs. Recent studies focus on the effects of diverse action costs on search algorithms, but not on their effects on domain-independent heuristics. In this paper, we demonstrate there are negative impacts of action cost diversity on merge-and-shrink (M&S), a successful abstraction method for producing high-quality heuristics for planning problems. We propose a new cost partitioning method for M&S to address the negative effects of diverse action costs. We investigate non-unit cost IPC domains, especially those for which diverse action costs have severe negative effects on the quality of the M&S heuristic. Our experiments demonstrate that in these domains, an additive set of M&S heuristics using the new cost partitioning method produces much more informative and effective heuristics than creating a single M&S heuristic which directly encodes diverse costs.

Diverse action costs are an essential feature of many real-world planning applications. Some recent studies have shown that diversity of action costs makes planning more difficult, and that searching using unit action costs can outperform searching the same domain with diverse action costs. In this paper, we provide experimental evidence and theoretical analysis showing that search can also benefit from action cost diversity. We show that on several IPC problems cost diversity has a positive effect (reduces search effort). We then present a theoretical analysis establishing that these positive cases are not accidental. Our main result is a "No Free Lunch" theorem showing that any negative effects of cost diversity are always perfectly counterbalanced by positive effects. Our theoretical analysis also shows that it is advantageous to have a strongly concentrated distribution of solution costs. In many domains, unit costs will give rise to a more concentrated distribution than diverse costs, but we give an example typifying domains in which the opposite is the case.

The efficient solution of state space search problems is often attempted by guiding search algorithms with heuristics (estimates of the distance from any state to the goal). A popular way for creating heuristic functions is by using an abstract version of the state space. However, the quality of abstraction-based heuristic functions, and thus the speed of search, can suffer from spurious transitions, i.e., state transitions in the abstract state space for which no corresponding transitions in the reachable component of the original state space exist. Our first contribution is a quantitative study demonstrating that the harmful effects of spurious transitions on heuristic functions can be substantial, in terms of both the increase in the number of abstract states and the decrease in the heuristic values, which may slow down search. Our second contribution is an empirical study on the benefits of removing a certain kind of spurious transition, namely those that involve states with a pair of mutually exclusive (mutex) variablevalue assignments. In the context of state space planning, a mutex pair is a pair of variable-value assignments that does not occur in any reachable state. Detecting mutex pairs is a problem that has been addressed frequently in the planning literature. Our study shows that there are cases in which mutex detection helps to eliminate harmful spurious transitions to a large extent and thus to speed up search substantially.

It is well-known that any admissible unidirectional heuristic search algorithm must expand all states whose f-value is smaller than the optimal solution cost when using a consistent heuristic. Such states are called “surely expanded” (s.e.). A recent study characterized s.e. pairs of states for bidirectional search with consistent heuristics: if a pair of states is s.e. then at least one of the two states must be expanded. This paper derives a lower bound, VC, on the minimum number of expansions required to cover all s.e. pairs, and present a new admissible front-to-end bidirectional heuristic search algorithm, Near-Optimal Bidirectional Search (NBS), that is guaranteed to do no more than 2VC expansions. We further prove that no admissible front-to-end algorithm has a worst case better than 2VC. Experimental results show that NBS competes with or outperforms existing bidirectional search algorithms, and often outperforms A* as well.

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.

The number of classification rules discovered in associative classification is typically quite large. In addition, these rules contain redundant information since classification rules are obtained from mined frequent itemsets and the latter are known to be repetitive. In this paper we investigate through an empirical study the performance of associative classifiers when the classification rules are generated from frequent, closed and maximal itemsets. We show that maximal itemsets substantially reduce the number of classification rules without jeopardizing the accuracy of the classifier. Our extensive analysis demonstrates that the performance remains stable and even improves in some cases. Our analysis using cost curves also provides recommendations on when it is appropriate to remove redundancy in frequent itemsets.

Automatic algorithm configuration addresses the problem of determining the settings of an algorithm’s parameters to optimize its performance. It has most prominently been applied to optimize solvers for hard combinatorial problems (for example, SAT, MIP, ASP, and AI planning) as well as to hyperparameter optimization of flexible machine-learning frameworks (such as deep neural networks, or the space of algorithms defined by the Waikato environment for knowledge analysis, WEKA), but it also has applications in many more areas. Additionally, algorithm configuration has been performed manually by domain experts in a tedious and time-consuming optimization process, a task humans are poorly suited for.

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.

We present a novel admissible pattern database heuristic (D) and tie-breaking rule (L) for Sokoban, allowing us to increase the number of optimally solved standard Sokoban instances from 20 to 28 and the number of proved optimal solutions from 25 to 32 compared to previous methods. The previously best heuristic for Sokoban (I) used the idea of an intermediate goal state to enable the effective use of pattern database heuristics in transportation domains, where the mapping of movable objects to goal locations is not fixed beforehand. We extend this idea to allow the use of multiple intermediate goal states and show that heuristic I is no longer effective. We solve this problem and show that our heuristic D is effective in this situation. Sokoban is a well-known single-agent search domain characterized by a large branching factor, long solution lengths, and the presence of unsolvable states. Given the exponential growth in the complexity of standard Sokoban instances, the increase in the number of optimally solved instances represents a major advance in our understanding of how to search in extremely large search spaces.