Suboptimal heuristic search algorithms such as weighted A* and greedy best-first search are widely used to solve problems for which guaranteed optimal solutions are too expensive to obtain. These algorithms crucially rely on a heuristic function to guide their search. However, most research on building heuristics addresses optimal solving. In this paper, we illustrate how established wisdom for constructing heuristics for optimal search can fail when considering suboptimal search. We consider the behavior of greedy best-first search in detail and we test several hypotheses for predicting when a heuristic will be effective for it. Our results suggest that a predictive characteristic is a heuristic's goal distance rank correlation (GDRC), a robust measure of whether it orders nodes according to distance to a goal. We demonstrate that GDRC can be used to automatically construct abstraction-based heuristics for greedy best-first search that are more effective than those built by methods oriented toward optimal search. These results reinforce the point that suboptimal search deserves sustained attention and specialized methods of its own.

Suboptimal heuristic search algorithms such as greedy best-first search allow us to find solutions when constraints of either time, memory, or both prevent the application of optimal algorithms such as A*. Guidelines for building an effective heuristic for A* are well established in the literature, but we show that if those rules are applied for greedy best-first search, performance can actually degrade. Observing what went wrong for greedy best-first search leads us to a quantitative metric appropriate for greedy heuristics, called Goal Distance Rank Correlation (GDRC). We demonstrate that GDRC can be used to build effective heuristics for greedy best-first search automatically.

In work on satisficing search, there has been substantial attention devoted to how to solve problems associated with local minima or plateaus in the heuristic function. One technique that has been shown to be quite promising is using an alternative heuristic function that does not estimate cost-to-go, but rather estimates distance-to-go. Empirical results generally favor using the distance-to-go heuristic over the cost-to-go heuristic, but there is currently little beyond intuition to explain the difference. We begin by empirically showing that the success of the distance-to-go heuristic appears related to its having smaller local minima. We then discuss a reasonable theoretical model of heuristics and show that, under this model, the expected size of local minima is higher for a cost- to-go heuristic than a distance-to-go heuristic, offering a possible explanation as to why distance-to-go heuristics tend to outperform cost-to-go heuristics.

There are many algorithms designed to solve the shortest path problem.Each of the published algorithms has a demonstrated use; a situationin which it is the clear choice. Unfortunately, if faced with a novelproblem, there is no reliable robust way to figure out which algorithmshould be used to solve the new problem.When classifying things, the first step is to identify relevantfeatures for classifications. In the context of heuristic search, itnot clear what pieces of information should be used to predict searchalgorithm performance, and the question of algorithm selection for anovel domain is an open question.We first analyze which domain attributes common algorithms leverage,and discuss how to identify domains containing these attributes. Inaddition to discussing how to classify domains, we also discuss whythe classifications matter for various algorithms. Ultimately, thiswill allow us to offer more accurate runtime predictions for variousalgorithms we analyze, allowing us to determine which algorithm willlikely offer the best performance.

Although the heuristic search algorithm A* is well-known to be optimally efficient, this result explicitly assumes forward search. Bidirectional search has long held promise for surpassing A*'s efficiency, and many varieties have been proposed, but it has proven difficult to achieve robust performance across multiple domains in practice. We introduce a simple bidirectional search technique called Incremental KKAdd that judiciously performs backward search to improve the accuracy of the forward heuristic function for any search algorithm. We integrate this technique with A*, assess its theoretical properties, and empirically evaluate its performance across seven benchmark domains. In the best case, it yields a factor of six reduction in node expansions and CPU time compared to A*, and in the worst case, its overhead is provably bounded by a user-supplied parameter, such as 1%. Viewing performance across all domains, it also surpasses previously proposed bidirectional search algorithms. These results indicate that Incremental KKAdd is a robust way to leverage bidirectional search in practice.

Weighted A* is the most popular satisficing algorithm for heuristic search. Although there is no formal guarantee that increasing the weight on the heuristic cost-to-go estimate will decrease search time, it is commonly assumed that increas- ing the weight leads to faster searches, and that greedy search will provide the fastest search of all. As we show, however, in some domains, increasing the weight slows down the search. This has an important consequence on the scaling behavior of Weighted A*: increasing the weight ad infinitum will only speed up the search if greedy search is effective. We examine several plausible hypotheses as to why greedy search would sometimes expand more nodes than A* and show that each of the simple explanations has flaws. Our contribution is to show that greedy search is fast if and only if there is a strong correlation between h(n) and d∗(n), the true distance-to-go, or if the heuristic is extremely accurate.

In many domains, different actions have different costs. In this paper, we show that various kinds of best-first search algorithms are sensitive to the ratio between the lowest and highest operator costs. First, we take common benchmark domains and show that when we increase the ratio of operator costs, the number of node expansions required to find a solution increases. Second, we provide a theoretical analysis showing one reason this phenomenon occurs. We also discuss additional domain features that can cause this increased difficulty. Third, we show that searching using distance-to-go estimates can significantly ameliorate this problem. Our analysis takes an important step toward understanding algorithm performance in the presence of differing costs. This research direction will likely only grow in importance as heuristic search is deployed to solve real-world problems.

We discuss the relationships between three approaches to greedy heuristic search: best-first, hill-climbing, and beam search. We consider the design decisions within each family and point out their oft-overlooked similarities. We consider the following best-first searches: weighted A*, greedy search, ASeps, window A* and multi-state commitment k-weighted A*. For hill climbing algorithms, we consider enforced hill climbing and LSS-LRTA*. We also consider a variety of beam searches, including BULB and beam-stack search. We show how to best configure beam search in order to maximize robustness. An empirical analysis on six standard benchmarks reveals that beam search and best-first search have remarkably similar performance, and outperform hill-climbing approaches in terms of both time to solution and solution quality. Of these, beam search is preferable for very large problems and best first search is better on problems where the goal cannot be reached from all states.