Planning research has returned to the issue of optimizing costs (rather than sizes) of plans. A prevalent perception, at least among non-experts in search, is that graph search for optimizing the size of paths generalizes more or less trivially to optimizing the cost of paths. While this kind of generalization is usually straightforward for graph theorems, graph algorithms are a different story. In particular, implementing a search evaluation function by substituting cost for size is a Bad Idea. Though experts have stated as much, cutting-edge practitioners are still learning of the consequences the hard way; here we mount a forceful indictment on the inherent dangers of cost-based search.

We show how edge partitioning, a technique originally developed for external-memory search, can be used to reduce the number of slow synchronization operations needed in parallel graph search. We show that edge partitioning improves on a previous technique called parallel structured duplicate detection by allowing a higher degree of concurrency, even for search problems with little or no inherent locality. For domain-independent graph search, we also show that edge partitioning significantly improves search speed by improving the efficiency of precondition checking. We demonstrate the effectiveness of this approach to parallel graph search for domain-independent STRIPS planning.

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.

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.

In this paper we explore a novel approach for anytime heuristic search, in which the node that is most probable to improve the incumbent solution is expanded first. This is especially suited for the "anytime aspect" of anytime algorithms - the possibility that the algorithm will be be halted anytime throughout the search. The potential of a node to improve the incumbent solution is estimated by a custom cost function, resulting in Potential Search, an anytime best-first search. Experimental results on the 15-puzzle and on the key player problem in communication networks (KPP-COM) show that this approach is competitive with state-of-the-art anytime heuristic search algorithms, and is more robust.

Branch-and-Bound search is a basic algorithm for solving combinatorial optimization problems. Here we introduce a new lower-bounding methodology that can be incorporated into any branch-and-bound solver, and demonstraint its use on the MaxSAT constraint optimization problem. The approach is to adapt a “minimum-height equivalent transformation” framework that was first developed in the context of computer vision. We present efficient algorithms to realize this framework within the MaxSAT domain, and demonstrate their feasibility by implementing them within the state-of-the-art maxsatz solver. We evaluate the solver on test sets from the 2009 MaxSAT competition; we observe a basic performance tradeoff whereby the (quadratic) time cost of computing the transformations may or may not be worthwhile in exchange for better bounds and more frequent pruning. For specific test sets, the trade-off does result in significant improvement in both prunings and overall run-time.

Motivated by the recent hardware evolution towards multi-core machines, we investigate parallel planning techniques in a shared-memory environment. We consider, more specifically, parallel versions of a best-first search algorithm that run K threads, each expanding the next best node from the open list. We show that the proposed technique has a number of advantages. First, it is (reasonably) simple: we show how the algorithm can be obtained from a sequential version mostly by adding parallel annotations. Second, we conduct an extensive empirical study that shows that this approach is quite effective.  It is also dynamic in the sense that the number of nodes expanded in parallel is adapted during the search. Overall we show that the approach is promising for parallel domain-independent, suboptimal planning.

Bounded suboptimal search algorithms attempt to find a solution quickly while guaranteeing that the cost does not exceed optimal by more than a desired factor. These algorithms generally use a single admissible heuristic both for guidance and guaranteeing solution quality. We present a new approach to bounded suboptimal search that separates these roles, consulting multiple sources of potentially inadmissible information to determine search order and using admissible information to guarantee quality. An empirical evaluation across six benchmark domains shows the new approach has better overall performance.

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.

In this paper we propose a new algorithm for solving general two-player turn-taking games that performs symbolic search utilizing binary decision diagrams (BDDs). It consists of two stages: First, it determines all breadth-first search (BFS) layers using forward search and omitting duplicate detection, next, the solving process operates in backward direction only within these BFS layers thereby partitioning all BDDs according to the layers the states reside in. We provide experimental results for selected games and compare to a previous approach. This comparison shows that in most cases the new algorithm outperforms the existing one in terms of runtime and used memory so that it can solve games that could not be solved before with a general approach.