Any-angle pathfinding is a common problem from robotics and computer games: it requires finding a Euclidean shortest path between a pair of points in a grid map. Prior research has focused on approximate online solutions. A number of exact methods exist but they all require supra-linear space and preprocessing time. In this paper we describe Anya: a new optimal any-angle pathfinding algorithm which searches over sets of states represented as intervals. Each interval is identified online. From each we select a representative point to derive a corresponding f-value for the set. Anya always returns an optimal path. Moreover it does so entirely online, without any preprocessing or memory overheads. This result answers an open question from the areas of Artificial Intelligence and Game Development: is there an any-angle pathfinding algorithm which is online and optimal? The answer is yes.

Perimeter search is a bidirectional search algorithm consisting of two phases. In the first phase, a limited regression search computes the perimeter, a region which must necessarily be passed in every solution. In the second phase, a heuristic forward search finds an optimal plan from the initial state to the perimeter. The drawback of perimeter search is the need to compute heuristic estimates towards every state on the perimeter in the forward phase. We show that this limitation can be effectively overcome when using pattern database (PDB) heuristics in the forward phase. The combination of perimeter search and PDB heuristics has been considered previously by Felner and Ofek for solving combinatorial puzzles. They claimed that, based on theoretical considerations and experimental evidence, the use of perimeter search in this context offers "limited or no benefits". Our theoretical and experimental results show that this assessment should be revisited.

Searching for computational tools that can further push the boundary of satisficing planning, we show that reasoning about state-space symmetries can substantially improve even the most effective heuristic-search satisficing planners, with respect to all standard performance measures. The improvement comes from the state-space pruning, as well as from transparent cost-to-state updates and heuristic enhancement by information obtained during the search at different symmetric states.

All-pairs shortest paths (APSP) can eliminate the need to search in a graph, providing optimal moves very fast. A major challenge is storing pre-computed APSP data efficiently. Recently, compression has successfully been employed to scale the use of APSP data to roadmaps and gridmaps of realistic sizes. We develop new techniques that improve the compression power of state-of-the-art methods by up to a factor of 5. We demonstrate our ideas on game gridmpaps and the roadmap of Australia. Part of our ideas have been integrated in the Copa CPD system, one of the two best optimal participants in the grid-based path planning competition GPPC.

An elegant way to tackle a problem that you cannot solve is to cast it to a problem that you can solve very well. Cyclic Scheduling problems are very similar to Resource Constrained Project Scheduling Problems (RCPSP), except that the project activities are repeated over time. Due to the similarity, reducing Cyclic Scheduling problems to RCPSPs seems an appealing approach. In this paper we discuss four methods to perform the reduction. The first two are existing techniques. The remaining ones are novel and include the first (to the best of our knowledge) equivalent RCPSP formulation of a cyclic problem. We compare the presented approaches in an experimental evaluation.

In this paper we propose an improved formulation for an unrelated parallel machine problem with machine and job sequence-dependent setup times that outperforms the previously published formulations regarding size of instances and CPU time to reach optimal solutions. The main difference between the proposed formulation and previous ones is the way the makespan has been linearized. It provides improved dual bounds which speeds up the solution process when using a branch-and-bound commercial solver. Computational experiments show that, using this model, it is possible to solve instances four times larger than what was previously possible using other mixed integer programming formulations in the literature and obtain optimal solutions on instances of the same size up to three orders of magnitude faster.

Most of the satisficing planners which are based on heuristic search iteratively improve their solution quality through an anytime approach. Typically, the lowest-cost solution found so far is used to constrain the search. This avoids areas of the state space which cannot directly lead to lower cost solutions. However, in this paper we show that when used in conjunction with a post-processing plan improvement system such as ARAS, this bounding approach can harm a planner’s performance since the bound may prevent the search from ever finding additional plans for the post-processor to improve. The new anytime search framework of Diverse Any-Time Search addresses this issue through the use of restarts, randomization, and by not bounding as strictly as is done by previous approaches. Below, we will show that by using these techniques, the framework is able to generate a more diverse set of “raw" input plans for the post-processor to work on. We then show that when adding both Diverse Any-Time Search and the ARAS post-processor to LAMA-2011, the winner of the most recent IPC planning competition, the performance according to the IPC scoring metric improves from 511 points to over 570 points when tested on the 550 problems from IPC 2008 and IPC 2011. Performance gains are also seen when these techniques are added to Anytime Explicit Estimation Algorithm (AEES), as the performance improves from 440 points to over 513 points on the same problem set.

In the last years, pruning techniques based on partial order reduction have found increasing attention in the planning community. One recent result is that the expansion core method is a special case of the strong stubborn sets method proposed in model checking. However, it is still an open question if there exist efficiently computable strong stubborn sets with strictly higher pruning power than expansion core. In this paper, we prove that the pruning power of strong stubborn sets is strictly higher than the pruning power of expansion core even for a straight-forward instantiation of strong stubborn sets. This instantiation is as efficiently computable as expansion core. Hence, our theoretical results suggest that strong stubborn sets should be preferred to expansion core. Our empirical evaluation on all optimal benchmarks from the international planning competitions up to 2011 supports the theoretical results.

When parts of the states in a goal POMDP are fully observable and some actions are deterministic it is possible to take advantage of these properties to efficiently generate approximate solutions. Actions that deterministically affect the fully observable component of the world state can be abstracted away and combined into macro actions, permitting a planner to converge more quickly. This processing can be separated from the main search procedure, allowing us to leverage existing POMDP solvers. Theoretical results show how a POMDP can be analyzed to identify the exploitable properties and formal guarantees are provided showing that the use of macro actions preserves solvability. The efficiency of the method is demonstrated with examples when used in combination with existing POMDP solvers.

Most bounded suboptimal algorithms in the search literature have been developed so as to be epsilon-admissible. This means that the solutions found by these algorithms are guaranteed to be no more than a factor of (1 + ε) greater than optimal. However, this is not the only possible form of suboptimality bounding. For example, another possible suboptimality guarantee is that of additive bounding, which requires that the cost of the solution found is no more than the cost of the optimal solution plus a constant gamma. In this work, we consider the problem of developing algorithms so as to satisfy a given, and arbitrary, suboptimality requirement. To do so, we develop a theoretical framework which can be used to construct algorithms for a large class of possible suboptimality paradigms. We then use the framework to develop additively bounded algorithms, and show that in practice these new algorithms effectively trade-off additive solution suboptimality for runtime.