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Significant advances have occurred in heuristic search for planning in the last eleven years. Many of these planners use A*-style search. We report on five sound and complete domain-independent forward state-space STRIPS planners in this paper. The planners are AWA* (Adjusted Weighted A*), MAWA* (Modified AWA*), AWA*-AC (AWA* with action conflict-based adjustment), AWA*-PD (AWA* with deleted preconditions-based adjustment), and AWA*-AC-LE (AWA*-AC with lazy evaluation). AWA* is the first planner to use node-dependent weighting in A*. MAWA*, AWA*-AC, AWA*-PD, and AWA*-AC-LE use conditional two-phase heuristic evaluation. MAWA* applies node-dependent weighting to a subset of the nodes in the fringe, after the two-phase evaluation. One novel idea in AWA*-AC-LE is lazy heuristic evaluation which does not construct relaxed plans to compute heuristic values for all nodes. We report on an empirical comparison of AWA*, MAWA*, AWA*-AC, AWA*-PD, and AWA*-AC-LE with classical planners AltAlt, FF, HSP-2 and STAN 4. Our variants of A* outperform these planners on several problems. The empirical evaluation shows that heuristic search planning is significantly benefitted by node-dependent weighting, conditional two-phase heuristic evaluation and lazy evaluation. We report on the insights about inferior performance of our planners in some domains using the notion of waiting time. We discuss many other variants of A*, state-space planners and directions for future work.

We argue that A*, the popular technique for path-finding for NPCs in games, suffers from three limitations that are pertinent to game worlds: (a) the grid maps often restrict the optimality of the paths, (b) A* paths exhibit wall-hugging behavior, and (c) optimal paths are more predictable. We present a new algorithm, VRA*, that varies map-resolution as needed, and repeatedly calls A*. We also present an extension of an existing post-smoothing technique, and show that these two techniques together produce more realistic looking paths than A*, that overcome the above limitations, while using significantly less memory and time than A*.

We propose a set of path planning tools including path generator, cost map generator, and path editor for racing games. The user can define the race by providing a racetrack as a 3D model and weights of the devised turn and heuristic functions in our system. Then, the proposed cost map generator automatically generates necessary information of the racetrack including cost map and distance to finish of any position on the race track. Different from the traditional A* problem, in our research the obstacles are dynamic and there are multiple sources and destinations. Our approach generates the path of each racer on the basis of time slots to which the path finding method applies on the fly. To further guarantee the quality of the path, we implement path smoothing using a Gaussian filter and provide an off-line path editor that allows users to edit the path in time-space domain intuitively, flexibly, and effectively. Our tools have been verified in a horse racing game to generate natural racer behaviors, demonstrating realistic and exciting racing.

A* search and its variants have been used in various fields for solving problems with large search spaces where state transitions occur because of application of operators. The key values in A* search are g(n) and h(n), where g(n) is the cost of the path from root (or start) node to node n, and h(n) is the estimated cost of cheapest path from n to goal. In this paper, we report on a space of variants of A* based on the following ideas: (i) using weighting functions for g(n) and h(n), (ii) evaluating different nodes with different heuristics, (iii) evaluating nodes with computationally cheap heuristics and re-evaluating some nodes with computationally expensive heuristics, and (iv) changing the size of the set of nodes from which the node to be expanded next is selected. We report on the bounds on the costs of solutions found by these variants of A*. We also report on the bounds for meta-variants of A* that invoke these variants sequentially. We show how the results can be used to obtain a more flexible search control without increasing the bound on the cost of the solution found by a variant or a meta-variant.

In this paper, we develop TCGD, a problem-independent, time-constrained, approximate guided depth-first search (GDFS) algorithm. The algorithm is designed to achieve the best ascertained approximation degree under a fixed time constraint. We consider only searches with finite search space and admissible heuristic functions. We study NP-hard combinatorial optimization problems with polynomial-time computable feasible solutions. For the problems studied, we observe that the execution time increases exponentially as approximation degree decreases, although anomalies may happen. The algorithms we study are evaluated by simulations using the symmetric traveling-salesperson problem.