Previous work introduced the concept of progress states. After expanding a progress state, a greedy best-first search (GBFS) will only expand states with lower heuristic values. Current methods can identify progress states only for a single task and only after a solution for the task has been found. We introduce a novel approach that learns a description logic formula characterizing all progress states in a classical planning domain. Using the learned formulas in a GBFS to break ties in favor of progress states often significantly reduces the search effort.

Most real-world project have a deadline and consist of completing tasks. In our setting, each task needs to be executed by a single supplier, chosen from a subset of suppliers that have the required proficiency to handle that task. The suppliers differ in their execution times, which are stochastically taken from known distributions. The Supplier Assignment for Meeting a Deadline (SAMD) problem is the problem of assigning a supplier to each task in a manner that maximizes the chance to meet the overall project deadline. We propose an A*-based approach, along with an efficient admissible heuristic function, that guarantees an optimal solution for this problem. Experimentally, we compare our A*-based approach to an exhaustive brute-force approach and several heuristic methods. The results show that our A*-based approach compares favorably with the heuristic methods, and is orders of magnitude faster than the exhaustive alternative.

In planning algorithms and in other domains, there is often a need to run long computations that involve summations, maximizations and other operations on random variables, and to store intermediate results. In this paper, as a main motivating example, we elaborate on the case of estimating probabilities of meeting deadlines in hierarchical plans. A source of computational complexity, often neglected in the analysis of such algorithms, is that the support of the variables needed as intermediate results may grow exponentially along the computation. Therefore, to avoid exponential memory and time complexities, we need to trim these variables. This is similar, in a sense, to rounding intermediate results in numerical computations. Of course, to maintain the quality of algorithms, the trimming procedure should be efficient and it must maintain accuracy as much as possible. In this paper, we propose an optimal trimming algorithm with polynomial time and memory complexities for the purpose of estimating probabilities of deadlines in plans. More specifically, we show that our algorithm, given the needed size of the representation of the variable, provides the best possible approximation, where approximation accuracy is considered with a measure that fits the goal of estimating deadline meeting probabilities.