While suboptimal best-first search algorithms like Greedy Best-First Search are frequently used when building automated planning systems, their greedy nature can make them susceptible to being easily misled by flawed heuristics. This weakness has motivated the development of best-first search variants like epsilon-greedy node selection, type-based exploration, and diverse best-first search, which all use random exploration to mitigate the impact of heuristic error. In this paper, we provide a theoretical justification for this increased robustness by formally analyzing how these algorithms behave on infinite graphs. In particular, we show that when using these approaches on any infinite graph, the probability of not finding a solution can be made arbitrarily small given enough time. This result is shown to hold for a class of algorithms that includes the three mentioned above, regardless of how misleading the heuristic is.

Finding diverse solutions has become important in many combinatorial search domains, including Automated Planning, Path Planning and Constraint Programming. Much of the work in these directions has however focussed on coming up with appropriate diversity metrics and compiling those metrics in to the solvers/planners. Most approaches use linear-time greedy algorithms for exploring the state space of solution combinations for generating a diverse set of solutions, limiting not only their completeness but also their effectiveness within a time bound. In this paper, we take a combinatorial search perspective on generating diverse solutions. We present a generic bi-level optimization framework for finding cost-sensitive diverse solutions. We propose complete methods under this framework, which guarantee finding a set of cost sensitive diverse solutions satisficing the given criteria whenever there exists such a set. We identify various aspects that affect the performance of these exhaustive algorithms and propose techniques to improve them. Experimental results show the efficacy of the proposed framework compared to an existing greedy approach.

Recent work has raised the challenge of efficient automated troubleshooting in domains where repairing a set of components in a single repair action is cheaper than repairing each of them separately. This corresponds to cases where there is a non-negligible overhead to initiating a repair action and to testing the system after a repair action. In this work we propose several algorithms for choosing which batch of components to repair, so as to minimize the overall repair costs. Experimentally, we show the benefit of these algorithms over repairing components one at a time.

We introduce a state space search method that identifies dead-end states, analyzes the reasons for failure, and learns to avoid similar mistakes in the future. Our work is placed in classical planning. The key technique are critical-path heuristics h C , relative to a set C of conjunctions. These recognize a dead-end state s, returning h C (s) = infty, if s has no solution even when allowing to break up conjunctive subgoals into the elements of C. Our key idea is to learn C during search. Starting from a simple initial C, we augment search to identify unrecognized dead-ends s, where h C (s) < infinity. We design methods analyzing the situation at such s, adding new conjunctions into C to obtain h C (s) = infty, thus learning to recognize s as well as similar dead-ends search may encounter in the future. We furthermore learn clauses phi where s' not satisfying phi implies hC(s') = infty, to avoid the prohibitive overhead of computing h C on every search state. Arranging these techniques in a depth-first search, we obtain an algorithm approaching the elegance of clause learning in SAT, learning to refute search subtrees. Our experiments show that this can be quite powerful. On problems where dead-ends abound, the learning reliably reduces the search space by several orders of magnitude.

Pathfinding is a common task across many domains and platforms, whether in games, robotics, or road maps. Given the breadth of domains, there are also a wide variety of representations used for pathfinding, and there are many techniques which have been shown to improve performance. In the last few years, the state-of-the-art in grid-based pathfinding has been significantly improved with domain-specific techniques such as Jump Point Search (JPS), Subgoal Graphs, and Compressed Path Databases. In this paper we look at a specific implementation of the general idea of Geometric Containers, showing that, while it is effective on grid maps, when combined with JPS+ it provides state-of-the-art performance.

Random k -CNF formulas at the anticipated k -SAT phase-transition point are prototypical hard k-SAT instances. We develop a stochastic local search algorithm and study it both theoretically and through a large-scale experimental study. The algorithm comes as a result of a systematic study that contrasts rates at which a certain measure concentration phenomenon occurs. This study yields a new stochastic rule for local search. A strong point of our contribution is the conceptual simplicity of our algorithm. More importantly, the empirical results overwhelmingly indicate that our algorithm outperforms the state-of-the-art. This includes a number of winners and medalist solvers from the recent SAT Competitions.

The design of strategies for branching in Mixed Integer Programming (MIP) is guided by cycles of parameter tuning and offline experimentation on an extremely heterogeneous testbed, using the average performance. Once devised, these strategies (and their parameter settings) are essentially input-agnostic. To address these issues, we propose a machine learning (ML) framework for variable branching in MIP.Our method observes the decisions made by Strong Branching (SB), a time-consuming strategy that produces small search trees, collecting features that characterize the candidate branching variables at each node of the tree. Based on the collected data, we learn an easy-to-evaluate surrogate function that mimics the SB strategy, by means of solving a learning-to-rank problem, common in ML. The learned ranking function is then used for branching. The learning is instance-specific, and is performed on-the-fly while executing a branch-and-bound search to solve the MIP instance. Experiments on benchmark instances indicate that our method produces significantly smaller search trees than existing heuristics, and is competitive with a state-of-the-art commercial solver.

Hash Distributed A* (HDA*) is an efficient parallel best first algorithm that asynchronously distributes work among the processes using a global hash function. Although Zobrist hashing, the standard hash function used by HDA*, achieves good load balance for many domains, it incurs significant communication overhead since it requires many node transfers among threads. We propose Abstract Zobrist hashing, a new work distribution method for parallel search which reduces node transfers and mitigates communication overhead by using feature projection functions. We evaluate Abstract Zobrist hashing for multicore HDA*, and show that it significantly outperforms previous work distribution methods.

We investigate the problem of repacking stations in the FCC's upcoming, multi-billion-dollar "incentive auction". Early efforts to solve this problem considered mixed-integer programming formulations, which we show are unable to reliably solve realistic, national-scale problem instances. We describe the result of a multi-year investigation of alternatives: a solver, SATFC, that has been adopted by the FCC for use in the incentive auction. SATFC is based on a SAT encoding paired with a wide range of techniques: constraint graph decomposition; novel caching mechanisms that allow for reuse of partial solutions from related, solved problems; algorithm configuration; algorithm portfolios; and the marriage of local-search and complete solver strategies. We show that our approach solves virtually all of a set of problems derived from auction simulations within the short time budget required in practice.

The paper investigates the potential of look-ahead in the con-text of AND/OR search in graphical models using the Mini-Bucket heuristic for combinatorial optimization tasks (e.g., MAP/MPE or weighted CSPs). We present and analyze the complexity of computing the residual (a.k.a Bellman update) of the Mini-Bucket heuristic and show how this can be used to identify which parts of the search space are more likely to benefit from look-ahead and how to bound its overhead. We also rephrase the look-ahead computation as a graphical model, to facilitate structure exploiting inference schemes. We demonstrate empirically that augmenting Mini-Bucket heuristics by look-ahead is a cost-effective way of increasing the power of Branch-And-Bound search.