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.

The use of the Monte Carlo playouts as an evaluation function has proved to be a viable, general technique for searching intractable game spaces. This facilitate the use of statistical techniques like Monte Carlo Tree Search (MCTS), but is also known to require significant processing overhead. We seek to improve the quality of information extracted from the Monte Carlo playout in three ways. Firstly, by nesting the evaluation function inside another evaluation function; secondly, by measuring and utilising the depth of the playout; and thirdly, by incorporating pruning strategies that eliminate unnecessary searches and avoid traps. Our experimental data, obtained on a variety of two-player games from past General Game Playing (GGP) competitions and others, demonstrate the usefulness of these techniques in a Nested Player when pitted against a standard, optimised UCT player.

Despite recent improvements in search techniques for cost-optimal classical planning, the exponential growth of the size of the search frontier in A* is unavoidable. We investigate tiebreaking strategies for A*, experimentally analyzing the performance of standard tiebreaking strategies that break ties according to the heuristic value of the nodes. We find that tiebreaking has a significant impact on search algorithm performance when there are zero-cost operators that induce large plateau regions in the search space. We develop a new framework for tiebreaking based on a depth metric which measures distance from the entrance to the plateau, and propose a new, randomized strategy which significantly outperforms standard strategies on domains with zero-cost actions.

Identifying a small number of features that can represent the data is a known problem that comes up in areas such as machine learning, knowledge representation, data mining, and numerical linear algebra. Computing an optimal solution is believed to be NP-hard, and there is extensive work on approximation algorithms. Classic approaches exploit the algebraic structure of the underlying matrix, while more recent approaches use randomization. An entirely different approach that uses the A* heuristic search algorithm to find an optimal solution was recently proposed. Not surprisingly it is limited to effectively selecting only a small number of features. We propose a similar approach related to the Weighted A* algorithm. This gives algorithms that are not guaranteed to find an optimal solution but run much faster than the A* approach, enabling effective selection of many features from large datasets. We demonstrate experimentally that these new algorithms are more accurate than the current state-of-the-art while still being practical. Furthermore, they come with an adjustable guarantee on how different their error may be from the smallest possible (optimal) error. Their accuracy can always be increased at the expense of a longer running time.

We introduce a roommate market model, in which 2n people need to be assigned to n rooms, with two people in each room. Each person has a valuation to each room, as well as a valuation to each of other people as a roommate. Each room has a rent shared by the two people living in the room, and we need to decide who live together in which room and how much each should pay. Various solution concepts on stability and envy-freeness are proposed, with their existence studied and the computational complexity of the corresponding search problems analyzed. In particular, we show that maximizing the social welfare is NP-hard, and we give a polynomial time algorithm that achieves at least 2/3 of the maximum social welfare. Finally, we demonstrate a pricing scheme that can achieve envy-freeness for each room.

We address the control of a vertically profiling float us- ing ocean-model-based predictions of future currents. While these problems are in reality continuous control problems, we solve them by searching a discrete space of future actions. Additionally, while the environment is a continuous space, the ocean model we use is a discrete cell-based model. We show that even with an imperfect model of ocean currents, planning in the ocean current model can significantly improve results for a specific problem of controlling a vertically profiling float when trading off remaining at the same location as a virtual mooring and collecting more data with more profiles.

Model-Based Diagnosis (MBD) is a principled and domain-independent way of analyzing why a system under examination is not behaving as expected. Given an abstract description (model) of the system's components and their behavior when functioning normally, MBD techniques rely on observations about the actual system behavior to reason about possible causes when there are discrepancies between the expected and observed behavior. Due to its generality, MBD has been successfully applied in a variety of application domains over the last decades. In many application domains of MBD, testing different hypotheses about the reasons for a failure can be computationally costly, e.g., because complex simulations of the system behavior have to be performed. In this work, we therefore propose different schemes of parallelizing the diagnostic reasoning process in order to better exploit the capabilities of modern multi-core computers. We propose and systematically evaluate parallelization schemes for Reiter's hitting set algorithm for finding all or a few leading minimal diagnoses using two different conflict detection techniques. Furthermore, we perform initial experiments for a basic depth-first search strategy to assess the potential of parallelization when searching for one single diagnosis. Finally, we test the effects of parallelizing "direct encodings" of the diagnosis problem in a constraint solver.