Modern society is critically dependent on the services provided by engineered infrastructure networks. When natural disasters (e.g. Hurricane Sandy) occur, the ability of these networks to provide service is often degraded because of physical damage to network components. One of the most critical of these networks is the electrical distribution grid, with medium voltage circuits often suffering the most severe damage. However, well-placed upgrades to these distribution grids can greatly improve post-event network performance. We formulate an optimal electrical distribution grid design problem as a two-stage, stochastic mixed-integer program with damage scenarios from natural disasters modeled as a set of stochastic events. We develop and investigate the tractability of an exact and several heuristic algorithms based on decompositions that are hybrids of techniques developed by the AI and operations research communities. We provide computational evidence that these algorithms have significant benefits when compared with commercial, mixed-integer programming software.

We present a data mining approach for reducing the search space of local search algorithms in large-scale set partitioning problems (SPPs). We construct a k-nearest neighbor graph by extracting variable associations from the instance to be solved, in order to identify promising pairs of flipping variables in the large neighborhood search. We incorporate the search space reduction technique into a 2-flip neighborhood local search algorithm with an efficient incremental evaluation of solutions and an adaptive control of penalty weights. We also develop a 4-flip neighborhood local search algorithm that flips four variables alternately along 4-paths or 4-cycles in the k-nearest neighbor graph. According to computational comparison with the latest solvers, our algorithm performs effectively for large-scale SPP instances with up to 2.57 million variables.

Dynamic programming (DP) is a fundamental tool used to obtain exact, optimal solutions for many combinatorial optimization problems. Among these problems, important ones including the knapsack problems and the computation of edit distances between string pairs can be solved with a kind of DP that corresponds to solving the shortest path problem on a directed acyclic graph (DAG). These problems can be solved efficiently with DP, however, in practical situations, we want to solve the customized problems made by adding logical constraints to the original problems. Developing an algorithm specifically for each combination of a problem and a constraint set is unrealistic. The proposed method, BDD-Constrained Search (BCS), exploits a Binary Decision Diagram (BDD) that represents the logical constraints in combination with the DAG that represents the problem. The BCS runs DP on the DAG while using the BDD to check the equivalence and the validity of intermediate solutions to efficiently solve the problem. The important feature of BCS is that it can be applied to problems with various types of logical constraints in a unified way once we represent the constraints as a BDD. We give a theoretical analysis on the time complexity of BCS and also conduct experiments to compare its performance to that of a state-of-the-art integer linear programming solver.

Stable matching problems have several practical applications. If preference lists are truncated and contain ties, finding a stable matching with maximal size is computationally difficult. We address this problem using a local search technique, based on Adaptive Search and present experimental evidence that this approach is much more efficient than state-of-the-art exact and approximate methods. Moreover, parallel versions (particularly versions with communication) improve performance so much that very large and hard instances can be solved quickly.

Rank K Binary Matrix Factorization (BMF) approximates a binary matrix by the product of two binary matrices of lower rank, K, using either L1 or L2 norm. In this paper, we first show that the BMF with L2 norm can be reformulated as an Unconstrained Binary Quadratic Programming (UBQP) problem. We then review several local search strategies that can be used to improve the BMF solutions obtained by previously proposed methods, before introducing a new local search dedicated to the BMF problem. We show in particular that the proposed solution is in general faster than the previously proposed ones. We then assess its behavior on several collections and methods and show that it significantly improves methods targeting the L2 norms on all the datasets considered; for the L1 norm, the improvement is also significant for real, structured datasets and for the BMF problem without the binary reconstruction constraint.

In this paper we show that the alpha-beta algorithm and its successor MT-SSS*, as two classic minimax search algorithms, can be implemented as rollout algorithms , a generic algorithmic paradigm widely used in many domains. Specifically, we define a family of rollout algorithms, in which the rollout policy is restricted to select successor nodes only from a certain subset of the children list. We show that any rollout policy in this family (either deterministic or randomized) is guaranteed to evaluate the game tree correctly with a finite number of rollouts. Moreover, we identify simple rollout policies in this family that ``implement'' alpha-beta and MT-SSS*. Specifically, given any game tree, the rollout algorithms with these particular policies always visit the same set of leaf nodes in the same order with alpha-beta and MT-SSS*, respectively. Our results suggest that traditional pruning techniques and the recent Monte Carlo Tree Search algorithms, as two competing approaches for game tree evaluation, may be unified under the rollout paradigm.

Generalized Adaptive A* (GAA*) is an incremental algorithm that replans using A* when solving goal-directed navigation problems in dynamic terrain. Immediately after each A* search, it runs an efficient procedure that updates the heuristic values of states that were just expanded by A*, making them more informed. Those updates allow GAA* to speed up subsequent A* searches. Being based on A*, it is simple to describe and communicate; however, it is outperformed by other incremental algorithms like the state-of-the-art D*Lite algorithm at goal-directed navigation. In this paper we show how GAA* can be modified to exploit more information from a previous search in addition to the updated heuristic function. Specifically, we show how GAA* can be modified to utilize the paths found by a previous A* search. Our algorithm — Multipath Generalized Adaptive A* (MPGAA*) — has the same theoretical properties of GAA* and differs from it by only a few lines of pseudocode. Arguably, MPGAA* is simpler to understand than D*Lite. We evaluate MPGAA* over various realistic dynamic terrain settings, and observed that it generally outperforms the state-of-the-art algorithm D*Lite in scenarios resembling outdoor and indoor navigation.

There are two major paradigms for linear-space heuristic search: iterative deepening (IDA*) and recursive best-first search (RBFS). While the node regeneration overhead of IDA* is easily characterized in terms of the heuristic branching factor, the overhead of RBFS depends on how widely the promising nodes are separated in the search tree, and is harder to anticipate. In this paper, we present two simple techniques for improving the performance of RBFS while maintaining its advantages over IDA*. While these techniques work well in practice, they do not provide any theoretical bounds on the amount of regeneration overhead. To this end, we introduce RBFScr, the first method for provably bounding the regeneration overhead of RBFS. We show empirically that this improves its performance in several domains, both for optimal and suboptimal search, and also yields a better linear-space anytime heuristic search. RBFScr is the first linear space best-first search robust enough to solve a variety of domains with varying operator costs.

Satisfiability Modulo Theories (SMT) is essential for many practical applications, e.g., in hard- and software verification, and increasingly also in other scientific areas like computational biology. A large number of applications in these areas benefit from bit-precise reasoning over finite-domain variables. Current approaches in this area translate a formula over bit-vectors to an equisatisfiable propositional formula, which is then given to a SAT solver. In this paper, we present a novel stochastic local search (SLS) algorithm to solve SMT problems, especially those in the theory of bit-vectors, directly on the theory level. We explain how several successful techniques used in modern SLS solvers for SAT can be lifted to the SMT level. Experimental results show that our approach can compete with state-of-the-art bit-vector solvers on many practical instances and, sometimes, outperform existing solvers. This offers interesting possibilities in combining our approach with existing techniques, and, moreover, new insights into the importance of exploiting problem structure in SLS solvers for SAT. Our approach is modular and, therefore, extensible to support other theories, potentially allowing SLS to become part of the more general SMT framework.

Minimum Vertex Cover (MinVC) is a well known NP-hard combinatorial optimization problem, and local search has been shown to be one of the most effective approaches to this problem. State-of-the-art MinVC local search algorithms employ edge weighting techniques and prefer to select vertices with higher weighted score. These algorithms are not robust and especially have poor performance on instances with structures which defeat greedy heuristics. In this paper, we propose a vertex weighting scheme to address this shortcoming, and combine it within the current best MinVC local search algorithm NuMVC, leading to a new algorithm called TwMVC. Our experiments show that TwMVC outperforms NuMVC on the standard benchmarks namely DIMACS and BHOSLIB. To the best of our knowledge, TwMVC is the first MinVC algorithm that attains the best known solution for all instances in both benchmarks. Further, TwMVC shows superiority on a benchmark of real-world networks.