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.

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.

We consider the Social Ridesharing (SR) problem, where a set of commuters, connected through a social network, arrange one-time rides at short notice. In particular, we focus on the associated optimisation problem of forming cars to minimise the travel cost of the overall system modelling such problem as a graph constrained coalition formation (GCCF) problem, where the set of feasible coalitions is restricted by a graph (i.e., the social network). Moreover, we significantly extend the state of the art algorithm for GCCF, i.e., the CFSS algorithm, to solve our GCCF model of the SR problem. Our empirical evaluation uses a real dataset for both spatial (GeoLife) and social data (Twitter), to validate the applicability of our approach in a realistic application scenario. Empirical results show that our approach computes optimal solutions for systems of medium scale (up to 100 agents) providing significant cost reductions (up to -36.22%). Moreover, we can provide approximate solutions for very large systems (i.e., up to 2000 agents) and good quality guarantees (i.e., with an approximation ratio of 1.41 in the worst case) within minutes (i.e., 100 seconds).

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.

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.

Computing prices in core-selecting combinatorial auctions is a computationally hard problem. Auctions with many bids can only be solved using a recently proposed core constraint generation (CCG) algorithm, which may still take days on hard instances. In this paper, we present a new algorithm that significantly outperforms the current state of the art. Towards this end, we first provide an alternative definition of the set of core constraints, where each constraint is weakly stronger, and prove that together these constraints define the identical polytope to the previous definition. Using these new theoretical insights we develop two new algorithmic techniques which generate additional constraints in each iteration of the CCG algorithm by 1) exploiting separability in allocative conflicts between participants in the auction, and 2) by leveraging non-optimal solutions. We show experimentally that our new algorithm leads to significant speed-ups on a variety of large combinatorial auction problems. Our work provides new insights into the structure of core constraints and advances the state of the art in fast algorithms for computing core prices in large combinatorial auctions.

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.

A* search is a fundamental topic in artificial intelligence. Recently, the general purpose computation on graphics processing units (GPGPU) has been widely used to accelerate numerous computational tasks. In this paper, we propose the first parallel variant of the A* search algorithm such that the search process of an agent can be accelerated by a single GPU processor in a massively parallel fashion. Our experiments have demonstrated that the GPU-accelerated A* search is efficient in solving multiple real-world search tasks, including combinatorial optimization problems, pathfinding and game solving. Compared to the traditional sequential CPU-based A* implementation, our GPU-based A* algorithm can achieve a significant speedup by up to 45x on large-scale search problems.

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.

Approximating a matrix by a small subset of its columns is a known problem in numerical linear algebra. Algorithms that address this problem have been used in areas which include, among others, sparse approximation, unsupervised feature selection, data mining, and knowledge representation. Such algorithms were investigated since the 1960's, with recent results that use randomization. The problem is believed to be NP-Hard, and to the best of our knowledge there are no previously published algorithms aimed at computing optimal solutions. We show how to model the problem as a graph search, and propose a heuristic based on eigenvalues of related matrices. Applying the A* search strategy with this heuristic is guaranteed to find the optimal solution. Experimental results on common datasets show that the proposed algorithm can effectively select columns from moderate size matrices, typically improving by orders of magnitude the run time of exhaustive search. We also show how to combine the proposed algorithm with other non-optimal (but much faster) algorithms in a ``two stage'' framework, which is guaranteed to improve the accuracy of the other algorithms.