This paper provides algorithms for predicting the size of the Expanded Search Tree (EST) of Depth-first Branch and Bound algorithms (DFBnB) for optimization tasks. The prediction algorithm is implemented and evaluated in the context of solving combinatorial optimization problems over graphical models such as Bayesian and Markov networks. Our methods extend to DFBnB the approaches provided by Knuth-Chen schemes that were designed and applied for predicting the EST size of backtracking search algorithms. Our empirical results demonstrate good predictions which are superior to competing schemes.

Distributed Constraint Optimization (DCOP) is a powerful framework for representing and solving distributed combinatorial problems, where the variables of the problem are owned by different agents. Many multi-agent problems include constraints that produce different gains (or costs) for the participating agents. Asymmetric gains of constrained agents cannot be naturally represented by the standard DCOP model. The present paper proposes a general framework for Asymmetric DCOPs (ADCOPs). In ADCOPs different agents may have different valuations for constraints that they are involved in. The new framework bridges the gap between multi-agent problems which tend to have asymmetric structure and the standard symmetric DCOP model. The benefits of the proposed model over previous attempts to generalize the DCOP model are discussed and evaluated. Innovative algorithms that apply to the special properties of the proposed ADCOP model are presented in detail. These include complete algorithms that have a substantial advantage in terms of runtime and network load over existing algorithms (for standard DCOPs) which use alternative representations. Moreover, standard incomplete algorithms (i.e., local search algorithms) are inapplicable to the existing DCOP representations of asymmetric constraints and when they are applied to the new ADCOP framework they often fail to converge to a local optimum and yield poor results. The local search algorithms proposed in the present paper converge to high quality solutions. The experimental evidence that is presented reveals that the proposed local search algorithms for ADCOPs achieve high quality solutions while preserving a high level of privacy.

The $k$-NN graph has played a central role in increasingly popular data-driven techniques for various learning and vision tasks; yet, finding an efficient and effective way to construct $k$-NN graphs remains a challenge, especially for large-scale high-dimensional data. In this paper, we propose a new approach to construct approximate $k$-NN graphs with emphasis in: efficiency and accuracy. We hierarchically and randomly divide the data points into subsets and build an exact neighborhood graph over each subset, achieving a base approximate neighborhood graph; we then repeat this process for several times to generate multiple neighborhood graphs, which are combined to yield a more accurate approximate neighborhood graph. Furthermore, we propose a neighborhood propagation scheme to further enhance the accuracy. We show both theoretical and empirical accuracy and efficiency of our approach to $k$-NN graph construction and demonstrate significant speed-up in dealing with large scale visual data.

Inference for latent feature models is inherently difficult as the inference space grows exponentially with the size of the input data and number of latent features. In this work, we use Kurihara & Welling (2008)'s maximization-expectation framework to perform approximate MAP inference for linear-Gaussian latent feature models with an Indian Buffet Process (IBP) prior. This formulation yields a submodular function of the features that corresponds to a lower bound on the model evidence. By adding a constant to this function, we obtain a nonnegative submodular function that can be maximized via a greedy algorithm that obtains at least a one-third approximation to the optimal solution. Our inference method scales linearly with the size of the input data, and we show the efficacy of our method on the largest datasets currently analyzed using an IBP model.

The Low Autocorrelation Binary Sequence problem has applications in telecommunications, is of theoretical interest to physicists, and has inspired many optimisation researchers. Metaheuristics for the problem have progressed greatly in recent years but complete search has not progressed since a branch-and-bound method of 1996. In this paper we find four ways of improving branch-and-bound, leading to a tighter relaxation, faster convergence to optimality, and better empirical scalability.

We investigate two systems of fully proportional representation suggested by Chamberlin & Courant and Monroe. Both systems assign a representative to each voter so that the "sum of misrepresentations" is minimized. The winner determination problem for both systems is known to be NP-hard, hence this work aims at investigating whether there are variants of the proposed rules and/or specific electorates for which these problems can be solved efficiently. As a variation of these rules, instead of minimizing the sum of misrepresentations, we considered minimizing the maximal misrepresentation introducing effectively two new rules. In the general case these "minimax" versions of classical rules appeared to be still NP-hard. We investigated the parameterized complexity of winner determination of the two classical and two new rules with respect to several parameters. Here we have a mixture of positive and negative results: e.g., we proved fixed-parameter tractability for the parameter the number of candidates but fixed-parameter intractability for the number of winners. For single-peaked electorates our results are overwhelmingly positive: we provide polynomial-time algorithms for most of the considered problems. The only rule that remains NP-hard for single-peaked electorates is the classical Monroe rule.

In this work we are interested in the problem of energy management in Mobile Ad-hoc Network (MANET). The solving and optimization of MANET allow assisting the users to efficiently use their devices in order to minimize the batteries power consumption. In this framework, we propose a modelling of the MANET in form of a Constraint Optimization Problem called COMANET. Then, in the objective to minimize the consumption of batteries power, we present an approach based on an adaptation of the A star algorithm to the MANET problem called MANED. Finally, we expose some experimental results showing utility of this approach.

The problem of optimizing unknown costly-to-evaluate functions has been studied for a long time in the context of Bayesian Optimization. Algorithms in this field aim to find the optimizer of the function by asking only a few function evaluations at locations carefully selected based on a posterior model. In this paper, we assume the unknown function is Lipschitz continuous. Leveraging the Lipschitz property, we propose an algorithm with a distinct exploration phase followed by an exploitation phase. The exploration phase aims to select samples that shrink the search space as much as possible. The exploitation phase then focuses on the reduced search space and selects samples closest to the optimizer. Considering the Expected Improvement (EI) as a baseline, we empirically show that the proposed algorithm significantly outperforms EI.

ExtractingMUCs(MinimalUnsatisfiableCores)fromanunsatisfiable constraint network is a useful process when causes of unsatisfiability must be understood so that the network can be re-engineered and relaxed to become sat- isfiable. Despite bad worst-case computational complexity results, various MUC- finding approaches that appear tractable for many real-life instances have been proposed. Many of them are based on the successive identification of so-called transition constraints. In this respect, we show how local search can be used to possibly extract additional transition constraints at each main iteration step. The approach is shown to outperform a technique based on a form of model rotation imported from the SAT-related technology and that also exhibits additional transi- tion constraints. Our extensive computational experimentations show that this en- hancement also boosts the performance of state-of-the-art DC(WCORE)-like MUC extractors.

Constraint Programming (CP) solvers classically explore the solution space using tree-search based heuristics. Monte-Carlo Tree-Search (MCTS) is a tree-search method aimed at optimal sequential decision making under uncertainty. At the crossroads of CP and MCTS, this paper presents the Bandit Search for Constraint Programming (BASCOP)  algorithm, adapting MCTS to the specifics of CP search trees. Formally, MCTS simultaneously estimates the average node reward, and uses it to bias the exploration towards the most promising regions of the tree, borrowing the multi-armed bandit (MAB) decision rule. The two contributions in BASCOP concern i) a specific reward function, estimating the relative failure depth conditionally to a (variable, value) assignment; ii) a new  decision rule, hybridizing the MAB framework and the spirit of local neighborhood search. Specifically, BASCOP guides the CP search in the neighborhood of the previous best solution, by exploiting statistical estimates gathered across multiple restarts. BASCOP, using Gecode as the underlying constraint solver, shows significant improvements over the depth-first search baseline on some  CP benchmark suites. For hard job-shop scheduling problems, BASCOP matches the results of state-of-the-art scheduling-specific CP approaches. These results demonstrate the potential of BASCOP as a generic yet robust search method for CP.