Mixed inference such as the marginal MAP query (some variables marginalized by summation and others by maximization) is key to many prediction and decision models. It is known to be extremely hard; the problem is NPPP-complete while the decision problem for MAP is only NP-complete and the summation problem is #P-complete. Consequently, approximation anytime schemes are essential. In this paper, we show that the framework of heuristic AND/OR search, which exploits conditional independence in the graphical model, coupled with variational-based mini-bucket heuristics can be extended to this task and yield powerful state-of-the-art schemes. Specifically, we explore the complementary properties of best-first search for reducing the number of conditional sums and providing time-improving upper bounds, with depth-first search for rapidly generating and improving solutions and lower bounds. We show empirically that a class of solvers that interleaves depth-first with best-first schemes emerges as the most competitive anytime scheme.

In this paper, we present a method using AI techniques to solve a case of pure mathematics applications for finding narrow admissible tuples. The original problem is formulated into a combinatorial optimization problem. In particular, we show how to exploit the local search structure to formulate the problem landscape for dramatic reductions in search space and for non-trivial elimination in search barriers, and then to realize intelligent search strategies for effectively escaping from local minima. Experimental results demonstrate that the proposed method is able to efficiently find best known solutions. This research sheds light on exploiting the local problem structure for an efficient search in combinatorial landscapes as an application of AI to a new problem domain.

This paper addresses the Traveling Salesman Problem with Drone (TSP-D), in which a truck and drone are used to deliver parcels to customers. The objective of this problem is to either minimize the total operational cost (min-cost TSP-D) or minimize the completion time for the truck and drone (min-time TSP-D). This problem has gained a lot of attention in the last few years since it is matched with the recent trends in a new delivery method among logistics companies. To solve the TSP-D, we propose a hybrid genetic search with dynamic population management and adaptive diversity control based on a split algorithm, problem-tailored crossover and local search operators, a new restore method to advance the convergence and an adaptive penalization mechanism to dynamically balance the search between feasible/infeasible solutions. The computational results show that the proposed algorithm outperforms existing methods in terms of solution quality and improves best known solutions found in the literature. Moreover, various analyses on the impacts of crossover choice and heuristic components have been conducted to analysis further their sensitivity to the performance of our method.

Millimeter wave (mmWave) communication with large antenna arrays is a promising technique to enable extremely high data rates due to large available bandwidth. Given the knowledge of an optimal directional beamforming vector, large antenna arrays have been shown to overcome both the severe signal attenuation in mmWave. However, fundamental limits and achievable learning of an optimal beamforming vector remain. This paper considers the problem of adaptive and sequential optimization of the beamforming vectors during the initial access phase of communication. With a single-path channel model, the problem is reduced to actively learning the Angle-of-Arrival (AoA) of the signal sent from the user to the Base Station (BS). Drawing on the recent results in the design of a hierarchical beamforming codebook [1], sequential measurement dependent noisy search [2], and active learning from an imperfect labeler [3], an adaptive and sequential alignment algorithm is proposed. For any given resolution and error probability of the estimated AoA, an upper bound on the expected search time of the proposed algorithm is derived via the Extrinsic Jensen Shannon Divergence. The upper bound demonstrates that the search time of the proposed algorithm asymptotically matches the performance of the noiseless bisection search up to a constant factor characterizing the AoA acquisition rate. Furthermore, the acquired AoA error probability decays exponentially fast with the search time with an exponent that is a decreasing function of the acquisition rate.Numerically, the proposed algorithm is compared with prior work where a significant improvement of the system communication rate is observed. Most notably, in the relevant regime of low (- 10dB to 5dB) raw SNR, this establishes the first practically viable solution for initial access and, hence, the first demonstration of stand-alone mmWave communication.

This document represents the proceedings of the 2018 XCSP3 Competition. The results of this competition of constraint solvers were presented at CP'18, the 24th International Conference on Principles and Practice of Constraint Programming, held in Lille, France from 27th August 2018 to 31th August, 2018.

Social media is an attention economy where users are constantly competing for attention in their followers' feeds. Users are likely to elicit greater attention from their followers, their audience, if their posts remain visible at the top of their followers' feeds for a longer period of time. However, this depends on the rate at which their followers receive information in their feeds, which in turn depends on the users their followers follow. Then, who should follow whom to maximize the visibility each user achieve? In this paper, we represent users' posts and feeds using the framework of temporal point processes. Under this representation, the problem reduces to optimizing a non-submodular nondecreasing set function under matroid constraints. Then, we show that the set function satisfies a novel property, $\xi$-submodularity, which allows a simple and efficient greedy algorithm to enjoy theoretical guarantees. In particular, we prove that the greedy algorithm offers a $(1/\xi + 1)$ approximation factor, where $\xi$ is the strong submodularity ratio, a new measure of approximate submodularity that we are able to bound in our problem. Experiments on both synthetic and real data gathered from Twitter show that our greedy algorithm is able to consistently outperform several baselines.

This paper proposes a new algorithm for solving MAX2SAT problems based on combining search methods with semidefinite programming approaches. Semidefinite programming techniques are well-known as a theoretical tool for approximating maximum satisfiability problems, but their application has traditionally been very limited by their speed and randomized nature. Our approach overcomes this difficult by using a recent approach to low-rank semidefinite programming, specialized to work in an incremental fashion suitable for use in an exact search algorithm. The method can be used both within complete or incomplete solver, and we demonstrate on a variety of problems from recent competitions. Our experiments show that the approach is faster (sometimes by orders of magnitude) than existing state-of-the-art complete and incomplete solvers, representing a substantial advance in search methods specialized for MAX2SAT problems.

Exploiting dependencies between labels is considered to be crucial for multi-label classification. Rules are able to expose label dependencies such as implications, subsumptions or exclusions in a human-comprehensible and interpretable manner. However, the induction of rules with multiple labels in the head is particularly challenging, as the number of label combinations which must be taken into account for each rule grows exponentially with the number of available labels. To overcome this limitation, algorithms for exhaustive rule mining typically use properties such as anti-monotonicity or decomposability in order to prune the search space. In the present paper, we examine whether commonly used multi-label evaluation metrics satisfy these properties and therefore are suited to prune the search space for multi-label heads.

Scheduling the maintenances of nuclear power plants is a complex optimization problem, formulated in 2-stage stochastic programming for the EURO/ROADEF 2010 challenge. The first level optimizes the maintenance dates and refueling decisions. The second level optimizes the production to fulfill the power demands and to ensure feasibility and costs of the first stage decisions. This paper solves a deterministic version of the problem, studying Mixed Integer Programming (MIP) formulations and matheuristics. Relaxing only two sets of constraints of the ROADEF challenge, a MIP formulation can be written using only binary variables for the maintenance dates. The MIP formulations are used to design constructive matheuristics and a Variable Neighborhood Descent (VND) local search. These matheuristics produce very high quality solutions. Some intermediate results explains results of the Challenge: the relaxation of constraints CT6 are justified and neighborhood analyses with MIP-VND justifies the choice of neighborhoods to implement for the problem. Lastly, an extension with stability costs for monthly reoptimization is considered, with efficient bi-objective matheuristics.

Given different types of constraints on human life, people must make decisions that satisfy social activity needs. Minimizing costs (i.e., distance, time, or money) associated with travel plays an important role in perceived and realized social quality of life. Identifying optimal interaction locations on road networks when there are multiple moving objects (MMO) with space-time constraints remains a challenge. In this research, we formalize the problem of finding dynamic ideal interaction locations for MMO as a spatial optimization model and introduce a context-based geoprocessing heuristic framework to address this problem. As a proof of concept, a case study involving identification of a meetup location for multiple people under traffic conditions is used to validate the proposed geoprocessing framework. Five heuristic methods with regard to efficient shortest-path search space have been tested. We find that the R* tree-based algorithm performs the best with high quality solutions and low computation time. This framework is implemented in a GIS environment to facilitate integration with external geographic contextual information, e.g., temporary road barriers, points of interest (POI), and real-time traffic information, when dynamically searching for ideal meetup sites. The proposed method can be applied in trip planning, carpooling services, collaborative interaction, and logistics management.