The defining characteristic the SDVRP, where vehicle capacity and customer demands of the SDVRP that distinguishes it from the classical are not required to be integer numbers, the number of vehicles vehicle routing problem (VRP) is that each customer is not limited to the minimum possible number, and can be served by more than one vehicle. Obviously, when the customer demands may exceed the vehicle capacity. The the demand of a customer is lager than the vehicle capacity, main contributions are threefold. First, we find a novel way it has to be split and the customer has to be visited more to represent the solutions of the SDVRP, which is the combination than once. As shown by (Dror and Trudeau 1989), when all of a set of vehicle routes and a forest. Second, based customer demands are less than or equal to the vehicle capacity, on this solution representation, we propose three classes of split delivery can also lead to substantial cost savings.

This work studies the Generalized Singular Value Thresholding (GSVT) operator associated with a nonconvex function g defined on the singular values of X. We prove that GSVT can be obtained by performing the proximal operator of g on the singular values since Proxg(.) is monotone when g is lower bounded. If the nonconvex g satisfies some conditions (many popular nonconvex surrogate functions, e.g., lp-norm, 0 < p < 1, of l0-norm are special cases), a general solver to find Proxg(b) is proposed for any b ≥ 0. GSVT greatly generalizes the known Singular Value Thresholding (SVT) which is a basic subroutine in many convex low rank minimization methods. We are able to solve the nonconvex low rank minimization problem by using GSVT in place of SVT.

Question and answer pairs in Community Question Answering (CQA) services are organized into hierarchical structures or taxonomies to facilitate users to find the answers for their questions conveniently. We observe that different CQA services have their own knowledge focus and used different taxonomies to organize their question and answer pairs in their archives. As there are no simple semantic mappings between the taxonomies of the CQA services, the integration of CQA services is a challenging task. The existing approaches on integrating taxonomies ignore the hierarchical structures of the source taxonomy. In this paper, we propose a novel approach that is capable of incorporating the parent-child and sibling information in the hierarchical structures of the source taxonomy for accurate taxonomy integration. Our experimental results with real world CQA data demonstrate that the proposed method significantly outperforms state-of-the-art methods.

Advanced e-applications require comprehensive knowledge about their users’ preferences in order to provide accurate personalized services. In this paper, we propose to learn users’ preferences to product brands from their implicit feedbacks such as their searching and browsing behaviors in user Web browsing log data. The user brand preference learning problem is challenge since (1) the users’ implicit feedbacks are extremely sparse in various product domains; and (2) we can only observe positive feedbacks from users’ behaviors. In this paper, we propose a latent factor model to collaboratively mine users’ brand preferences across multiple domains simultaneously. By collective learning, the learning processes in all the domains are mutually enhanced and hence the problem of data scarcity in each single domain can be effectively addressed. On the other hand, we learn our model with an adaption of the Bayesian personalized ranking (BPR) optimization criterion which is a general learning framework for collaborative filtering from implicit feedbacks. Experiments with both synthetic and real world datasets show that our proposed model significantly outperforms the baselines.

State-of-the-art branch-and-bound algorithms for the maximum clique problem (Maxclique) frequently use an upper bound based on a partition P of a graph into independent sets for a maximum clique of the graph, which cannot be very tight for imperfect graphs. In this paper we propose a new encoding from Maxclique into MaxSAT and use MaxSAT technology to improve the upper bound based on the partition P. In this way, the strength of specific algorithms for Maxclique in partitioning a graph and the strength of MaxSAT technology in propositional reasoning are naturally combined to solve Maxclique. Experimental results show that the approach is very effective on hard random graphs and on DIMACS Maxclique benchmarks, and allows to close an open DIMACS problem.