Abstract Triggered by earlier work on random walks in the quarter-plane, we study the issue of two-queue systems whereby, at least for states ( m , n ) in some interior part of the state space, the stationary joint system-content distribution u ( m , n ) can be expressed as a finite linear combination of bivariate geometric terms of type $$\gamma ^m \delta ^n$$ γ m δ n . Using a transform-based approach, we prove that this is certainly the case if the steady-state joint probability generating function $$U(z_1,z_2)$$ U ( z 1 , z 2 ) of the two system contents can be expressed as a bivariate rational function of its two arguments, with mutually prime numerator and denominator, whereby the denominator is the product of two univariate polynomials in $$z_1$$ z 1 and $$z_2$$ z 2 , respectively, whose zeroes $$\hat{z_1}$$ z 1 ^ and $$\hat{z_2}$$ z 2 ^ all have multiplicity one . We show that the decay rates $$\gamma $$ γ and $$\delta $$ δ appearing in u ( m , n ) are the inverse values of (some of) the zeroes $$\hat{z_1}$$ z 1 ^ and $$\hat{z_2}$$ z 2 ^ , but, in general, there may be zero-pairs $$(\hat{z_1}, \hat{z_2})$$ ( z 1 ^ , z 2 ^ ) that do not contribute a bivariate geometric term in u ( m , n ). For two specific classes of discrete-time two-queue systems, we prove that, when $$U(z_1,z_2)$$ U ( z 1 , z 2 ) has the prescribed form, only the zero-pairs that are zero-tuples of the kernel of the system contribute a term in u ( m , n ). In an extended series of examples, we then demonstrate that, within the two classes, specific instances (corresponding with specific arrival processes) that comply with the condition on $$U(z_1,z_2)$$ U ( z 1 , z 2 ) indeed exist. In some examples, we can use existing solutions, but in other cases, we also construct entirely new solutions, thereby identifying several new solvable two-queue models. We observe that, in most cases, the zero-pairs that do contribute terms in u ( m , n ) are mutually connected , in the sense that each of them has its first or second component in common with at least one other pair that contributes, but we also construct a remarkable example where this is not the case.

Abstract The weighted total domination problem (WTDP) belongs to the family of dominating set problems. Given an edge- and vertex- weighted graph, the WTDP consists in selecting a total dominating set D, such that the sum of vertices and edges weights of the subgraph induced by D plus, for each vertex not in D, the minimum weight of its edge to a vertex in D is minimized. A total dominating set D is a subset of the graph’s vertices, such that every vertex, including those in D, is at least adjacent to one vertex in D. This problem arises in many real-life applications closely related to covering and independent set problems; however, it remains computationally challenging due to its $$\mathcal{N}\mathcal{P}$$ N P -hardness. This work presents a variable neighborhood search (VNS) procedure to tackle the WTDP, and investigates the advantages and disadvantages of a multi-start strategy within VNS methodology. In addition, we develop a biased greedy randomized adaptive search procedure (Biased GRASP) that keeps adding elements once a feasible solution is found to produce high-quality initial solutions. We perform extensive numerical analysis to look into the influences of the algorithmic components and to disclose the contribution of the elements and strategies of our method. Finally, the empirical analysis shows that our proposal outperforms the state-of-art results, and the statistical analysis confirms the superiority of our proposal to find the best total dominating sets.

The design of new strategies that exploit methods from machine learning to facilitate the resolution of challenging and large-scale mathematical optimization problems has recently become an avenue of prolific and promising research. In this paper, we propose a novel learning procedure to assist in the solution of a well-known computationally difficult optimization problem in power systems: The Direct Current Optimal Transmission Switching (DC-OTS) problem. The DC-OTS problem consists in finding the configuration of the power network that results in the cheapest dispatch of the power generating units. With the increasing variability in the operating conditions of power grids, the DC-OTS problem has lately sparked renewed interest, because operational strategies that include topological network changes have proved to be effective and efficient in helping maintain the balance between generation and demand. The DC-OTS problem includes a set of binaries that determine the on/off status of the switchable transmission lines. Therefore, it takes the form of a mixed-integer program, which is NP-hard in general. In this paper, we propose an approach to tackle the DC-OTS problem that leverages known solutions to past instances of the problem to speed up the mixed-integer optimization of a new unseen model. Although our approach does not offer optimality guarantees, a series of numerical experiments run on a real-life power system dataset show that it features a very high success rate in identifying the optimal grid topology (especially when compared to alternative competing heuristics), while rendering remarkable speed-up factors.

Predicting the demographics of Twitter users has become a problem with a large interest in computational social sciences. However, the limited amount of public datasets with ground truth labels and the tremendous costs of hand-labeling make this task particularly challenging. Recently, programmatic weak supervision has emerged as a new framework to train classifiers on noisy data with minimal human labeling effort. In this paper, demographic prediction is framed for the first time as a programmatic weak supervision problem. A new three-step methodology for gender, age category, and location prediction is provided, which outperforms traditional programmatic weak supervision and is competitive with the state-of-the-art deep learning model. The study is performed in Flanders, a small Dutch-speaking European region, characterized by a limited number of user profiles and tweets. An evaluation conducted on an independent hand-labeled test set shows that the proposed methodology can be generalized to unseen users within the geographic area of interest.