In the quadratic minimum spanning tree problem (QMSTP) one wants to find the minimizer of a quadratic function over all possible spanning trees of a graph. We give two formulations of the QMSTP as mixed-integer semidefinite programs exploiting the algebraic connectivity of a graph. Based on these formulations, we derive a doubly nonnegative relaxation for … Read more
University students benefit academically, personally and professionally from an expansion of their in-class social network. To facilitate this, we present a novel and broadly applicable optimization approach that exposes individuals to as many as possible peers that they do not know. This novel class of ‘social seating assignment problems’ is parameterized by the social network, … Read more
The b-matching problem is a well-known generalization of the classical matching problem with various applications in operations research and computer science. Given an undirected graph, each vertex v has a capacity b(v), indicating the maximum number of times it can be matched, while edges can also be used multiple times. The problem is solvable in … Read more
The most successful approaches for the TSP use the integer programming model proposed in 1954 by Dantzig, Fulkerson, and Johnson (DFJ). Although this model has exponentially many subtour elimination constraints (SECs), it has been observed that relatively few of them are needed to prove optimality in practice. This leads us to wonder: What is the … Read more
\(\) Peak cost is a novel objective for flows over time that describes the amount of workforce necessary to run a system. We focus on minimising peak costs in the context of maximum temporally repeated flows and formulate the corresponding MPC-MTRF problem. First, we discuss the limitations that emerge when restricting the solution space to … Read more
\(\) Given a \(\{0,1\}\)-matrix \(M\), the graph realization problem for \(M\) asks if there exists a spanning forest such that the columns of \(M\) are incidence vectors of paths in the forest. The problem is closely related to the recognition of network matrices, which are a large subclass of totally unimodular matrices and have many … Read more
Given a simple graph G = (V, E) with vertex set V and edge set E, the minimum biclique cover problem seeks to cover all edges of the graph with a minimum number of bicliques (i.e., complete bipartite subgraphs). This paper proposes two compact mixed integer programming (MIP) formulations for solving the minimum biclique cover … Read more
We introduce the class of SO-friendly neural networks, which include several models used in practice including networks with 2 layers of hidden weights where the number of inputs islarger than the number of outputs. SO-friendly networks have the property that performing a precise line search to set the step size on each iteration has the … Read more
We study the reliable (uncapacitated) facility location (RFL) problem in a data-driven environment where historical observations of random demands and disruptions are available. Owing to the combinatorial optimization nature of the RFL problem and the mixed-binary randomness of parameters therein, the state-of-the-art RFL models applied to the data-driven setting either suggest overly conservative solutions, or … Read more
Centrality metrics have become a popular concept in network science and optimization. Over the years, centrality has been used to assign importance and identify influential elements in various settings, including transportation, infrastructure, biological, and social networks, among others. That said, most of the literature has focused on nodal versions of centrality. Recently, group counterparts of … Read more