This paper addresses combined location/routing problems defined on trees. Several problems are studied, which consider service demand both at the vertices and the edges of the input tree. Greedy type optimal heuristics are presented for the cases when all vertices have to be visited and facilities have no set-up costs. Facilities set-up costs can also … Read more
We consider the problem of minimizing a Lipschitz differentiable function over a class of sparse symmetric sets that has wide applications in engineering and science. For this problem, it is known that any accumulation point of the classical projected gradient (PG) method with a constant stepsize $1/L$ satisfies the $L$-stationarity optimality condition that was introduced … Read more
We present a branch-and-bound framework to solve the following problem: Given a graph G and an integer k, find a subgraph of G formed by removing no more than k edges that contains the most symmetry. We call symmetries on such a subgraph “almost symmetries” of G. We implement our branch-and-bound framework in PEBBL to … Read more
We study the problem of constructing minimum power-$p$ Euclidean $k$-Steiner trees in the plane. The problem is to find a tree of minimum cost spanning a set of given terminals where, as opposed to the minimum spanning tree problem, at most $k$ additional nodes (Steiner points) may be introduced anywhere in the plane. The cost … Read more
In this work we study the sets of two-party correlations generated from a Bell scenario involving two spatially separated systems with respect to various physical models. We show that the sets of classical, quantum, no-signaling and unrestricted correlations can be expressed as projections of affine sections of appropriate convex cones. As a by-product, we identify … Read more
This paper considers a family of cutting planes, recently developed for mixed 0-1 polynomial programs and shows that they define facets for the maximum edge-weighted clique problem. There exists a polynomial time exact separation algorithm for these in- equalities. The result of this paper may contribute to the development of more efficient algorithms for the … Read more
This problem is about to schedule a number of jobs of different lengths on two uniform machines with given speeds $1$ and $s \geq 1$, so that the overall completion time, i.e., the makespan, is earliest possible. We consider a semi-online variant (introduced for equal speeds) by Azar and Regev, where the jobs arrive one … Read more
We consider a semi-online version of the problem of scheduling a sequence of jobs of different lengths on two uniform machines with given speeds $1$ and $s$. Jobs are revealed one by one (the assignment of a job has to be done before the next job is revealed), and the objective is to minimize the … Read more
The Simple Plant Location Problem is a well-known (and NP-hard) combinatorial optimisation problem, with applications in logistics. We present a new family of valid inequalities for the associated family of polyhedra, and show that it contains an exponentially large number of new facet-defining members. We also present a new procedure, called facility augmentation, which enables … Read more
Sequencing activities over time is a fundamental optimization problem. The problem can be modeled using a directed network in which activities are represented by nodes and pairs of activities that can be performed consecutively are represented by arcs. A sequence of activities then corresponds to a path in the directed network, and an optimal sequence … Read more