@misc{D'AndreagiovanniMettPulaj, author = {D'Andreagiovanni, Fabio and Mett, Fabian and Pulaj, Jonad}, title = {An (MI)LP-based Primal Heuristic for 3-Architecture Connected Facility Location in Urban Access Network Design}, issn = {1438-0064}, doi = {10.1007/978-3-319-31204-0_19}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-57139}, abstract = {We investigate the 3-architecture Connected Facility Location Problem arising in the design of urban telecommunication access networks integrating wired and wireless technologies. We propose an original optimization model for the problem that includes additional variables and constraints to take into account wireless signal coverage represented through signal-to-interference ratios. Since the problem can prove very challenging even for modern state-of-the art optimization solvers, we propose to solve it by an original primal heuristic that combines a probabilistic fixing procedure, guided by peculiar Linear Programming relaxations, with an exact MIP heuristic, based on a very large neighborhood search. Computational experiments on a set of realistic instances show that our heuristic can find solutions associated with much lower optimality gaps than a state-of-the-art solver.}, language = {en} } @misc{PulajRaymondTheis, author = {Pulaj, Jonad and Raymond, Annie and Theis, Dirk}, title = {New Conjectures For Union-Closed Families}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-56804}, abstract = {The Frankl conjecture, also known as the union-closed sets conjecture, states that there exists an element in at least half of the sets of any (non-empty) union-closed family. From an optimization point of view, one could instead prove that 2a is an upper bound to the number of sets in a union-closed family with n elements where each element is in at most a sets, where a and n are non-negative integers. Formulating these problems as integer programs we observe that computed optimal values do not vary with n. We formalize these observations as conjectures, and show that they are not equivalent to the Frankl conjecture while still having wide-reaching implications if proven true. Finally, we partially prove the new conjectures and discuss possible approaches to solve them completely.}, language = {en} }