In this paper, we consider a recently introduced packing problem in which a given set of weighted items with colors has to be packed into a set of identical bins, while respecting capacity constraints and minimizing the total number of times that colors appear in the bins. We review exact methods from the literature and … Read more
Besides training, mathematical optimization is also used in deep learning to model and solve formulations over trained neural networks for purposes such as verification, compression, and optimization with learned constraints. However, solving these formulations soon becomes difficult as the network size grows due to the weak linear relaxation and dense constraint matrix. We have seen … Read more
A physical limitation in quantum circuit design is the fact that gates in a quantum system can only act on qubits that are physically adjacent in the architecture. To overcome this problem, SWAP gates need to be inserted to make the circuit physically realizable. The nearest neighbour compliance problem (NNCP) asks for an optimal embedding … Read more
\(\) We derive the error bounds for multilinear terms in $[0,1]^n$ using a proof methodology based on the polyhedral representation of the convex hull. We extend the result for multilinear terms in $[\boldsymbol{L},\boldsymbol{0}] \times [\boldsymbol{0},\boldsymbol{U}]\subset\mathbb{R}^n$. Article Download View A proof for multilinear error bounds
We tackle the problem of coordinating a three-echelon last-mile delivery system. In the first echelon, trucks transport parcels from distribution centres outside the city to public transport stops. In the second echelon, the parcels move on public transport and reach the city centre. In the third echelon, zero-emission vehicles pick up the parcels at public … Read more
We study the lift-and-project rank of the stable set polytopes of graphs with respect to the Lovász-Schrijver SDP operator LS_+, with a particular focus on finding and characterizing the smallest graphs with a given LS_+-rank (the least number of iterations of the LS_+ operator on the fractional stable set polytope to compute the stable set … 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
Patient-to-room assignment (PRA) is a scheduling problem in decision support for large hospitals. This work proposes Integer Programming (IP) formulations for dynamic PRA, where either full, limited or uncertain information on incoming patients is available. The applicability is verified through a computational study. Results indicate that large, real world instances can be solved to a … Read more
Consider the task of dividing a state into k contiguous political districts whose populations must not differ by more than one person, following current practice for congressional districting in the USA. A widely held belief among districting experts is that this task requires at least k-1 county splits. This statement has appeared in expert testimony, … Read more
We present a family of integer programming formulations for the maximum cut problem. These formulations encode the incidence vectors of the cuts of a connected graph by employing a subset of the odd-cycle inequalities that relate to a spanning tree, and they require only the corresponding edge variables to be integral explicitly. They so describe … Read more