Mixed-integer programming (MIP) problem is arguably among the hardest classes of optimization problems. This paper describes how we solved 21 previously unsolved MIP instances from the MIPLIB benchmark sets. To achieve these results we used an enhanced version of ParaSCIP, setting a new record for the largest scale MIP computation: up to 80,000 cores in … Read more
Bayesian Networks (BNs) represent conditional probability relations among a set of random variables (nodes) in the form of a directed acyclic graph (DAG), and have found diverse applications in knowledge discovery. We study the problem of learning the sparse DAG structure of a BN from continuous observational data. The central problem can be modeled as … Read more
Sparse Principal Component Analysis (SPCA) is designed to enhance the interpretability of traditional Principal Component Analysis (PCA) by optimally selecting a subset of features that comprise the first principal component. Given the NP-hard nature of SPCA, most current approaches resort to approximate solutions, typically achieved through tractable semidefinite programs (SDPs) or heuristic methods. To solve SPCA to … Read more
k-means clustering is a classic method of unsupervised learning with the aim of partitioning a given number of measurements into k clusters. In many modern applications, however, this approach suffers from unstructured measurement errors because the k-means clustering result then represents a clustering of the erroneous measurements instead of retrieving the true underlying clustering structure. … Read more
We develop and test linearization and parallelization schemes for convex mixed-integer nonlinear programming. Several linearization approaches are proposed for LP/NLP based branch-and-bound. Some of these approaches strengthen the linear approximation to nonlinear constraints at the root node and some at the other branch-and-bound nodes. Two of the techniques are specifically applicable to commonly found univariate … Read more
This paper addresses a real-life personnel scheduling problem in the context of Covid-19 pandemic, arising in a large Italian pharmaceutical distribution warehouse. In this case study, the challenge is to determine a schedule that attempts to meet the contractual working time of the employees, considering the fact that they must be divided into mutually exclusive … Read more
Multiple interconnected energy production systems are a common solution to satisfy the energy demand of industrial processes. Such energy demand is usually the combination of various energy types such as heat and electricity. This implies the installation of different technologies able to produce one or multiple energy types, to satisfy all energy needs. However, multiple … Read more
Sparse principal component analysis (PCA) is a popular dimensionality reduction technique for obtaining principal components which are linear combinations of a small subset of the original features. Existing approaches cannot supply certifiably optimal principal components with more than $p=100s$ of variables. By reformulating sparse PCA as a convex mixed-integer semidefinite optimization problem, we design a … Read more
In this paper, we study the decision process of assigning elective surgery patients to available surgical blocks in multiple operating rooms (OR) under random surgery durations, random postoperative length-of-stay in the intensive care unit (ICU), and limited capacity of ICU. The probability distributions of random parameters are assumed to be ambiguous, and only the mean … Read more
In this paper, we consider binary quadratically constrained quadratic problems and propose a new approach to generate stronger bounds than the ones obtained using the Semidefinite Programming relaxation. The new relaxation is based on the Boolean Quadric Polytope and is solved via a Dantzig-Wolfe Reformulation in matrix space. For block-decomposable problems, we extend the relaxation … Read more