The problem of identifying a specific design or architecture that allows to satisfy all the system requirements becomes more difficult when uncertainties are taken into account. When a requirement is subject to uncertainty there are a number approaches available to the system engineer, each one with its own benefits and disadvantages. Classical robust optimization is … Read more
We describe pyomo.dae, an open source Python-based modeling framework that enables high-level abstract specification of optimization problems with differential and algebraic equations. The pyomo.dae framework is integrated with the Pyomo open source algebraic modeling language, and is available at http: //www.pyomo.org. One key feature of pyomo.dae is that it does not restrict users to standard, … Read more
In Riemannian optimization problems, commonly encountered manifolds are $d$-dimensional matrix manifolds whose tangent spaces can be represented by $d$-dimensional linear subspaces of a $w$-dimensional Euclidean space, where $w > d$. Therefore, representing tangent vectors by $w$-dimensional vectors has been commonly used in practice. However, using $w$-dimensional vectors may be the most natural but may not … Read more
This work is inspired by very challenging issues arising in space logistics. The problem of scheduling a number of activities, in a given time elapse, optimizing the resource exploitation is discussed. The available resources are not constant, as well as the request, relative to each job. The mathematical aspects are illustrated, providing a time-indexed MILP … Read more
This chapter examines the problem of packing tetris-like items, orthogonally, with the possibility of rotations, into a convex domain, in the presence of additional conditions. An MILP (Mixed Integer Linear Programming) and an MINLP (Mixed Integer Nonlinear Programming) models, previously studied by the author, are surveyed. An efficient formulation of the objective function, aimed at … Read more
The International Space Station poses very challenging issues from the logistic point of view. Its on-orbit stay is to be significantly extended in the near future and ever increasing experimental activity in microgravity is expected, giving rise to a renewed interest in the related optimization aspects. A permanent logistic support is necessary to guarantee its … Read more
Assume that a linear random-effects model (LRM) $\by = \bX \bbe + \bve = \bX\bbe+ \bve$ with $\bbe = \bA \bal + \bga$ is transformed as $\bT\by = \bT\bX\bbe + \bT\bve = \bT\bX\bA \bal + \bT\bX\bga + \bT\bve$ by pre-multiplying a given matrix $\bT$. Estimations/predictions of the unknown parameters under the two models are not … Read more
We address a bilevel location problem where a leader first decides which facilities to open and their access prices; then, customers make individual decisions minimizing individual costs. In this note we prove that, when access costs do not fulfill metric properties, the problem is NP-hard even if facilities can be opened at no fixed cost. … Read more
This work discusses the following general packing problem-class: given a finite collection of d-dimensional spheres with arbitrarily chosen radii, find the smallest sphere in R^d that contains the entire collection of these spheres in a non-overlapping arrangement. Generally speaking, analytical solution approaches cannot be expected to apply to this general problem-type, except for very small … Read more
This article presents a new investigation to the linear mixed model $\by = \bX \bbe + \bZ\bga + \bve$ with fixed effect $\bX\bbe$ and random effect $\bZ\bga$ under a general assumption via some novel algebraic tools in matrix theory, and reveals a variety of deep and profound properties hidden behind the linear mixed model. We … Read more