The industrial treatment of waste paper in order to regain valuable fibers from which recovered paper can be produced, involves several steps of preparation. One important step is the separation of stickies that are normally attached to the paper. If not properly separated, remaining stickies reduce the quality of the recovered paper or even disrupt … Read more
The open-pit mine production scheduling problem has received a great deal of attention in recent years, both in the academic literature, and in the mining industry. Optimization approaches to strategic planning for mine exploitation have become the industry standard. However most of these approaches focus on extraction sequencing, and don’t consider the material flow after … Read more
We examine the problem of placing stationary monitors in a continuous space, with the goal of minimizing an adversary’s maximum probability of traversing an origin-destination route without being detected. The problem arises, for instance, in defending against the transport of illicit material through some area of interest. In particular, we consider the deployment of monitors … Read more
This paper considers a quadratically-constrained cardinality minimization problem with applications to digital filter design, subset selection for linear regression, and portfolio selection. Two relaxations are investigated: the continuous relaxation of a mixed integer formulation, and an optimized diagonal relaxation that exploits a simple special case of the problem. For the continuous relaxation, an absolute upper … Read more
Logical implications appear in a number of important mixed-integer nonlinear optimal control problems (MIOCPs). Mathematical optimization offers a variety of different formulations that are equivalent for boolean variables, but result in different relaxations. In this article we give an overview over a variety of different modeling approaches, including outer versus inner convexification, generalized disjunctive programming, … Read more
We develop a new modeling and exact solution method for stochastic programming problems that include a joint probabilistic constraint in which the multirow random technology matrix is discretely distributed. We binarize the probability distribution of the random variables in such a way that we can extract a threshold partially defined Boolean function (pdBf) representing the … Read more
A common structure in convex mixed-integer nonlinear programs is separable nonlinear functions. In the presence of such structures, we propose three improvements to the outer approximation algorithms. The first improvement is a simple extended formulation, the second is a refined outer approximation, and the third is a heuristic inner approximation of the feasible region. These … Read more
In this paper we study valid inequalities for a fundamental set that involves a continuous vector variable x in [0,1]^n, its associated quadratic form x x’ and its binary indicators. This structure appears when deriving strong relaxations for mixed integer quadratic programs (MIQPs). We treat valid inequalities for this set as lifted from QPB, which … Read more
We consider N-fold 4-block decomposable integer programs, which simultaneously generalize N-fold integer programs and two-stage stochastic integer programs with N scenarios. In previous work [R. Hemmecke, M. Koeppe, R. Weismantel, A polynomial-time algorithm for optimizing over N-fold 4-block decomposable integer programs, Proc. IPCO 2010, Lecture Notes in Computer Science, vol. 6080, Springer, 2010, pp. 219–229], … Read more
Detecting and solving aircraft conflicts, which occur when aircraft sharing the same airspace are too close to each other according to their predicted trajectories, is a crucial problem in Air Traffic Management. We focus on mixed-integer optimization models based on speed regulation. We first solve the problem to global optimality by means of an exact … Read more