Frauke Liers Mathematical optimization problems including a time dimension abound. For example, logistics, process optimization and production planning tasks must often be optimized for a range of time periods. Usually, these problems incorporating time structure are very large and cannot be solved to global optimality by modern solvers within a reasonable period of time. Therefore, the so-called … Read more
Γ-uncertainties have been introduced for adjusting the degree of conservatism ofrobust counterparts of (discrete) linear optimization problems under interval uncertainty. Thisarticle’s contribution is a generalization of this approach to (mixed-integer) nonlinear optimizationproblems. We focus on the cases in which the uncertainty is linear but also derive formulationsfor the general case. We present cases where the … Read more
Solving mixed-integer nonlinear optimization problems (MINLPs) to global optimality is extremely challenging. An important step for enabling their solution consists in the design of convex relaxations of the feasible set. Known solution approaches based on spatial branch-and-bound become more effective the tighter the used relaxations are. Relaxations are commonly established by convex underestimators, where each … Read more
Globalized robust optimization has been proposed as a generalization of the standard robust optimization framework in order to allow for a controlled decrease in protection depending on the distance of the realized scenario from the predefined uncertainty set. In this work, we specialize the notion of globalized robustness to Gamma-uncertainty in order to extend its … Read more
For a mixed-integer linear problem (MIP) with uncertain constraints, the radius of robust feasibility (RRF) determines a value for the maximal “size” of the uncertainty set such that robust feasibility of the MIP can be guaranteed. To the best of our knowledge, the approaches for the RRF presented in the literature are restricted to continuous … Read more
In the course of the energy transition, load and supply centers are growing apart in electricity markets worldwide, rendering regional price signals even more important to provide adequate locational investment incentives. This paper focuses on electricity markets that operate under a zonal pricing market design. For a fixed number of zones, we endogenously derive the … Read more
Mathematical modeling of market design issues in liberalized electricity markets often leads to mixed-integer nonlinear multilevel optimization problems for which no general-purpose solvers exist and which are intractable in general. In this work, we consider the problem of splitting a market area into a given number of price zones such that the resulting market design … Read more
We study a single-commodity Robust Network Design problem (sRND) defined on an undirected graph. Our goal is to determine minimum cost capacities such that any traffic demand from a given uncertainty set can be satisfied by a feasible single-commodity flow. We consider two ways of representing the uncertainty set, either as a finite list of … Read more
In this paper we study the Steiner tree problem with degree constraints. Motivated by an application in computational biology we first focus on binary Steiner trees in which all node degrees are required to be at most three. We then present results for general degree-constrained Steiner trees. It is shown that finding a binary Steiner … Read more
The minimum k-partition (MkP) problem is the problem of partitioning the set of vertices of a graph into k disjoint subsets so as to minimize the total weight of the edges joining vertices in the same partition. The main contribution of this paper is the design and implementation of a branch-and-cut algorithm based on semidefinite … Read more