Frauke Liers

Followers

Following

Co-author

Public Views

Interests

Uploads

Papers by Frauke Liers

Robust Approximation of Chance Constrained DC Optimal Power Flow under Decision-Dependent Uncertainty

European Journal of Operational Research

Radius of Robust Feasibility for Mixed-Integer Problems

INFORMS Journal on Computing

For a mixed-integer linear problem (MIP) with uncertain constraints, the radius of robust feasibi... 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. The approaches for the RRF in the literature are restricted to continuous optimization problems. We first analyze relations between the RRF of a MIP and its continuous linear (LP) relaxation. In particular, we derive conditions under which a MIP and its LP relaxation have the same RRF. Afterward, we extend the notion of the RRF such that it can be applied to a large variety of optimization problems and uncertainty sets. In contrast to the setting commonly used in the literature, we consider for every constraint a potentially different uncertainty set that is not necessarily full-dimensional. Thus, we generalize the RRF to MIPs and to include safe variables and constraints; that is, where uncertainties do not affect certain variables or constraints. In the e...

Solving mixed-integer nonlinear optimization problems using simultaneous convexification: a case study for gas networks

Journal of Global Optimization

Solving mixed-integer nonlinear optimization problems (MINLPs) to global optimality is extremely ... 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 constraint function is considered separately. Instead, a considerably tighter relaxation can be found via so-called simultaneous convexification, where convex underestimators are derived for more than one constraint function at a time. In this work, we present a global solution approach for solving mixed-integer nonlinear problems that uses simultaneous convexification. We introduce a separation method that relies on determining the convex envelope of linear combinations of the constraint functions and on solving a nonsmooth convex problem. In particular, we apply the metho...

Download

Joint Model of Probabilistic-Robust (Probust) Constraints Applied to Gas Network Optimization

Vietnam Journal of Mathematics

Optimization problems under uncertain conditions abound in many real-life applications. While sol... more Optimization problems under uncertain conditions abound in many real-life applications. While solution approaches for probabilistic constraints are often developed in case the uncertainties can be assumed to follow a certain probability distribution, robust approaches are usually applied in case solutions are sought that are feasible for all realizations of uncertainties within some predefined uncertainty set. As many applications contain different types of uncertainties that require robust as well as probabilistic treatments, we deal with a class of joint probabilistic/robust constraints. Focusing on complex uncertain gas network optimization problems, we show the relevance of this class of problems for the task of maximizing free booked capacities in an algebraic model for a stationary gas network. We furthermore present approaches for finding their solution. Finally, we study the problem of controlling a transient system that is governed by the wave equation. The task consists in...

Download

Global optimization of batch and steady-state recycling chromatography based on the equilibrium model

Computers & Chemical Engineering

A decomposition approach for optimal gas network extension with a finite set of demand scenarios

Optimization and Engineering

Decomposable robust two-stage optimization: An application to gas network operations under uncertainty

Networks

Deciding Robust Feasibility and Infeasibility Using a Set Containment Approach: An Application to Stationary Passive Gas Network Operations

SIAM Journal on Optimization

Endogenous Price Zones and Investment Incentives in Electricity Markets: An Application of Multilevel Optimization With Graph Partitioning

SSRN Electronic Journal

Optimal price zones of electricity markets: a mixed-integer multilevel model and global solution approaches

Optimization Methods and Software

Structural Investigation of Piecewise Linearized Network Flow Problems

SIAM Journal on Optimization

In this work we study polyhedra in the context of network flow problems, in which the flow value ... more In this work we study polyhedra in the context of network flow problems, in which the flow value on each arc lies in one of several predefined intervals. This is motivated by nonlinear problems on transportation networks, where nonlinearities are handled by piecewise linear approximation or relaxation-a common and established approach in many applications. Several methods for modeling piecewise linear functions which provide a complete description for a single network arc are known. However, in general this property is lost when considering multiple arcs. We show how to strengthen the formulation for specific substructures consisting of multiple arcs by linear inequalities. For the case of paths of degree-two-nodes we give a complete description of the polyhedron projected to the integer variables. Our model is based on-but not limited to-the connection between binary variables and flow variables that is used in the multiple choice method or the convex combination method; we also show how to transfer our results to a formulation based on the incremental method. Computational results show that a state-of-the-art MIP-solver greatly benefits from using our cutting planes for random and realistic network topologies.

Download

Binary Steiner trees: Structural results and an exact solution approach

Discrete Optimization, 2016

Pre-tactical optimization of runway utilization under uncertainty

Journal of Air Transport Management, 2016

Single-commodity robust network design with finite and Hose demand sets

Mathematical Programming, 2016

This preprint also appeared as technical report OR-14-11 at the University of Bologna. We study a... more This preprint also appeared as technical report OR-14-11 at the University of Bologna. 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 scenarios or as a polytope. We propose a branch-andcut algorithm to derive optimal solutions to sRND, built on a capacity-based integer linear programming formulation. It is strenghtened with valid inequalities derived as {0, 1 2 }-Chvátal-Gomory cuts. Since the formulation contains exponentially many constraints, we provide practical separation algorithms. Extensive computational experiments show that our approach is effective, in comparison to existing approaches from the literature as well as to solving a flow based formulation by a general purpose solver.

Download

Robust runway scheduling under uncertain conditions

Journal of Air Transport Management, 2016

LETTER: A non-disordered glassy model with a tunable interaction range

J Stat Mech Theory Exp, 2010

We study a model of opinion formation where the opinions in conflict are not equivalent. This is ... more We study a model of opinion formation where the opinions in conflict are not equivalent. This is the case when the subject of the decision is to respect a norm or a law. In such scenarios, one of the possible behaviors is to abide by the norm and the other to ignore it. The evolution of the dynamics is implemented through an imitation mechanism, in which agents can change their opinions based on the opinions of a set of partners and their own state. We determine, for different social situations, the minimum percentage of supporters of the law necessary to arrive to a state of consensus of law-abiders.

Download

Contributions to Determining Exact Ground-States of Ising Spin-Glasses and to their Physics

2 Computing Exact Ground Statesof Hard Ising Spin Glass Problemsby Branch-and-Cut

Solving network design problems via iterative aggregation

Mathematical Programming Computation, 2015

ABSTRACT

Computing Exact Ground States of Hard Ising Spin Glass Problems by Branch-and-Cut

HARTMANN:NEW OPT.ALG.PHY. O-BK, 2004

Page 1. 4 Computing Exact Ground States of Hard Ising Spin Glass Problems by Branch-and-cut Frauk... more

Frauke Liers

Uploads

Papers by Frauke Liers

Log In