Sven Oliver Krumke

Online Optimization of Large Scale Systems

I Optimal Control for Ordinary Differential Equations.- Sensitivity Analysis and Real-Time Optimization of Parametric Nonlinear Programming Problems.- Sensitivity Analysis and Real-Time Control of Parametric Optimal Control Problems Using Boundary Value Methods.- Sensitivity Analysis and Real-Time Control of Parametric Optimal Control Problems Using Nonlinear Programming Methods.- Sensitivity Analysis and Real-Time Control of a Container Crane under State Constraints.- Real-Time Control of an Industrial Robot under Control and State Constraints.- Real-Time Optimal Control of Shape Memory Alloy Actuators in Smart Structures.- Real-Time Solutions for Perturbed Optimal Control Problems by a Mixed Open- and Closed-Loop Strategy.- Real-Time Optimization of DAE Systems.- Real-Time Solutions of Bang-Bang and Singular Optimal Control Problems.- Conflict Avoidance During Landing Approach Using Parallel Feedback Control.- II Optimal Control for Partial Differential Equations.- Optimal Control Problems with a First Order PDE System - Necessary and Sufficient Optimality Conditions.- Optimal Control Problems for the Nonlinear Heat Equation.- Fast Optimization Methods in the Selective Cooling of Steel.- Real-Time Optimization and Stabilization of Distributed Parameter Systems with Piezoelectric Elements.- Instantaneous Control of Vibrating String Networks.- Modelling, Stabilization, and Control of Flow in Networks of Open Channels.- Optimal Control of Distributed Systems with Break Points.- to Model Based Optimization of Chemical Processes on Moving Horizons.- Multiscale Concepts for Moving Horizon Optimization.- Real-Time Optimization for Large Scale Processes: Nonlinear Model Predictive Control of a High Purity Distillation Column.- Towards Nonlinear Model-Based Predictive Optimal Control of Large-Scale Process Models with Application to Air Separation Plants.- IV Delay Differential Equations in Medical Decision Support Systems.- Differential Equations with State-Dependent Delays.- Biomathematical Models with State-Dependent Delays for Granulocytopoiesis.- Stochastic Optimization for Operating Chemical Processes under Uncertainty.- A Multistage Stochastic Programming Approach in Real-Time Process Control.- Optimal Control of a Continuous Distillation Process under Probabilistic Constraints.- Adaptive Optimal Stochastic Trajectory Planning.- Stochastic Optimization Methods in Robust Adaptive Control of Robots.- Multistage Stochastic Integer Programs: An Introduction.- Decomposition Methods for Two-Stage Stochastic Integer Programs.- Modeling of Uncertainty for the Real-Time Management of Power Systems.- Online Scheduling of Multiproduct Batch Plants under Uncertainty.- VIII Combinatorial Online Planning in Transportation.- Combinatorial Online Optimization in Real Time.- Online Optimization of Complex Transportation Systems.- Stowage and Transport Optimization in Ship Planning.- IX Real-Time Annealing in Image Segmentation.- Basic Principles of Annealing for Large Scale Non-Linear Optimization.- Multiscale Annealing and Robustness: Fast Heuristics for Large Scale Non-linear Optimization.- Author Index.

Models and approximation algorithms for channel assignment in radio networks

We consider the frequency assignment (broadcast scheduling) problem for packet radio networks. Such networks are naturally modeled by graphs with a certain geometric structure. The problem of broadcast scheduling can be cast as a variant of the vertex coloring problem (called the distance-2 coloring problem) on the graph that models a given packet radio network. We present efficient approximation algorithms for the distance-2 coloring problem for various geometric graphs including those that naturally model a large class of packet radio networks. The class of graphs considered include (r,s)-civilized graphs, planar graphs, graphs with bounded genus, etc.

Online Dial-a-Ride Problems: Minimizing the Completion Time

We consider the following online dial-a-ride problem (OLDARP): Objects are to be transported between points in a metric space. Transportation requests arrive online, specifying the objects to be transported and the corresponding source and destination. These requests are to be handled by a server which starts its work at a designated origin and which picks up and drops objects at their sources and destinations. The server can move at constant unit speed. After the end of its service the server returns to its start in the origin. The goal of OLDARP is to come up with a transportation schedule for the server which finishes as early as possible, i.e., which minimizes the makespan. We analyze several competitive algorithms for OLDARP and establish tight competitiveness results. The first two algorithms, REPLAN and IGNORE are very simple and natural: REPLAN completely discards its (preliminary) schedule and recomputes a new one when a new request arrives. IGNORE always runs a (locally optimal) schedule for a set of known requests and ignores all new requests until this schedule is completed. We show that both strategies, REPLAN and IGNORE, are 5/2-competitive. We then present a somewhat less natural strategy SMARTSTART, which in contrast to the other two strategies may leave the server idle from time to time although unserved requests are known. The SMARTSTART-algorithm has an improved competitive ratio of 2, which matches our lower bound.

On the minimum label spanning tree problem

We study the Minimum Label Spanning Tree Problem. In this problem, we are given an undirected graph whose edges are labeled with colors. The goal is to find a spanning tree which uses as little different colors as possible. We present an approximation algorithm with logarithmic performance guarantee. On the other hand, our hardness results show that the problem cannot be approximated within a constant factor.

The Online Dial-a-Ride Problem under Reasonable Load

In this paper, we analyze algorithms for the online dial-aride problem with request sets that fulfill a certain worst-case restriction: roughly speaking, a set of requests for the online dial-a-ride problem is reasonable if the requests that come up in a sufficiently large time period can be served in a time period of at most the same length. This new notion is a stability criterion implying that the system is not overloaded. The new concept is used to analyze the online dial-a-ride problem for the minimization of the maximal resp. average flow time. Under reasonable load it is possible to distinguish the performance of two particular algorithms for this problem, which seems to be impossible by means of classical competitive analysis.

News from the Online Traveling Repairman

In the traveling repairman problem (TRP), a tour must be found through every one of a set of points (cities) in some metric space such that the weighted sum of completion times of the cities is minimized. Given a tour, the completion time of a city is the time traveled on the tour before the city is reached. In the online traveling repairman problem OLTRP requests for visits to cities arrive online while the repairman is traveling. We analyze the performance of algorithms for the online problem using competitive analysis, where the cost of an online algorithm is compared to that of an optimal offline algorithm. Feuerstein and Stougie [8] present a 9-competitive algorithm for the OlTrp on the real line. In this paper we show how to use techniques from online-scheduling to obtain a 6-competitive deterministic algorithm for the OlTrp on any metric space. We also present a randomized algorithm with competitive ratio of 3/ln 2 2.1282 for the L-OLDARP on the line, 4e-5/2e-3 > 2.41041 for the L-OLDARP on general metric spaces, 2 for the OLTRP on the line, and 7/3 for the OLTRP on general metric spaces.

Topology Control Problems under Symmetric and Asymmetric Power Thresholds

We consider topology control problems where the goal is to assign transmission powers to the nodes of an ad hoc network so as to induce graphs satisfying specific properties. The properties considered are connectivity, bounded diameter and minimum node degree. The optimization objective is to minimize the total power assigned to nodes. As these problems are NP-hard in general, our focus is on developing approximation algorithms with provable performance guarantees. We present results under both symmetric and asymmetric power threshold models.

Approximation Algorithms for Certain Network Improvement Problems

We study budget constrained network upgrading problems. Such problems aim at finding optimal strategies for improving a network under some cost measure subject to certain budget constraints. Given an edge weighted graph G = (V, E), in the edge based upgrading model, it is assumed that each edge e of the given network also has an associated function ce (t) that specifies the cost of upgrading the edge by an amount t. A reduction strategy specifies for each edge e the amount by which the length ℓ(e) is to be reduced. In the node based upgrading model, a node v can be upgraded at an expense of c(v). Such an upgrade reduces the delay of each edge incident on v. For a given budget B, the goal is to find an improvement strategy such that the total cost of reduction is at most the given budget B and the cost of a subgraph (e.g. minimum spanning tree) under the modified edge lengths is the best over all possible strategies which obey the budget constraint.After providing a brief overview of the models and definitions of the various problems considered, we present several new results on the complexity and approximability of network improvement problems.

A Decomposition-Based Pseudoapproximation Algorithm for Network Flow Inhibition

In the network inhibition problem, we wish to expend a limited budget attacking a given edge-capacitated graph by “paying” to remove edge capacity from some subset of the edges. We wish to minimize the resulting maximum flow between two designated vertices s and t. The problem is strongly NP-hard. Previous approximation algorithms applied only to planar graphs. In this chapter, we give a polynomial-time algorithm, based on a linear-programming relaxation of an integer program, that finds an attack with cost B a and residual network capacity (max flow) C a such that