Jörg Rambau

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.

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.

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.

TOPCOM: Triangulations of Point Configurations and Oriented Matroids

TOPCOM is a package for computing triangulations of point configurations and oriented matroids. For example, for a point configuration one can compute the chirotope, components of the flip graph of triangulations, enumerate all triangulations. The core algorithms implemented in TOPCOM are described, and implentation issues are discussed.

Triangulations of cyclic polytopes and higher Bruhat orders

Recently Edelman and Reiner suggested two poset structures, ( n , d ) and ( n , d ) on the set of all triangulations of the cyclic d -polytope C ( n , d ) with n vertices. Both posets are generalizations of the well-studied Tamari lattice. While ( n , d ) is bounded by definition, the same is not obvious for ( n , d ). In the paper by Edelman and Reiner the bounds of ( n , d ) were also confirmed for ( n , d ) whenever d ≤5, leaving the general case as a conjecture.

Real-Time Dispatching of Guided and Unguided Automobile Service Units with Soft Time Windows

We investigate a real-world large scale vehicle dispatching problem with strict real-time requirements, posed by our cooperation partner, the German Automobile Association. We present computational experience on real-world data with a dynamic column generation method employing a portfolio of acceleration techniques. Our computer program ZIBDIP yields solutions on heavy-load real-world instances (215 service requests, 95 service units) in less than a minute that are no worse than 1% from optimum on state-of-the-art personal computers.

On the Hegselmann-Krause conjecture in opinion dynamics

We give an elementary proof of a conjecture by Hegselmann and Krause in opinion dynamics, concerning a symmetric bounded confidence interval model: If there is a truth and all individuals take each other seriously by a positive amount bounded away from zero, then all truth seekers will converge to the truth. Here, truth seekers are the individuals who are attracted by the truth by a positive amount. In the absence of truth seekers, it was already shown by Hegselmann and Krause that the opinions of the individuals converge.

Projections of polytopes and the generalized baues conjecture

Associated with every projection π:P→π(P) of a polytopeP is a partially ordered set of all “locally coherent strings”: the families of proper faces ofP that project to valid subdivisions of π(P), partially ordered by the natural inclusion relation. The “Generalized Baues Conjecture” posed by Billeraet al. [4] asked whether this partially ordered set always has the homotopy type of a sphere of dimension dim(P—dim(π(P))−1. We show that this is true in the cases when dim(π(P))=1 (see[4]) and when dim(P)—dim(π(P))≤2, but fails in general. For an explicit counterexample we produce a nondegenerate projection of a five-dimensional, simplicial, 2-neighborly polytopeP with 10 vertices and 42 facets to a hexagon π(P)⊆ℝ2. The construction of the counterexample is motivated by a geometric analysis of the relation between the fibers in an arbitrary projection of polytopes.

Online Bin Coloring

We introduce a new problem that was motivated by a (more complicated) problem arising in a robotized assembly environment. The bin coloring problem is to pack unit size colored items into bins, such that the maximum number of different colors per bin is minimized. Each bin has size B ∈ N. The packing process is subject to the constraint that at any moment in time at most q ∈ N bins are partially filled. Moreover, bins may only be closed if they are filled completely. An online algorithm must pack each item without knowledge of any future items. We investigate the existence of competitive online algorithms for the bin coloring problem. We prove an upper bound of 3q-1 and a lower bound of 2q for the competitive ratio of a natural greedy-type algorithm, and show that surprisingly a trivial algorithm which uses only one open bin has a strictly better competitive ratio of 2q -1. Moreover, we show that any deterministic algorithm has a competitive ratio Ω(q) and that randomization does not improve this lower bound even when the adversary is oblivious.

Combinatorial Online Optimization in Real Time

Optimization is the task of finding a best solution to a given problem. When the decision variables are discrete we speak of a combinatorial optimization problem. Such a problem is online when decisions have to be made before all data of the problem are known. And we speak of a real-time online problem when online decisions have to be computed within very tight time bounds. This paper surveys the art of combinatorial online and realtime optimization, it discusses, in particular, the concepts with which online and real-time algorithms can be analyzed.