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Keywords
- online optimization (2)
- Gemischt-ganzzahlige Optimierung (1)
- Laserschweißen (1)
- Markov decision problem (1)
- Scheduling (1)
- column generation (1)
- destination call system (1)
- elevator control (1)
- elevator group control (1)
- linear programming (1)
- real time optimation (1)
- vehicle dispatching (1)
Today's telecommunication networks are configured statically. Whenever a connection
is established, the customer has permanent access to it. However, it is
observed that usually the connection is not used continuously. At this point, dynamic
provisioning could increase the utilization of network resources. WDM
based Optical Transport Networks (OTNs) will shortly allow for fast dynamic
network reconfiguration. This enables optical broadband leased line services on
demand. Since service requests competing for network resources may lead to service
blocking, it is vital to use appropriate strategies for routing and wavelength
assignment in transparent optical networks. We simulate the service blocking
probabilities of various dynamic algorithms for this problem using a well-founded
traffic model for two realistic networks. One of the algorithms using shortest path
routings performs best on all instances. Surprisingly, the tie-breaking rule between
equally short paths in different wavelengths decides between success or
failure.
Many online problems encountered in real-life involve a two-stage decision process: upon arrival of a new request, an irrevocable
first-stage decision (the assignment of a specific resource to the request) must be made immediately, while in a second stage process, certain ``subinstances'' (that is, the instances of all requests assigned to a particular resource) can be solved to optimality (offline) later.
We introduce the novel concept of an Online Target Date Assignment Problem (OnlineTDAP) as a general framework for online problems with this nature. Requests for the OnlineTDAP become known at certain dates. An online algorithm has to assign a target date to each request, specifying on which date the request should be processed (e.g., an appointment with a customer for a
washing machine repair). The cost at a target date is given by the downstream cost, the optimal cost of processing all requests
at that date w.r.t. some fixed downstream offline optimization problem (e.g., the cost of an optimal dispatch for service
technicians). We provide general competitive algorithms for the OnlineTDAP independently of the particular downstream problem,
when the overall objective is to minimize either the sum or the maximum of all downstream costs. As the first basic examples, we analyze the competitive ratios of our algorithms for the particular academic downstream problems of bin-packing, nonpreemptive scheduling on identical parallel machines, and routing a traveling salesman.
The standard computational methods for computing the optimal value functions of Markov Decision Problems (MDP) require the exploration of the entire state space. This is practically infeasible for applications with huge numbers of states as they arise, e.g., from modeling the decisions in online optimization problems by MDPs. Exploiting column generation techniques, we propose and apply an LP-based method to determine an epsilon-approximation of the optimal value function at a given state by inspecting only states in a small neighborhood. In the context of online optimization problems, we use these methods in order to evaluate the quality of concrete policies with respect to given initial states. Moreover, the tools can also be used to obtain evidence of the impact of single decisions. This way, they can be utilized in the design of policies.
Ein gemischt-ganzzahliges lineares Optimierungsmodell für ein Laserschweißproblem im Karosseriebau
(2006)
Wir betrachten das Problem der Betriebsplanung von Laserschweißrobotern im Karosseriebau. Gegeben ist eine Menge von Schweißnähten, die innerhalb einer Fertigungszelle an einem Karosserieteil gefertigt werden müssen. Die Schweißnähte werden durch mehrere parallel betriebene Roboter bearbeitet. Die Aufgabe besteht darin, für jeden Roboter eine Reihenfolge und eine zeitliche Koordinierung seiner Bewegungen zu finden, so dass alle Schweißnähte innerhalb der Taktzeit der Fertigungszelle bearbeitet werden und so wenig Laserquellen wie möglich eingesetzt werden. Dabei müssen einige Nebenbedingungen berücksichtigt werden. Für dieses spezielle Schweißproblem haben wir eine Formulierung als gemischt-ganzzahliges lineares Programm entwickelt, welches sich für die untersuchten praktischen Fälle sehr schnell lösen lässt.
We introduce new elevator group control algorithms that can be implemented to be real-time compliant on embedded microcontrollers. The algorithms operate a group of elevators in a destination call system, i.e. passengers specify the destination floor instead of the travel direction only. The aim is to achieve small waiting and travel times for the passengers. We provide evidence, using simulation, that the algorithms offer good performance. One of our algorithms has been implemented by our industry partner and is used in real-world systems.
In "classical optimization" it is assumed that full information about the problem to be solved is given. This, in particular, includes that all data are at hand. The real world may not be so "nice" to optimizers. Some problem constraints may not be known, the data may be corrupted, or some data may not be available at the moments when decisions have to be made. The last issue is the subject of "online optimization" which will be addressed here. We explain some theory that has been developed to cope with such situations and provide examples from practice where unavailable information is not
the result of bad data handling but an inevitable phenomenon.