Dagstuhl Seminar Proceedings, Volume 5031
Dagstuhl Seminar Proceedings
DagSemProc
https://www.dagstuhl.de/dagpub/1862-4405
https://dblp.org/db/series/dagstuhl
1862-4405
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
5031
2005
https://drops.dagstuhl.de/entities/volume/DagSemProc-volume-5031
05031 Abstracts Collection – Algorithms for Optimization with Incomplete Information
From 16.01.05 to 21.01.05, the Dagstuhl Seminar 05031 ``Algorithms for Optimization with Incomplete Information'' was held
in the International Conference and Research Center (IBFI),
Schloss Dagstuhl.
During the seminar, several participants presented their current
research, and ongoing work and open problems were discussed. Abstracts of
the presentations given during the seminar as well as abstracts of
seminar results and ideas are put together in this paper. The first section
describes the seminar topics and goals in general.
Links to extended abstracts or full papers are provided, if available.
Online optimization
robust optimization
stochastic programming
stochastic scheduling
1-25
Regular Paper
Susanne
Albers
Susanne Albers
Rolf H.
Möhring
Rolf H. Möhring
Georg Ch.
Pflug
Georg Ch. Pflug
Rüdiger
Schultz
Rüdiger Schultz
10.4230/DagSemProc.05031.1
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05031 Summary – Algorithms for Optimization with Incomplete Information
This paper summarizes the objectives and structure of a seminar with the same title, held from January 16th to 21th 2005 at Schloss Dagstuhl, Germany
Online Optimization
Robust Optimization
Stochastic Programming
Stochastic Scheduling
1-2
Regular Paper
Susanne
Albers
Susanne Albers
Rolf H.
Möhring
Rolf H. Möhring
Georg Ch.
Pflug
Georg Ch. Pflug
Rüdiger
Schultz
Rüdiger Schultz
10.4230/DagSemProc.05031.2
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An adaptive trust-region approach for nonlinear stochastic optimisation with an application in discrete choice theory
We consider stochastic nonlinear programs, restricting ourself to differentiable, but possibly non-convex, problems. The non-convexity leads us to consider non-linear approaches, designed to find second-order critical solutions. We focus here on the use of trust-region approaches when solving a sample average approximation, and adapt the technique to only use sub-samples when possible, adjusting the sample size at each iteration. We show that under reasonable assumptions, we solve the original SAA problem. We also consider an extension to the estimation of mixed logit models, that are popular in discrete choice theory when the population heterogeneity is taken into account. We present numerical experimentations underlining the practical interest of the method. We finally examine some avenues and preliminary experimentations for future research.
Nonlinear Stochastic Programming
Monte-Carlo
Mixed Logit
Discrete Choice
Trust-Region
1-4
Regular Paper
Fabian
Bastin
Fabian Bastin
10.4230/DagSemProc.05031.3
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An improved algorithm for CIOQ switches
The problem of maximizing the weighted throughput in various switching settings has been intensively studied recently through competitive analysis. To date, the most general model that has been investigated is the standard CIOQ (Combined Input and Output Queued) switch architecture with internal fabric speedup $S \geq 1$. CIOQ switches, that comprise the backbone of packet routing networks, are $N \times N$ switches controlled by a switching policy that incorporates two components: Admission control and scheduling. An admission control strategy is essential to determine the packets stored in the FIFO queues in input and output ports, while the scheduling policy conducts the transfer of packets through the internal fabric, from input ports to output ports. The online problem of maximizing the total weighted throughput of CIOQ switches was recently investigated by Kesselman and Ros\'{e}n [SPAA03]. They presented two different online algorithms for the general problem that achieve non-constant competitive ratios (linear in either the speedup or the number of distinct values, or logarithmic in the value range). We introduce the first constant-competitive algorithm for the general case of the problem, with arbitrary speedup and packet values. Specifically, our algorithm is $8$-competitive, and is also simple and easy to implement.
On-line algorithms
Competitive ratio
CIOQ Switch
Packet Switching
Buffer Management
Quality of Service.
1-4
Regular Paper
Yossi
Azar
Yossi Azar
Yossi
Richter
Yossi Richter
10.4230/DagSemProc.05031.4
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Approximation Algorithms for 2-stage and Multi-stage Stochastic Optimization
Stochastic optimization problems attempt to model uncertainty in the data by assuming that (part of) the input is specified by a probability distribution. We consider the well-studied paradigm of stochastic recourse models, where the uncertainty evolves through a series of stages and one can take decisions in each stage in response to the new information learned. We obtain the first approximation algorithms for a variety of 2-stage and k-stage stochastic integer optimization problems where the underlying random data is given by a "black box" and no restrictions are placed on the costs of the two stages: one can merely sample data from this distribution, but no direct information about the distributions is given. Our results are based on two principal components. First, we show that for a broad class of 2-stage and k-stage linear programs, where k is not part of the input, given only a "black box" to draw independent samples from the distribution, one can, for any \epsilon>0, compute a solution of cost guaranteed to be within a (1+\epsilon) factor of the optimum, in time polynomial in 1/\epsilon, the size of the input, and a parameter \lambda that is the ratio of the cost of the same action in successive stages which is a lower bound on the sample complexity in the "black-box" model. This is based on reformulating the stochastic linear program, which has both an exponential number of variables and an exponential number of constraints, as a compact convex program, and adapting tools from convex optimization to solve the resulting program to near optimality. In doing so, a significant difficulty that we must overcome is that even evaluating the objective function of this convex program at a given point may be quite difficult and provably hard. To the best of our knowledge, this is the first such result for multi-stage stochastic programs. Second, we give a rounding approach for stochastic integer programs that shows that approximation algorithms for a deterministic analogue yields, with a small constant-factor loss, provably near-optimal solutions for the stochastic generalization. Thus we obtain approximation algorithms for several stochastic problems, including the stochastic versions of the set cover, vertex cover, facility location, multicut (on trees) and multicommodity flow problems.
Algorithms
Approximation Algorithms
Optimization
Convex Optimization
Stochastic Optimization
1-5
Regular Paper
Chaitanya
Swamy
Chaitanya Swamy
David
Shmoys
David Shmoys
10.4230/DagSemProc.05031.5
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Assessing Solution Quality in Stochastic Programs
Assessing whether a solution is of high quality
(optimal or near optimal) is a fundamental
question in optimization. We develop Monte Carlo
sampling-based procedures for assessing solution
quality in stochastic programs. Quality is defined
via the optimality gap and our procedures' output
is a confidence interval on this gap. We review a
multiple-replications procedure and then present a
result that justifies a computationally simplified
single-replication procedure. Even though the
single replication procedure is computationally
significantly less demanding, the resulting
confidence interval may have low coverage for
small sample sizes on some problems. We provide
variants of this procedure and provide preliminary
guidelines for selecting a candidate solution.
Both are designed to improve the basic procedure's
performance.
stochastic programming
Monte Carlo simulation
1-3
Regular Paper
David P.
Morton
David P. Morton
Guzin
Bayraksan
Guzin Bayraksan
10.4230/DagSemProc.05031.6
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Average Case and Smoothed Competitive Analysis of the Multi-Level Feedback Algorithm
In this paper we introduce the notion of smoothed competitive analysis of online algorithms. Smoothed analysis has been proposed by Spielman and Teng to explain the behaviour of algorithms that work well in practice while performing very poorly from a worst case analysis point of view. We apply this notion to analyze the Multi-Level Feedback (MLF) algorithm to minimize the total flow time on a sequence of jobs released over time when the processing time of a job is only known at time of completion. The initial processing times are integers in the range $[1,2^K]$. We use a partial bit randomization model, i.e., the initial processing times are smoothed by changing the $k$ least significant bits under a quite general class of probability distributions. We show that MLF admits a smoothed competitive ratio of $O((2^k/\psigma)^3 + (2^k/\psigma)^2 2^{K-k}})$, where $\sigma$ denotes the standard deviation of the distribution. In particular, we obtain a competitive ratio of $O(2^{K-k})$ if $\sigma = \Theta(2^k)$. We also prove an $\Omega(2^{K-k})$ lower bound for any deterministic algorithm that is run on processing times smoothed according to the partial bit randomization model. For various other smoothing models, including the additive symmetric smoothing one, which is a variant of the model used by Spielman and Teng, we give a higher lower bound of $\Omega(2^K)$. A direct consequence of our result is also the first average case analysis of MLF. We show a constant expected ratio of the total flow time of MLF to the optimum under several distributions including the uniform one.
Competitive analysis
average case analysis
smoothed analysis
scheduling
5-28
Regular Paper
Luca
Becchetti
Luca Becchetti
Stefano
Leonardi
Stefano Leonardi
Alberto
Marchetti-Spaccamela
Alberto Marchetti-Spaccamela
Guidouca
Schaefer
Guidouca Schaefer
Tjark
Vredeveld
Tjark Vredeveld
10.4230/DagSemProc.05031.7
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Average-Case Competitive Analyses for Ski-Rental Problems
Let $s$ be the ratio of the cost for purchasing skis over the cost for renting them. Then the famous result for the ski-rental problem shows that skiers should buy their skis after renting them $(s-1)$ times, which gives us an optimal competitive ratio of $2-\frac{1}{s}$. In practice, however, it appears that many skiers buy their skis before this optimal point of time and also many skiers keep renting them forever. In this paper we show that these behaviors of skiers are quite reasonable by using an {\em average-case competitive ratio}. For an exponential input distribution $f(t) = \lambda e^{-\lambda t}$, optimal strategies are (i) if $\frac{1}{\lambda} \leq s$, then skiers should rent their skis forever and (ii) otherwise should purchase them after renting approximately $s^2\lambda \;\;(
online algorithm
competitive analysis
1-3
Regular Paper
Hiroshi
Fujiwara
Hiroshi Fujiwara
Kazuo
Iwama
Kazuo Iwama
10.4230/DagSemProc.05031.8
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Deferment Control for Reoptimization – How to Find Fair Reoptimized Dispatches
The german automobile association ADAC maintains a fleet of 1700 vehicles and has agreements with around 5000 service contractors. With these ressources, they help people whose cars have broken down on the road. Those people can call an ADAC help center, and within 10 seconds, an assignment of a service ressource to their request is made. At the same time, for all service vehicles, tours through the assigned requests have to be planned so as to minimize a certain (complicated) cost function for this so-called dispatch. No usefule knowledge about future requests is available at the time being. Therefore, the current policy of the automated system, developed in joint work with Sven O. Krumke, is to reoptimize the whole dispatch upon the occurrence of each relevant event, like the arrival of a new request. A similar online-optimization problem appears in the pallet elevator group control in a large distribution center of Herlitz PBS AG in Falkensee near Berlin. The problem with reoptimization policies in general is that, depending on the reoptimization objective, an arbitrarily large deferment of individual requests can be observed. In a way, individual requests are sacrificed in favor of a good performance according to the reoptimization objective. Nevertheless, w.r.t. the reoptimization objective, the reoptimization policies in the long run usually perform much better than the currently known policies that can not cause infinite deferment. Therefore, the goal is to modify reoptimization policies so as to prevent deferment. Sometimes deferment can be almost eliminated by enhancing the reoptimization objective with some terms that penalize waiting, but service in a fixed time can still not be guaranteed, and this kind of objective function engineering is a very time consuming tuning issue, interfering with the orgininal management objective. In this talk, the new policy of flow and makespan constrained reoptimization with reoptimization admission control is introduced. The main result is that, under d-reasonable load, for any reoptimization model, this policy yields a maximal flow time that is bounded by a constant 2d, depending only on the system load parameter d, not on the instance. In simulation experiments for the elevator group control problem we still obtain a very satisfactory average performance w.r.t. the reoptimization objective.
online optimization
dynamic vehicle dispatching
reoptimization
integer linear program
dynamic column generation
infinite deferment ,
1-4
Regular Paper
Jörg
Rambau
Jörg Rambau
10.4230/DagSemProc.05031.9
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Disruption Management and Planning with Uncertainties in Aircraft Planning
An important insufficiency of modern industrial plans still is their lack of robustness. Disruptions prevent companies from operating as planned before and induce high costs for trouble shooting. The main reason for the severe impact of disruptions stems from the fact that planners do traditionally consider deterministic input data to be available at planning time. In practice, there are often only distributions over the possible input data available. The Repair Game is a formalization of a planning task, which brings two branches of computer science --- game tree search and logistic planning optimization with OR tools --- together. Playing it performs disruption management and generates robust plans with the help of game tree search. Our method significantly outperformed the traditional one by means of simulations.
uncertainty
planning
game playing
aviation application
1-5
Regular Paper
Jan
Ehrhoff
Jan Ehrhoff
Sven
Grothklags
Sven Grothklags
Ulf
Lorenz
Ulf Lorenz
10.4230/DagSemProc.05031.10
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Facility location with uncertain demand and economies of scale
This paper adresses facility location under uncertain demand. The problem is to determine the optimal location of facilities and allocation of uncertain customer demand to these facilities. The costs of operating the facilities are subject to economies of scale. The objective is to minimize the total expected costs. These costs can be split into two parts: firstly the costs of investing in a facility as well as maintaining and operating it with strictly diminishing average costs, and secondly linear transportation cost. We formulate the problem as a two-stage stochastic programming model and present a solution method based on Lagrangian Relaxation. We also show some computional results based on data from the Norwegian meat industry regarding the location of slaughterhouses.
facility location
stochastic
economies of scale
1-11
Regular Paper
Peter
Schütz
Peter Schütz
Leen
Stougie
Leen Stougie
Asgeir
Tomasgard
Asgeir Tomasgard
10.4230/DagSemProc.05031.11
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Getting rid of stochasticity: applicable sometimes
We consider the single-machine scheduling problem of minimizing the
number of late jobs. This problem is well-studied and well-understood in case of deterministic processing times. We consider the problem with stochastic processing times, and we show that for a number of probability distributions the problem can be reformulated as a deterministic problem (and solved by the corresponding algorithm) when we use the concept of minimum success probabilities, which is, that we require that the probability that a job complete on time is `big enough'. We further show that we can extend our approach to the case of machines with stochastic output.
Scheduling
sequencing
single machine
number of late jobs
stochastic processing times
minimum success probability
dynamic programming unreliable machines
1-4
Regular Paper
Han
Hoogeveen
Han Hoogeveen
Marjan
Van den Akker
Marjan Van den Akker
10.4230/DagSemProc.05031.12
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Marginal productivity index policies for scheduling restless bandits with switching penalties
We address the problem of designing a tractable, well-grounded policy for the dynamic allocation of effort to a collection of restless bandit projects, i.e. binary-action (active/passive) Markov decision processes, in which sequence-independent switching penalties (costs or delays) are incurred when switching from one project to another. We deploy the framework of partial conservation laws, introduced by NiÃ?Â±o-Mora (2001, 2002), to establish the existence of and calculate a marginal productivity index (MPI), under certain conditions. The MPI, which extends earlier indices proposed by Gittins (1979) and Whittle (1988), yields a corresponding MPI policy, which prescribes to dynamically engage the project with larger index.
stochastic scheduling
restless bandits
index policies
switching penalties
1-6
Regular Paper
José
Niño-Mora
José Niño-Mora
10.4230/DagSemProc.05031.13
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Minorant methods for stochastic global optimization
We develop numerical methods for solution of stochastic global optimization problems: min$[F(x)=Ef(x,Ã‚Â¦ÃƒËœ)| xin X]$ and $min[F(x)=P{f(x, Ã‚Â¦ÃƒËœ) Ã‚Â¡ÃƒÅ“0} | xin X]$, where x is a finite dimensional decision vector with possible values in the set X, Ã‚Â¦ÃƒËœ is a random variable, $f(x,Ã‚Â¦ÃƒËœ)$ is a nonlinear function of variable x, E and P denote mathematical expectation and probability signs respectively.
These methods are based on the concept of stochastic tangent minorant, which is a random function $Ã‚Â¦Ãƒâ€¢(x,y, Ã‚Â¦ÃƒËœ)$ of two variables x and y with expected value $Ã‚Â¦Ã‚Âµ(x,y)=E Ã‚Â¦Ãƒâ€¢(x,y, Ã‚Â¦ÃƒËœ)$ satisfying conditions: (i) $Ã‚Â¦Ã‚Âµ(x,x)=F(x)$, (ii) $Ã‚Â¦Ã‚Âµ(x,y) Ã‚Â¡ÃƒÅ“F(x)$ for all x,y. Tangent minorant is a source of information on a function global behavior. We develop a calculus of (stochastic) tangent minorants.
We develop a stochastic analogue of PijavskiÃ‚Â¡Ã‚Â¯s global optimization method and a branch and bound method with stochastic minorant bounds.
Applications to optimal facility location and network reliability optimization are discussed.
Stochastic global optimization
stochastic tangent minorant
branch and bound method
1-9
Regular Paper
Vladimir
Norkin
Vladimir Norkin
Boris.
Onischenko
Boris. Onischenko
10.4230/DagSemProc.05031.14
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Models and Algorithms for Stochastic Online Scheduling
We introduce a model for non-preemptive scheduling under uncertainty. In this model, we combine the main characteristics of online and stochastic scheduling in a simple and natural way. Job processing times are assumed to be stochastic, but in contrast to the classical stochastic scheduling models, we assume that jobs arrive online over time, and there is no knowledge about the jobs that will arrive in the future. The model incorporates both, stochastic scheduling and online scheduling as a special case. The particular setting we analyze is parallel machine scheduling, with the objective to minimize the total weighted completion times of jobs. We propose simple, combinatorial online scheduling policies for that model, and derive performance guarantees that match the currently best known performance guarantees for stochastic parallel machine scheduling. For processing times that follow NBUE distributions, we improve upon previously best known performance bounds, even though we consider a more general setting.
stochastic scheduling
online optimization
weighted completion time
1-4
Regular Paper
Nicole
Megow
Nicole Megow
Marc
Uetz
Marc Uetz
Tjark
Vredeveld
Tjark Vredeveld
10.4230/DagSemProc.05031.15
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Modification of Recourse Data for Mixed-Integer Recourse Models
We consider modification of the recourse data, consisting of the second-stage parameters and the underlying distribution, as an approximation technique for solving two-stage recourse problems. This approach is applied to several specific classes of mixed-integer recourse problems; in each case, the resulting recourse problem is much easier to solve.
stochastic programming
integer programming
approximation
1-3
Regular Paper
Maarten H. van der
Vlerk
Maarten H. van der Vlerk
10.4230/DagSemProc.05031.16
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Network Discovery and Verification
Consider the problem of discovering (or verifying) the edges and non-edges of a network, modelled as a connected undirected graph, using a minimum number of queries. A query at a vertex v discovers (or verifies) all edges and non-edges whose endpoints have different distance from v. In the network discovery problem, the edges and non-edges are initially unknown, and the algorithm must select the next query based only on the results of previous queries. We study the problem using competitive analysis and give a randomized on-line algorithm with competitive ratio O(sqrt(n*log n)) for graphs with n vertices. We also show that no deterministic algorithm can have competitive ratio better than 3. In the network verification problem, the graph is known in advance and the goal is to compute a minimum number of queries that verify all edges and non-edges. This problem has previously been studied as the problem of placing landmarks in graphs or determining the metric dimension of a graph. We show that there is no approximation algorithm for this problem with ratio o(log n) unless P=NP. Furthermore, we prove that the optimal number of queries for d-dimensional hypercubes is Theta(d/log d).
on-line algorithms
set cover
landmarks
metric dimension
1-4
Regular Paper
Zuzana
Beerliova
Zuzana Beerliova
Felix
Eberhard
Felix Eberhard
Thomas
Erlebach
Thomas Erlebach
Alexander
Hall
Alexander Hall
Michael
Hoffmann
Michael Hoffmann
Matus
Mihalak
Matus Mihalak
L. Shankar
Ram
L. Shankar Ram
10.4230/DagSemProc.05031.17
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New Old Algorithms for Stochastic Scheduling
We consider the stochastic identical parallel machine scheduling problem and its online extension, when the objective is to minimize the expected total weighted completion time of a set of jobs that are released over time. We give randomized as well as deterministic online and offline algorithms that have the best known performance guarantees in either setting, online or offline and deterministic or randomized. Our analysis is based on a novel linear programming relaxation for stochastic scheduling problems that can be solved online.
stochastic scheduling
online algorithms
competitive analysis
approximation algorithms
linear programming relaxations
1-9
Regular Paper
Andreas S.
Schulz
Andreas S. Schulz
10.4230/DagSemProc.05031.18
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Note on Negative Probabilities and Observable Processes
A mathematical framework for observable processes is introduced via the model of systems whose states may be time dependent and described by possibly "negative probabilities". The model generalizes and includes the linearly dependent models or observable operator models for classical discrete stochastic processes. Within this model a general convergence result for finite-dimensional processes, which generalize finite state (hidden) Markov models, is derived. On the philosophical side, the model furthermore offers an explanation for Bell's inequality in quantum mechanics.
Negative Probability
Observable Process
Markov Chain
Stochastic Process
BellÃ¢â‚¬â„¢s Inequality
HHM
LDP
OOM
1-14
Regular Paper
Ulrich
Faigle
Ulrich Faigle
Alexander
Schoenhuth
Alexander Schoenhuth
10.4230/DagSemProc.05031.19
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Online Scheduling
We survey some recent results on scheduling unit jobs. The emphasis of the talk is both on presenting some basic techniques and providing an overview of the current state of the art. The techniques presented cover charging schemes, potential function arguments, and lower bounds based on Yao's principle. The studied problem is equivalent to the following buffer management problem: packets with specified weights and deadlines arrive at a network switch and need to be forwarded so that the total weight of forwarded packets is maximized. A packet not forwarded before its deadline brings no profit. The presented algorithms improve upon 2-competitive greedy algorithm, the competitive ratio is 1.939 for deterministic and 1.582 for randomized algorithms.
online algorithms
scheduling
1-3
Regular Paper
Jiri
Sgall
Jiri Sgall
10.4230/DagSemProc.05031.20
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Online scheduling of splittable tasks
We consider online scheduling of splittable tasks on parallel machines. In our model, each task can be split into a limited number of parts, that can then be scheduled independently. We consider both the case where the machines are identical and the case where some subset of the machines have a (fixed) higher speed than the others. We design a class of algorithms which allows us to give tight bounds for a large class of cases where tasks may be split into relatively many parts. For identical machines we also improve upon the natural greedy algorithm in other classes of cases.
online scheduling
splittable tasks
parallel machines
greedy algorithm
1-3
Regular Paper
Leah
Epstein
Leah Epstein
Rob van
Stee
Rob van Stee
10.4230/DagSemProc.05031.21
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Online Scheduling with Bounded Migration
Consider the classical online scheduling problem where jobs that arrive one by one are assigned to identical parallel machines with the objective of minimizing the makespan. We generalize this problem by allowing the current assignment to be changed whenever a new job arrives, subject to the constraint that the total size of moved jobs is bounded by~$\beta$ times the size of the arriving job. Our main result is a linear time `online approximation scheme', that is, a family of online algorithms with competitive ratio~$1+\epsilon$ and constant migration factor~$\beta(\epsilon)$, for any fixed~$\epsilon>0$. This result is of particular importance if considered in the context of sensitivity analysis: While a newly arriving job may force a complete change of the entire structure of an optimal schedule, only very limited `local' changes suffice to preserve near-optimal solutions. We believe that this concept will find wide application in its own right. We also present simple deterministic online algorithms with migration factors~$\beta=2$ and~$\beta=4/3$, respectively. Their competitive ratio~$3/2$ beats the lower bound on the performance of any online algorithm in the classical setting without migration. We also present improved algorithms and similar results for closely related problems. In particular, there is a short discussion of corresponding results for the objective to maximize the minimum load of a machine. The latter problem has an application for configuring storage servers that was the original motivation for this work.
scheduling
sensitivity analysis
online algorithm
1-3
Regular Paper
Peter
Sanders
Peter Sanders
Naveen
Sivadasan
Naveen Sivadasan
Martin
Skutella
Martin Skutella
10.4230/DagSemProc.05031.22
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Polyhedral Risk Measures and Lagrangian Relaxation in Electricity Portfolio Optimization
We present a multistage stochastic programming model for mean-risk optimization of electricity portfolios containing physical components and energy derivative products. Stochasticity enters the model via the uncertain (time-dependent) prices and electricity demand. The objective is to maximize the expected overall revenue and, simultaneously, to minimize a multiperiod risk measure, i.e., a risk measure that takes into account the intermediate time cash values. We compare the effect of different multiperiod risk measures taken from the class of polyhedral risk measures which was suggested in our earlier work. Furthermore, we discuss how such a mean-risk optimization problem can be solved by dual decomposition techniques (Lagrangian relaxation).
Stochastic Programming
Mean-Risk Optimization
Risk Measure
Lagrangian Relaxation
Electricity;
1-3
Regular Paper
Andreas
Eichhorn
Andreas Eichhorn
Werner
Römisch
Werner Römisch
Isabel
Wegner
Isabel Wegner
10.4230/DagSemProc.05031.23
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Properties and Calculation of Singular Normal Distributions
The need for calculating and characterizing singular normal distributions arises in a natural way when considering chance constraints of the type P(Az <= b(x) >= p, where A is a rectangular matrix having more rows than columns, b is some function and z is a random vector having some nondegenerate multivariate normal distribution. Such situation is typical, for instance, in stochastic networks, where a comparatively small random vector may induce a possibly large number of linear inequality constraints. Passing to the transformed random variable q:=Az, the constraint can be equivalently rewritten as F(b(x))>= p, where F is the distribution function of q. In contrast to the original random vector z, the transformed vector q has a singular normal distribution. The talk demonstrates how to get back from here to (a sum of) regular normal distributions under a full rank regularity condition. This allows for an efficient calculation of singular normal distributions and provides a numerical method which outperforms competing procedures in moderate dimensions. Computational results for test examples are provided for the sake of comparison. In general, if the mentioned regularity condition is violated, then the singular normal distribution function F may even lack continuity. The talk provides an equivalent criterion for Lipschitz continuity of F and characterizes differentiability and subdifferentiability of F.
singular normal distribution
chance constraints
normal probability of polyhedra
1-2
Regular Paper
René
Henrion
René Henrion
Tamas
Szantai
Tamas Szantai
10.4230/DagSemProc.05031.24
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Rowing to Barbados
In October 2003, sixteen boats set off from La Gomera in the Canary Islands headed for Barbados 4800 km distant. Each boat was manned by two oarsmen who were competing in the Transatlantic Challenge, an ocean rowing endurance event. This paper describes an optimization model developed for route planning in this event. It was used successfully by the Holiday Shoppe team to win the race in world record time. We describe the tool, its history, and the way it was used in the race.
ocean rowing
weather routing
dynamic programming
isochrones
1-6
Regular Paper
Andy
Philpott
Andy Philpott
Geoff
Leyland
Geoff Leyland
10.4230/DagSemProc.05031.25
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Scenario Optimization for Multi-Stage Stochastic Programming Problems
The field of multi-stage stochastic programming provides a rich modelling framework to tackle a broad range of real-world decision problems. In order to numerically solve such programs - once they get reasonably large - the infinite-dimensional optimization problem has to be discretized. The stochastic optimization program generally consists of an optimization model and a stochastic model. In the multi-stage case the stochastic model is most commonly represented as a multi-variate stochastic process. The most common technique to calculate an useable discretization is to generate a scenario tree from the underlying stochastic process. In the first part of the talk we take a look at scenario optimization from the viewpoint of a decision taker, to provide rather non-technical insights into the problem. In the second part of the talk we examplify scenario tree generation by reviewing one specific algorithm based on multi-dimensional facility location applying backward stagewise clustering. An example from the area of financial engineering concludes the talk.
Stochastic programming
scenario generation
facility location
financial engineering
1-3
Regular Paper
Ronald
Hochreiter
Ronald Hochreiter
10.4230/DagSemProc.05031.26
Creative Commons Attribution 4.0 International license
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Searching with an Autonomous Robot
We discuss online strategies for visibility-based
searching for an object hidden behind a corner,
using Kurt3D, a real autonomous mobile robot. This task
is closely related to a number of well-studied problems.
Our robot uses a three-dimensional laser scanner in a
stop, scan, plan, go fashion for building a virtual
three-dimensional environment.
Besides planning trajectories and avoiding obstacles, Kurt3D is capable of identifying objects like a chair.
We derive a practically useful and asymptotically
optimal strategy that guarantees a competitive ratio of 2,
which differs remarkably from the well-studied scenario
without the need of stopping for surveying the environment. Our strategy is used by Kurt3D, documented in a separate video.
Searching
visibility problems
watchman problems
online searching
competitive strategies
autonomous mobile robots three-dimensional laser scanning
Kurt3D
1-2
Regular Paper
Sándor
Fekete
Sándor Fekete
Rolf
Klein
Rolf Klein
Andreas
Nüchter
Andreas Nüchter
10.4230/DagSemProc.05031.27
Creative Commons Attribution 4.0 International license
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Subtree decomposition for multistage stochastic programs
A class of algorithms for solving multistage stochastic recourse problems is described. The scenario tree is decomposed using a covering collection of subtrees. The approach is illustrated with two examples: adapting the diagonal quadratic approximation algorithm and adapting nested Bender's decomposition. The approach leads to a class of methods based on the subtree cover chosen (including the original implementation of the algorithm adapted). This approach increases flexibility in the size, number and structure of subproblems for multistage stochastic programming decomposition methods.
Stochastic programming
scenario tree
decomposition
1-3
Regular Paper
Shane
Dye
Shane Dye
10.4230/DagSemProc.05031.28
Creative Commons Attribution 4.0 International license
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Topology Matters: Smoothed Competitiveness of Metrical Task Systems
We consider online problems that can be modeled as metrical task systems: An online algorithm resides in a graph of n nodes and may move in this graph at a cost equal to the distance. The algorithm has to service a sequence of tasks that arrive over time; each task specifies for each node a request cost that is incurred if the algorithm services the task in this particular node. The objective is to minimize the total request plus travel cost. Borodin, Linial and Saks gave a deterministic work function algorithm (WFA) for metrical task systems having a tight competitive ratio of 2n-1. We present a smoothed competitive analysis of WFA. Given an adversarial task sequence, we add some random noise to the request costs and analyze the competitive ratio of WFA on the perturbed sequence. We prove upper and matching lower bounds. Our analysis reveals that the smoothed competitive ratio of WFA is much better than its (worst case) competitive ratio and that it depends on several topological parameters of the graph underlying the metric, such as maximum degree, diameter, etc. For example, already for moderate perturbations, the smoothed competitive ratio of WFA is O(log(n)) on a clique and O(\sqrt{n}) on a line. We also provide the first average case analysis of WFA. For a large class of probability distributions, we prove that WFA has O(log(D)) expected competitive ratio, where D is the maximum degree of the underlying graph.
online algorithm
metrical task systems
work function algorithm
smoothed competitive analysis
1-5
Regular Paper
Guido
Schäfer
Guido Schäfer
Naveen
Sivadasan
Naveen Sivadasan
10.4230/DagSemProc.05031.29
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Tracking mobile users
Cellular telephony systems, where locations of a mobile users may be unknown at some times, are becoming more common. Mobile users are roaming in a zone. A user reports its location only if it leaves the zone entirely. We consider cellular zones with n cells and m mobile users roaming among the cells. The location of the users is uncertain and is given by m probability distribution vectors. The Conference Call Search problem (CCS) deals with tracking a set of mobile users, in order to establish a call between all of them. The search is performed in a limited number of rounds, and the goal is to minimize the expected search cost. In the "unit cost model", a single query for a cell outputs a list of users located in that cell. The "bounded bandwidth" model allows a query for a single user per cell in each round. We discuss three types of protocols; oblivious, semi-adaptive and adaptive search protocols. An oblivious search protocol decides on all requests in advance, and stops only when all users are found. A semi-adaptive search protocol decides on all the requests in advance, but it stops searching for a user once it is found. An adaptive search protocol stops searching for a user once it has been found (and its search strategy may depend on the subsets of users that were found in each previous round). We establish the differences between the distinct protocol types and answer some open questions which were posed in previous work on the subject.
mobile users
PTAS
1-3
Regular Paper
Leah
Epstein
Leah Epstein
Asaf
Levin
Asaf Levin
10.4230/DagSemProc.05031.30
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Tree-Sparse Modeling and Solution of Multistage Stochastic Programs
Multistage stochastic programs are prototypical for nonlinear programs with an inherent tree structure inducing characteristic sparsity patterns in the KKT systems of interior methods. We present an integrated modeling and solution approach for such tree-sparse programs. Three closely related natural formulations having desirable control-theoretic properties lead to KKT system solution algorithms with linear complexity. Application examples from computational finance and process engineering demonstrate the efficiency of the approach.
Tree-sparse programs
multistage stochastic optimization
KKT systems
hierarchical sparsity
1-3
Regular Paper
Marc
Steinbach
Marc Steinbach
10.4230/DagSemProc.05031.31
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Uncertainties in stochastic programming models: The minimax approach
50 years ago, stochastic programming was introduced to deal with uncertain values of coefficients which were observed in applications of mathematical programming. These uncertainties were modeled as random and the assumption of complete knowledge of the probability distribution of random parameters became a standard. Hence, there is a new type of uncertainty concerning the probability distribution. Using a hypothetical, ad hoc distribution may lead to bad, costly decisions. Besides of a subsequent output analysis it pays to include the existing, possibly limited information into the model, cf. the minimax approach which will be the main item of this presentation. It applies to cases when the probability distribution is only known to belong to a specified class of probability distributions and one wishes to hedge against the least favorable distribution. The minimax approach has been developed for special types of stochastic programs and special choices of the class of probability distributions and there are recent results aiming at algorithmic solution of minimax problems and on stability properties of minimax solutions.
stochastic programming models
minimax approach
1-2
Regular Paper
Jitka
Dupacová
Jitka Dupacová
10.4230/DagSemProc.05031.32
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