2,492 research outputs found
Changing Bases: Multistage Optimization for Matroids and Matchings
This paper is motivated by the fact that many systems need to be maintained
continually while the underlying costs change over time. The challenge is to
continually maintain near-optimal solutions to the underlying optimization
problems, without creating too much churn in the solution itself. We model this
as a multistage combinatorial optimization problem where the input is a
sequence of cost functions (one for each time step); while we can change the
solution from step to step, we incur an additional cost for every such change.
We study the multistage matroid maintenance problem, where we need to maintain
a base of a matroid in each time step under the changing cost functions and
acquisition costs for adding new elements. The online version of this problem
generalizes online paging. E.g., given a graph, we need to maintain a spanning
tree at each step: we pay for the cost of the tree at time
, and also for the number of edges changed at
this step. Our main result is an -approximation, where is
the number of elements/edges and is the rank of the matroid. We also give
an approximation for the offline version of the problem. These
bounds hold when the acquisition costs are non-uniform, in which caseboth these
results are the best possible unless P=NP.
We also study the perfect matching version of the problem, where we must
maintain a perfect matching at each step under changing cost functions and
costs for adding new elements. Surprisingly, the hardness drastically
increases: for any constant , there is no
-approximation to the multistage matching maintenance
problem, even in the offline case
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\u27\u27 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
A Multistage Stochastic Programming Approach to the Dynamic and Stochastic VRPTW - Extended version
We consider a dynamic vehicle routing problem with time windows and
stochastic customers (DS-VRPTW), such that customers may request for services
as vehicles have already started their tours. To solve this problem, the goal
is to provide a decision rule for choosing, at each time step, the next action
to perform in light of known requests and probabilistic knowledge on requests
likelihood. We introduce a new decision rule, called Global Stochastic
Assessment (GSA) rule for the DS-VRPTW, and we compare it with existing
decision rules, such as MSA. In particular, we show that GSA fully integrates
nonanticipativity constraints so that it leads to better decisions in our
stochastic context. We describe a new heuristic approach for efficiently
approximating our GSA rule. We introduce a new waiting strategy. Experiments on
dynamic and stochastic benchmarks, which include instances of different degrees
of dynamism, show that not only our approach is competitive with
state-of-the-art methods, but also enables to compute meaningful offline
solutions to fully dynamic problems where absolutely no a priori customer
request is provided.Comment: Extended version of the same-name study submitted for publication in
conference CPAIOR201
Performance Analysis of Modified SRPT in Multiple-Processor Multitask Scheduling
In this paper we study the multiple-processor multitask scheduling problem in
both deterministic and stochastic models. We consider and analyze Modified
Shortest Remaining Processing Time (M-SRPT) scheduling algorithm, a simple
modification of SRPT, which always schedules jobs according to SRPT whenever
possible, while processes tasks in an arbitrary order. The M-SRPT algorithm is
proved to achieve a competitive ratio of for
minimizing response time, where denotes the ratio between maximum job
workload and minimum job workload, represents the ratio between maximum
non-preemptive task workload and minimum job workload. In addition, the
competitive ratio achieved is shown to be optimal (up to a constant factor),
when there are constant number of machines. We further consider the problem
under Poisson arrival and general workload distribution (\ie, system),
and show that M-SRPT achieves asymptotic optimal mean response time when the
traffic intensity approaches , if job size distribution has finite
support. Beyond finite job workload, the asymptotic optimality of M-SRPT also
holds for infinite job size distributions with certain probabilistic
assumptions, for example, system with finite task workload
Comparison of different approaches to multistage lot sizing with uncertain demand
We study a new variant of the classical lot sizing problem with uncertain demand where neither the planning horizon nor demands are known exactly. This situation arises in practice when customer demands arriving over time are confirmed rather lately during the transportation process. In terms of planning, this setting necessitates a rolling horizon procedure where the overall multistage problem is dissolved into a series of coupled snapshot problems under uncertainty. Depending on the available data and risk disposition, different approaches from online optimization, stochastic programming, and robust optimization are viable to model and solve the snapshot problems. We evaluate the impact of the selected methodology on the overall solution quality using a methodology-agnostic framework for multistage decision-making under uncertainty. We provide computational results on lot sizing within a rolling horizon regarding different types of uncertainty, solution approaches, and the value of available information about upcoming demands
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Decision support for build-to-order supply chain management through multiobjective optimization
This paper aims to identify the gaps in decision-making support based on
multiobjective optimization for build-to-order supply chain management (BTOSCM).
To this end, it reviews the literature available on modelling build-to-order
supply chains (BTO-SC) with the focus on adopting multiobjective optimization
(MOO) techniques as a decision support tool. The literature has been classified based
on the nature of the decisions in different part of the supply chain, and the key
decision areas across a typical BTO-SC are discussed in detail. Available software
packages suitable for supporting decision making in BTO supply chains are also
identified and their related solutions are outlined. The gap between the modelling and
optimization techniques developed in the literature and the decision support needed in
practice are highlighted and future research directions to better exploit the decision
support capabilities of MOO are proposed
Optimal advertising campaign generation for multiple brands using MOGA
The paper proposes a new modified multiobjective
genetic algorithm (MOGA) for the problem of optimal television (TV) advertising campaign generation for multiple brands. This NP-hard combinatorial optimization problem with numerous constraints is one of the key issues for an advertising agency when producing the optimal TV mediaplan. The classical approach to the solution of this problem is the greedy heuristic, which relies on the strength of the preceding commercial breaks when selecting
the next break to add to the campaign. While the greedy heuristic is capable of generating only a group of solutions that are closely related in the objective space, the proposed modified MOGA produces a Pareto-optimal set of chromosomes that: 1) outperform the greedy heuristic and 2) let the mediaplanner choose from a variety of uniformly distributed tradeoff solutions. To achieve these
results, the special problem-specific solution encoding, genetic operators, and original local optimization routine were developed for the algorithm. These techniques allow the algorithm to manipulate with only feasible individuals, thus, significantly improving its performance that is complicated by the problem constraints. The efficiency of the developed optimization method is verified using
the real data sets from the Canadian advertising industry
Decision support for build-to-order supply chain management through multiobjective optimization
This is the post-print version of the final paper published in International Journal of Production Economics. The published article is available from the link below. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. Copyright @ 2010 Elsevier B.V.This paper aims to identify the gaps in decision-making support based on multiobjective optimization (MOO) for build-to-order supply chain management (BTO-SCM). To this end, it reviews the literature available on modelling build-to-order supply chains (BTO-SC) with the focus on adopting MOO techniques as a decision support tool. The literature has been classified based on the nature of the decisions in different part of the supply chain, and the key decision areas across a typical BTO-SC are discussed in detail. Available software packages suitable for supporting decision making in BTO supply chains are also identified and their related solutions are outlined. The gap between the modelling and optimization techniques developed in the literature and the decision support needed in practice are highlighted. Future research directions to better exploit the decision support capabilities of MOO are proposed. These include: reformulation of the extant optimization models with a MOO perspective, development of decision supports for interfaces not involving manufacturers, development of scenarios around service-based objectives, development of efficient solution tools, considering the interests of each supply chain party as a separate objective to account for fair treatment of their requirements, and applying the existing methodologies on real-life data sets.Brunel Research Initiative and Enterprise Fund (BRIEF
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