Generalized multiple objective bottleneck problems

Gorski, Jochen; Klamroth, Kathrin; Ruzika, Stefan

doi:10.1016/j.orl.2012.03.007

Cited by 12 publications

(5 citation statements)

References 22 publications

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“…If we use Dijkstra's algorithm to solve the nominal problem we obtain the following running time. For more details on bicriteria problems of this type, we refer to [GKR12].…”

Section: Generalized Manhattan Normmentioning

confidence: 99%

Variable-sized uncertainty and inverse problems in robust optimization

Chassein

Goerigk

2018

European Journal of Operational Research

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In robust optimization, the general aim is to find a solution that performs well over a set of possible parameter outcomes, the so-called uncertainty set. In this paper, we assume that the uncertainty size is not fixed, and instead aim at finding a set of robust solutions that covers all possible uncertainty set outcomes. We refer to these problems as robust optimization with variable-sized uncertainty. We discuss how to construct smallest possible sets of min-max robust solutions and give bounds on their size.A special case of this perspective is to analyze for which uncertainty sets a nominal solution ceases to be a robust solution, which amounts to an inverse robust optimization problem. We consider this problem with a min-max regret objective and present mixed-integer linear programming formulations that can be applied to construct suitable uncertainty sets.Results on both variable-sized uncertainty and inverse problems are further supported with experimental data.

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“…If we use Dijkstra's algorithm to solve the nominal problem we obtain the following running time. For more details on bicriteria problems of this type, we refer to [GKR12].…”

Section: Generalized Manhattan Normmentioning

confidence: 99%

Variable-sized uncertainty and inverse problems in robust optimization

Chassein

Goerigk

2018

European Journal of Operational Research

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“…In the context of multiobjective optimization, Gorski () and Gorski et al . () considered problems with one general objective function f :

scriptX

→ ℝ, which could, for example, be a sum objective with cost coefficients c 1 ( e ), and ( q − 1) k – max objectives with possibly different values of k and different cost coefficients c 2 ,…, c q :

\begin{matrix} m i n (\sum_{e \in x} c^{1} (e), k_{2} - max_{e \in x} c^{2} (e), \dots, k_{q} - max_{e \in x} c^{q} (e)) \\ s . t . x \in X . \end{matrix}

…”

Section: Bottleneck Objective Functionsmentioning

confidence: 99%

“…Theorem 3.1 in Section 3) can be obtained (Gorski et al . ):Theorem Consider a MOCO problem with one arbitrary objective function and with ( q − 1) k – max objective functions. Then the cardinality of the nondominated set

Y_{N}

is bounded by ( n + 1) q − 1 ; that is,

true| Y_{N} true| \leq {(n + 1)}^{q - 1}

.…”

Section: Bottleneck Objective Functionsmentioning

confidence: 99%

“…This result has been used in Gorski et al . () to derive efficient solution methods for problems with one sum objective and ( q − 1) k – max objectives. These methods are based on the recursive solution of at most O ( n q − 1 ) ε ‐constraint scalarizations of this class of problems, with ε ‐values defined by the cost coefficients in the respective objectives.…”

Section: Bottleneck Objective Functionsmentioning

confidence: 99%

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Easy to say they are Hard, but Hard to see they are Easy- Towards a Categorization of Tractable Multiobjective Combinatorial Optimization Problems

Figueira

Fonseca

Halffmann

et al. 2016

J. Multi-Crit. Decis. Anal.

Self Cite

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Multiobjective combinatorial optimization problems are known to be hard problems for two reasons: their decision versions are often NP-complete, and they are often intractable. Apart from this general observation, are there also variants or cases of multiobjective combinatorial optimization problems that are easy and, if so, what causes them to be easy? This article is a first attempt to provide an answer to these two questions. Thereby, a systematic description of reasons for easiness is envisaged rather than a mere collection of special cases. In particular, the borderline of easy and hard multiobjective optimization problems is explored.

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“…This fairness maintains the heterogeneity of the resource pool for longer periods by maximizing the lifetime of every single SP. This is a combinatorial optimization problem with multiple bottleneck objectives, which in short is referred to as a Multi-objective Combinatorial Bottleneck Problem (M-CBP) [16].…”

Section: B Phase Ii: Stage-wise Multi-objective Optimizationmentioning

confidence: 99%

Enabling Real-Time In-Situ Processing of Ubiquitous Mobile-Application Workflows

Viswanathan

Lee

Pompili

2013

2013 IEEE 10th International Conference on Mobile Ad-Hoc and Sensor Systems

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Abstract-The heterogeneous sensing and computing capabilities of sensor nodes, mobile handhelds, as well as computing and storage servers in remote datacenters can be harnessed to enable innovative mobile applications that rely on real-time in-situ processing of data generated in the field. There is, however, uncertainty associated with the quality and quantity of data from mobile sensors as well as with the availability and capabilities of mobile computing resources on the field. Data and computing-resource uncertainty, if unchecked, may propagate up the "raw data→information→knowledge" chain and have an adverse effect on the relevance of the generated results. A unified uncertainty-aware framework for data and computingresource management is proposed to enable in-situ processing of application workflows on mobile sensing and computing platforms and, hence, to generate actionable knowledge from raw data within realistic time bounds. A two-phase solution that captures the propagation of data-uncertainty up the dataprocessing chain using interval arithmetic in the first phase and that employs multi-objective optimization for task allocation in the second phase is presented and evaluated in detail.

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Generalized multiple objective bottleneck problems

Cited by 12 publications

References 22 publications

Variable-sized uncertainty and inverse problems in robust optimization

Variable-sized uncertainty and inverse problems in robust optimization

Easy to say they are Hard, but Hard to see they are Easy- Towards a Categorization of Tractable Multiobjective Combinatorial Optimization Problems

Enabling Real-Time In-Situ Processing of Ubiquitous Mobile-Application Workflows

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