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Developing Embodied Agents for Education Applications with Accurate Synchronization of Gesture and Speech Kapitel lesen Erstes Kapitel lesen

2015 | OriginalPaper | Buchkapitel

Abstraction of Heterogeneous Supplier Models in Hierarchical Resource Allocation

verfasst von : Alexander Schiendorfer, Gerrit Anders, Jan-Philipp Steghöfer, Wolfgang Reif

Erschienen in: Transactions on Computational Collective Intelligence XX

Verlag: Springer International Publishing

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Abstract

Resource allocation problems such as finding a production schedule given a set of suppliers’ capabilities are generally hard to solve due to their combinatorial nature, in particular beyond a certain problem size. Large-scale instances among them, however, are prominent in several applications relevant to smart grids including unit commitment and demand response. Decomposition constitutes a classical tool to deal with this increasing complexity. We present a hierarchical “regio-central” decomposition based on abstraction that is designed to change its structure at runtime. It requires two techniques: (1) synthesizing several models of suppliers into one optimization problem and (2) abstracting the direct composition of several suppliers to reduce the complexity of high-level optimization problems. The problems we consider involve limited maximal and, in particular, minimal capacities along with on/off constraints. We suggest a formalization termed supply automata to capture suppliers and present algorithms for synthesis and abstraction. Our evaluation reveals that the obtained solutions are comparable to central solutions in terms of cost efficiency (within 1 % of the optimum) but scale significantly better (between a third and a half of the runtime) in the case study of scheduling virtual power plants.

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Vorheriges Kapitel Developing Embodied Agents for Education Applications with Accurate Synchronization of Gesture and Speech
Nächstes Kapitel Shape Recognition Through Tactile Contour Tracing
Fußnoten
1
In the application domain, we also need to consider so-called must-run plants [48], leading to \(L^a= \langle [P_{\mathrm {min}}^a, P_{\mathrm {max}}^a] \rangle \).
 
2
Supply is not limited to positive production, since negative production, e.g., consumption or storage of a resource, can be vital to meet the demand, reflecting the concept of a prosumer.
 
3
The expressiveness depends on the function and relation symbols of the underlying constraint language, we assume basic linear arithmetic, boolean algebra and standard inequalities.
 
4
We adopt a functional view, i.e., each constraint \(c \in C\) maps an assignment \(v \in [X \rightarrow D]\) to \(\mathbb {B} = \{ \mathrm {true}, \mathrm {false}\}\) and consequently, c is satisfied w.r.t. v iff \(c(v) = \mathrm {true}\).
 
5
Note that the distinction between \(\mathtt {x_a}\) and \(\mathtt {S[a]}\) emphasizes that \(\mathtt {S}\) is defined for every agent and \(\mathtt {x_a}\) is generated specifically for a.
 
6
Consider a supplier with limited fuel resource in-flow such as, e.g., a biogas plant. At a future time step t, the supply could actually be higher if no gas had been spent in the previous steps rather than ramping-up upfront and needing to ramp-down at t due to the lack of fuel.
 
7
The value of \(\alpha _{\varDelta }\) effectively acts as a “market price” since violations would have to be compensated by buying additional energy.
 
9
Note that the temporal abstraction execution is already included in the runtime per time step for the hierarchical setting.
 
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Metadaten
Titel
Abstraction of Heterogeneous Supplier Models in Hierarchical Resource Allocation
verfasst von
Alexander Schiendorfer
Gerrit Anders
Jan-Philipp Steghöfer
Wolfgang Reif
Copyright-Jahr
2015
Buch
Transactions on Computational Collective Intelligence XX

Print ISBN: 978-3-319-27542-0

Electronic ISBN: 978-3-319-27543-7

Copyright-Jahr: 2015

DOI
https://doi.org/10.1007/978-3-319-27543-7_2