Algorithmic System Design Using Scaling and Affinity Laws
Energy-efficient components do not automatically lead to energy-efficient systems. Technical Operations Research (TOR) shifts the focus from the single component to the system as a whole and finds its optimal topology and operating strategy simultaneously
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Abstract Energy-efficient components do not automatically lead to energy-efficient systems. Technical Operations Research (TOR) shifts the focus from the single component to the system as a whole and finds its optimal topology and operating strategy simultaneously. In previous works, we provided a preselected construction kit of suitable components for the algorithm. This approach may give rise to a combinatorial explosion if the preselection cannot be cut down to a reasonable number by human intuition. To reduce the number of discrete decisions, we integrate laws derived from similarity theory into the optimization model. Since the physical characteristics of a production series are similar, it can be described by affinity and scaling laws. Making use of these laws, our construction kit can be modeled more efficiently: Instead of a preselection of components, it now encompasses whole model ranges. This allows us to significantly increase the number of possible set-ups in our model. In this paper, we present how to embed this new formulation into a mixed-integer program and assess the run time via benchmarks. We present our approach on the example of a ventilation system design problem.
L.C. Altherr (B) · C. Schänzle · P.F. Pelz Chair of Fluid Systems, TU Darmstadt, Darmstadt, Germany e-mail: [email protected] C. Schänzle e-mail: [email protected] P.F. Pelz e-mail: [email protected] T. Ederer Discrete Optimization, TU Darmstadt, Darmstadt, Germany e-mail: [email protected] U. Lorenz Chair of Technology Management, Universität Siegen, Siegen, Germany e-mail: [email protected] © Springer International Publishing Switzerland 2017 K.F. Dœrner et al. (eds.), Operations Research Proceedings 2015, Operations Research Proceedings, DOI 10.1007/978-3-319-42902-1_82
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? VENTILATION SYSTEM
OFFICE
OFFICE 25 15 5
25 15 5 8
12 16 20
CONFERENCE ROOM 25 15 5
8
TIME
12 16 20
8
TIME
12 16
20
TIME
Fig. 1 We illustrate our approach by planning the energy optimal ventilation system for an office floor. Office staff, lights and computers produce heat. A time-dependent occupation density depicts how many people are working on average in each room at a given daytime Table 1 Load scenarios considered in the optimization problem Scenario Volume flow in m3 /s Pressure in Pa 1 2 3
6.88 5.16 3.44
200 175 150
Time fraction (%) 15 30 55
1 Technical Application The ventilation system design problem will be introduced very briefly. For more information please refer to [5]. We consider a ventilation system for a building with several offices and a conference room, cf. Fig. 1. The function of the ventilation system is to provide fresh air. Following guideline VDI 2078, each person corre˙ = 120 W and each technical device to a heat source sponds to a heat source of Q ˙ = 30 W. For a comfort cooling system, a temperature difference of ΔT = 2 K of Q between the supplied air and the room temperature is recommended [3]. For every
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