scholarly journals Multiple Optimal Solutions and the Best Lipschitz Constants Between an Aggregation Function and Associated Idempotized Aggregation Function

Axioms ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 52
Author(s):  
Hui-Chin Tang ◽  
Wei-Ting Chen

This paper presents and compares the optimal solutions and the theoretical and empirical best Lipschitz constants between an aggregation function and associated idempotized aggregation function. According to an exhaustive search we performed, the multiple optimal solutions and the empirical best Lipschitz constants are presented explicitly. The results indicate that differences of the multiple optimal solutions exist among the Minkowski norm, the number of steps, and the type of aggregation function. We demonstrate that these differences can affect the theoretical and empirical best Lipschitz constants of an aggregation function.

2019 ◽  
Vol 4 ◽  
pp. 5
Author(s):  
Tobias Weiss ◽  
Christoph Moser ◽  
David Venus ◽  
Björn Berggren ◽  
Ase Togerro

Possible cost saving potentials in planning and construction of high performing nearly zero energy buildings (nZEBs) with advanced energy standards are often not sufficiently assessed, as only a few, out of numerous possible variants of technology sets are considered in the traditional planning process. Often planning and analysis are not carried out in parallel, and the alternative technical options are discarded at an early stage. If, on the other hand, possible variants are realistically compared in the planning phase, a profound decision can be made. nZEB-design is also a multi-objective optimization problem where stakeholder interests' conflict with each other. This research addresses a methodological approach to better understand the effects that technical variables have on energy, environmental and economic performance over the whole life cycle of a multi-family residential building in Sweden. The research goal is to identify the most significant technical nZEB design variables organized into a consistent framework. In this paper, in a first step an exhaustive search method is assessed for a multi-family residential building in Sweden that systematically investigates all possible variant combinations. In a second step the derived results are applied to multiple objectives and optimisation goals for a multi-target decision-making framework so that different actors can decide between optimal solutions for different objectives. This approach seeks to explore a set of optimal solutions rather than to find a single optimal solution. On the one hand, a variety of technologies, such as insulation of the building envelope, ventilation or electricity and heat supply, and on the other hand a variation of the boundary conditions (such as observation period, user behaviour, energy price increases or CO2 costs) was investigated. The results were analysed energetically and economically over the life cycle of the building with the objectives of identifying coherences, deriving trends and optimizations over a time span of 40 years. The results show that the variance in the financing costs (20%) and the net present value (15%) is relatively low, whereas the primary energy demand (66%) and the CO2 (73%) emission vary in a broader range. The optimum cost curve in relation to CO2 emissions is very flat. Low emissions and energy requirements can, therefore, be achieved with different energy concepts as long as the envelope is very efficient. Due to the nature of an exhaustive search approach, it is also possible to find technical solution sets and design strategies with nearly equal financing cost and/or net present values, but with less primary energy consumption and/or CO2 emissions.


2018 ◽  
Author(s):  
Jordan Stevens ◽  
Douglas Steinley ◽  
Cassandra L. Boness ◽  
Timothy J Trull ◽  
...  

Using complete enumeration (e.g., generating all possible subsets of item combinations) to evaluate clustering problems has the benefit of locating globally optimal solutions automatically without the concern of sampling variability. The proposed method is meant to combine clustering variables in such a way as to create groups that are maximally different on a theoretically sound derivation variable(s). After the population of all unique sets is permuted, optimization on some predefined, user-specific function can occur. We apply this technique to optimizing the diagnosis of Alcohol Use Disorder. This is a unique application, from a clustering point of view, in that the decision rule for clustering observations into the diagnosis group relies on both the set of items being considered and a predefined threshold on the number of items required to be endorsed for the diagnosis to occur. In optimizing diagnostic rules, criteria set sizes can be reduced without a loss of significant information when compared to current and proposed, alternative, diagnostic schemes.


2005 ◽  
Vol 45 (supplement) ◽  
pp. S103
Author(s):  
R. Minai ◽  
M. Iwasaki ◽  
H. Murakmai ◽  
Y. Matsuo

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