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1-20 of 22 Search Results for

#### pareto

Book Chapter

Book: Toward Better Photovoltaic Systems: Design, Simulation, Optimization, Analysis, and Operations

Series: AIPP Books, Principles

Published: March 2023

10.1063/9780735425613_002

EISBN: 978-0-7354-2561-3

ISBN: 978-0-7354-2560-6

...-objective optimization problem in practice. To make a trade-off between multiple objectives, the solution approach can be classified into two categories: aggregating weight function methods and Pareto-based optimization methods. Herein, note that the multi-objective optimization problem can also...

Book Chapter

Book: Toward Better Photovoltaic Systems: Design, Simulation, Optimization, Analysis, and Operations

Series: AIPP Books, Principles

Published: March 2023

10.1063/9780735425613_003

EISBN: 978-0-7354-2561-3

ISBN: 978-0-7354-2560-6

...-objective problem since it is an efficient and widely used method to generate Pareto curves to allow observation of the trade-off between objectives. Integration of PV system in existing grids and other systems A crucial stage regarding solar photovoltaic systems is to consider the potential effects...

Book

Series: AIPP Books, Principles

Published: March 2023

10.1063/9780735425613

EISBN: 978-0-7354-2561-3

ISBN: 978-0-7354-2560-6

Book Chapter

Book: Toward Better Photovoltaic Systems: Design, Simulation, Optimization, Analysis, and Operations

Series: AIPP Books, Principles

Published: March 2023

10.1063/9780735425613_005

EISBN: 978-0-7354-2561-3

ISBN: 978-0-7354-2560-6

...), weather data, and production data. First, the keyword recognition technique was used to analyze the O&M tickets from different climate zones in the United States and extract information describing maintenance owing to unexpected events. The extracted information was then subjected to a Pareto analysis...

Book Chapter

Series: AIPP Books, Principles

Published: July 2022

10.1063/9780735424272_011

EISBN: 978-0-7354-2427-2

ISBN: 978-0-7354-2424-1

..., loss of energy, and time of charging. The suggested solutions of Pareto fronts can supply guidance on techniques for operating the systems. From the adopted technological viewpoint, the research has indicated an efficient strategy of improved eco-technology performance for integrated systems of energy...

Book Chapter

Series: AIPP Books, Principles

Published: July 2022

10.1063/9780735424272_002

EISBN: 978-0-7354-2427-2

ISBN: 978-0-7354-2424-1

.... According to the Pareto optimal solution, if a small proportion of unserved load can be accepted (5% LPSP), significant reduction in the PV size and thus capital costs can be achieved. Another study on a stand-alone PV–PHS power system ( Shabani and Mahmoudimehr, 2018 ) carried out an optimal design...

Book

Series: AIPP Books, Principles

Published: July 2022

10.1063/9780735424272

EISBN: 978-0-7354-2427-2

ISBN: 978-0-7354-2424-1

Images

**Published:**December 2021

FIG. 15.2 Lévy process simulation: a) Simulation of the Pareto process Par(

*α*,*β*,*γt*;*u*) as defined in ( 15.30 ), with*α*= 1.7,*β*= −0.1,*γ*= 88.3. The simulation has been performed using*ε*= 0.01 in the principal value integrals in ( 15.5 ), and this represents the minimum size of step available to the simulation. The simulation was performed for 500 000 jumps, leading to a total time of 500 time units. The figure plots the value of*u*at times that are multiples of Δ*t*= 0.5 time units. b) The jumps Δ*u*between successive values of*u*at times that are multiples of Δ*t*= 0.5 obtained from the simulation in a). c) Simulation of the distribution of Par(*α*,*β*,*γ*Δ*t*;*x*) at time Δ*t*= 0.5 obtained from the data of b). More about this image found in Lévy process simulation: a) Simulation of the Pareto process Par(...Images

**Published:**December 2021

FIG. 3.3 a)

*Blue curve*: Linear plot showing a log-normal distribution*p*_{ log‐normal }(*x*), with*x*_{0}= 10, and*σ*= 1.*Pink curve*: A comparable Pareto distribution with*α*= 1.8 and*x*_{0}= 10. b)*Blue curve*: Log-log plot of the log-normal distribution function*p*_{ log‐normal }(*x*), with*x*_{0}= 10, and*σ*= 1.*Black dots*: For comparison, we plot 20 000 simulated points from this distribution, assigned to 200 bins.*Pink plot*: A Pareto distribution with*α*= 1.8 and*x*_{0}= 10. It can be seen that this fits the data in the simulated tail as credibly as does the log-normal distribution. More about this image found in a)*Blue curve*: Linear plot showing a log-normal distribut...Book Chapter

Series: AIPP Books, Principles

Published: December 2021

10.1063/9780735423718_003

EISBN: 978-0-7354-2371-8

ISBN: 978-0-7354-2368-8

... consider the observational background, the history, and the relevance of this concept. Only then can one reasonably consider formal mathematics. Pareto’s Law It is generally understood that some people are wealthy, others are very wealthy, and indeed some are billionaires. And even if the numbers...

Images

**Published:**September 2021

FIG. 5.9 (a) Comparison between the target colors and the colors obtained with one of the optimal solutions found on the 3D Pareto front. The table below corresponds to the geometrical parameters of the Pareto solution. (b) Reflexion spectra of the optimal structure presented in (a). (c) Distribut... More about this image found in (a) Comparison between the target colors and the colors obtained with one o...

Images

**Published:**September 2021

FIG. 5.8 3D Pareto fronts obtained by minimizing (

*g*_{1},*g*_{2},*g*_{3}), two realizations with different initial random population are reported. Inset: 3D Pareto front shown in the projected*a*^{∗}*b*^{∗}plane. More about this image found in 3D Pareto fronts obtained by minimizing (*g*_{1}, ...Images

**Published:**December 2021

FIG. 3.2 Log-log plot of population size

*S*versus rank*r*of the 134 largest U. S. metropolitan areas in 1991 [ 3.6 ]. The pink line represents*Zipf’s law*, that is, the equation*S*= 3.9 × 10^{7}/*r*, which closely matches the asymptotic behavior of the data at large*r*and small*S*. In contrast, the blue line represents the equation*S*= 2.2 × 10^{7}*r*^{−η}, with*η*= 0.75, which closely matches the asymptotic behavior of the data at large*S*and small*r*. This corresponds to a form of*Pareto’s law*, that is*p*(*S*) = 1.62 × 10^{−10}*S*^{−(1+α)}, with*α*= 1/*η*= 1.33. More about this image found in Log-log plot of population size*S*versus rank*r*...Images

**Published:**December 2021

FIG. 3.1 a) Plot of the data on income distribution in the USA in 2007, as reported in [ 3.1 ], together with a corresponding Pareto distribution fit f ( I ) = α I 0 α / I α + 1 , with

*α*= 1.6 and*I*_{0}= $35,126. In b) the same data are plotted on a log-log plot. The value of*α*chosen fits the slope of the curve for incomes greater than about $60 000, and the value of*I*_{0}ensures that the areas under both curves are the same and equal to one. The data set plotted excludes very high incomes, either positive or negative, such that |*I*| > $418,000. The full range of incomes is from about −$500 000 to $190 000 000. More about this image found in a) Plot of the data on income distribution in the USA in 2007, as reported...Book

Series: AIPP Books, Principles

Published: December 2021

10.1063/9780735423718

EISBN: 978-0-7354-2371-8

ISBN: 978-0-7354-2368-8

Book Chapter

Series: AIPP Books, Principles

Published: December 2021

0

EISBN: 978-0-7354-2371-8

ISBN: 978-0-7354-2368-8

... , Power laws in economics and finance , Ann. Rev. Econ. 1 , 255 ( 2009 ). [3.3] B. B. , Mandelbrot , The Pareto–Lévy law and the distribution of income , Int. Econ. Rev. 1 , 79 ( 1960 ). [3.4] G. K. , Zipf , Human Behavior and the Principle of Least Effort ( Addison-Wesley...

Book Chapter

Series: AIPP Books, Principles

Published: December 2021

10.1063/9780735423718_015

EISBN: 978-0-7354-2371-8

ISBN: 978-0-7354-2368-8

... of stability of the Paretian distribution, as discussed in Sec. 3.4.7a. This generalizes to arbitrary linear combinations. Thus for two variables

*U*_{1},*U*_{2}, distributed according to the same Pareto law in the sense that if (15.43) U 1 has the distribution Par...Book Chapter

Series: AIPP Books, Principles

Published: September 2021

10.1063/9780735422902_005

EISBN: 978-0-7354-2290-2

ISBN: 978-0-7354-2287-2

..., it will generate a set of trade-off solutions, known as the Pareto front, that share common parameters and that also satisfy the fabrication constraints. The Pareto front fully determines the whole set of potential choices that optimally satisfy the trade-offs among the different objective functions...

Book

Series: AIPP Books, Principles

Published: September 2021

10.1063/9780735422902

EISBN: 978-0-7354-2290-2

ISBN: 978-0-7354-2287-2

Book Chapter

Series: AIPP Books, Perspectives

Published: February 2021

10.1063/9780735421769_002

EISBN: 978-0-7354-2176-9

ISBN: 978-0-7354-2177-6

... reflect some important characteristics of the systems being analyzed. Avalanche! The existence of natural random phenomena described by potential laws, namely,

*x*or 1/^{−α}*x*, was independently discovered by economist Vilfredo Pareto and mathematician Paul Lévy...^{α}1