A super-network equilibrium optimization method for operation architecture with fuzzy demands

doi:10.23919/JSEE.2020.000072

Abstract

Abstract:

From the view of information flow, a super-network equilibrium optimization model is proposed to compute the solution of the operation architecture which is made up of a perceptive level, a command level and a firepower level. Firstly, the optimized conditions of the perceptive level, command level and firepower level are analyzed respectively based on the demand of information relation, and then the information supply-and-demand equilibrium model of the operation architecture super-network is established. Secondly, a variational inequality transformation (VIT) model for equilibrium optimization of the operation architecture is given. Thirdly, the contraction projection algorithm for solving the operation architecture super-network equilibrium optimization model with fuzzy demands is designed. Finally, numerical examples are given to prove the validity and rationality of the proposed method, and the influence of fuzzy demands on the super-network equilibrium solution of operation architecture is discussed.

Key words: super-network equilibrium, operation architecture, fuzzy demand, information flow, variational inequality transformation

Qinghua XING, Jiale GAO. A super-network equilibrium optimization method for operation architecture with fuzzy demands[J]. Journal of Systems Engineering and Electronics, 2020, 31(5): 969-982.

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Solution	Δ, Δ
Solution	(0.1, 0.1)	(0.1, 0.2)	(0.1, 0.3)
${\left( {q_{ij}^{1*}} \right)_{2 \times 2}}$	$\left[ {\begin{array}{*{20}{l}}{0.738751}&{0.740729}\\{0.540398}&{0.746047}\end{array}} \right]$	$\left[ {\begin{array}{*{20}{l}}{0.745517}&{0.741164}\\{0.540444}&{0.748228}\end{array}} \right]$	$\left[\begin{array}{ll}0.748187 & 0.741311 \\0.540460 & 0.748979\end{array}\right]$
${\left( {q_{jk}^{2*}} \right)_{2 \times 2}}$	$ \left[ {\begin{array}{*{20}{l}}{0.332965}&{0.461255}\\{0.354305}&{0.537711}\end{array}} \right]$	$\left[ {\begin{array}{*{20}{l}}{0.332965}&{0.461255}\\{0.354305}&{0.537711}\end{array}} \right] $	$\left[ {\begin{array}{*{20}{l}}{0.332965}&{0.461255}\\{0.354305}&{0.537711}\end{array}} \right] $
f₁	5.383~737	5.618~464	5.804~293
f₂	5.484~444	5.719~171	5.905~000
f₃	5.037~161	5.192~352	5.245~138
f₄	6.946~881	7.102~072	7.154~858
f₅	3.502~892	3.506~619	3.508~080
f₆	3.603~598	3.607~325	3.608~787
f₇	2.202~057	2.369~927	2.429~921
f₈	4.111~776	4.279~647	4.339~641
f_alls	36.272~547	37.395~578	37.995~718

Solution	Δ, Δ
Solution	(0.05, 0.15)	(0.15, 0.15)	(0.25, 0.15)
${\left( {q_{ij}^{1*}} \right)_{2 \times 2}} $	$\left[ {\begin{array}{*{20}{l}}{0.746082}&{0.746623}\\{0.542023}&{0.753959}\end{array}} \right]$	$\left[ {\begin{array}{*{20}{l}}{0.739391}&{0.736535}\\{0.535276}&{0.742692}\end{array}} \right]$	$\left[ {\begin{array}{*{20}{l}}{0.732455}&{0.728982}\\{0.522958}&{0.737964}\end{array}} \right]$
${\left( {q_{jk}^{2*}} \right)_{2 \times 2}} $	$\left[ {\begin{array}{*{20}{l}}{0.332965}&{0.461255}\\{0.354305}&{0.537711}\end{array}} \right] $	$\left[ {\begin{array}{*{20}{l}}{0.332965}&{0.461255}\\{0.354305}&{0.537711}\end{array}} \right] $	$\left[ {\begin{array}{*{20}{l}}{0.332965}&{0.461255}\\{0.354305}&{0.537711}\end{array}} \right] $
f₁	5.450~146	5.429~956	5.412~106
f₂	5.550~852	5.530~662	5.512~813
f₃	5.153~658	5.125~557	5.099~989
f₄	7.063~378	7.035~277	7.009~708
f₅	3.728~150	3.403~675	3.309~222
f₆	3.828~857	3.504~381	3.409~929
f₇	2.290~700	2.326~105	2.334~961
f₈	4.200~420	4.235~825	4.244~681
f_alls	37.266~160	36.591~438	36.333~409