文档介绍：Principles of Information Science
Chapter 9
anization
-- System Optimization Theory
§ System Fundamentals - Definitions
System: Definitions
System – integrity of elements that form a certain structure
internally and perform certain functions externally.
L. von Bertalanffy: “System -- set of interrelated elements”
Basic Features of Systems include:
(1) Integrity as an entirety; (2) Interrelated among elements; (3) Multilevel (4) Relativity (5) Goal-Keeping (6) Dynamic
§ System Fundamentals - Features
§ & Information
Information and Stochastic System’anism
A stochastic system S = {(s1, p1), …, (sn, pn), …, (sN, pN)}
Uncertainty: H(S) = - pn log pn
n
0 = [H(S)]min H(S) [H(S)]max = H0 = logN
Organization: =
H0 – H(S)
H0
= R
§ anizing & Information
Conditions Required for anizing
A system, S, under environment, E, is anizable iff
H(S) > H(E) 0
or
dR
dt
> 0,
The latter means
H(S)
dH0
dt
> H0
dH(S)
dt
, and this leads to
1) If N is given, dH0/dt = 0, then it must have
dH(S)
dt
< 0;
2) If H(S) = Const and N is variable, then it must have
dH0
dt
> 0.
§ Information & Optimization
Mechanism for Optimization
Functions
Detected
System to be
Optimized
Observer
Structure
Information
Structure
Adjusting
§ Optimization Algorithm
The structure of the System to be optimized:
S: c1, …, cn, …, cN
x1, …, xn, …, xN
t1, …, tn, …, tN
{
}
The utility of the system related to the structure: u1, …, uN,
Thus, the optimal structure of the system should be
Sopt = {S| I() = max I()}
{S}
§ Examples
Optimization algorithm may be reduced to various cases:
-- Linear Programming
-- Non-Linear Programming
-- Networking (Minimum Route, Maximum Traffic,
Minimum Cost, etc)
-- Decision-Making Game (MIniMax, MaxMin, etc)
-- Dynamic Programming
§ Systems and Order Decreasing
A Natural trend in closed systems
From higher order to lower order (Maxwell Demon)
§ Systems and Order Inc