· For simple examples use derivatives and find the maxima/minima
· Consider the example below to find the
· local and global optimums
· search functions, gradient descent, random walk, simplex
· Objectives are those things we want to minimize, or maximize.
- money
- time
- mass
- volume
- power consumption
- some combination of factors
· Expressed as a function of variables that provides a value
· Consider the example of building a fenced pasture. In this case when the area becomes too large, there is a reduced value. We want to maximize the value of V.
Figure 26.1 Example cost function for building a fence around a pasture
· The cost function can be written as..
Figure 26.2 A subroutine for cost function calculation
· Constraints are boundaries that cannot be crossed.
· Example of constraints, the pasture cannot be larger than one 1600m be 1600m beacuse of the constraints of an existing road system.
Figure 26.3 Example constraint functions for a pasture
· The cost function can be written as..
Figure 26.4 A subroutine for cost function calculation
· Slack variables allow constraints to be considered as part of the cost function. Helps with a system with many local minimum.
Figure 26.5 Example of slack variables for including constraints
· The cost function can be written as..
Figure 26.6 A subroutine for cost function calculation
· Local Search Space
· A topographical map shows the relationship between search parameters and cost values.
Figure 26.7 Local searches
· Global Search space. In this case the system becomes 'stuck' in a local mimina.
Figure 26.8 Global searches
· Global Search space. In this case the system searches all maxim.
Figure 26.9 A Global Search
· The search algorithms change system parameters and try to lower system parameters.
· The main question is how to change the system paramters to minimize the system value.
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