7.3 Cost Functions and Constraints

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Cost functions quantify things that we want to minimize, or maximize. These should be aligned with system objectives. Typical cost functions include,

- money

- time

- some combination of factors

Systems also have constraints that limit available solutions

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 1.29 Example cost function for building a fence around a pasture

The cost function can be written as..

Figure 1.30 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 1.31 Example constraint functions for a pasture

The cost function can be written as..

Figure 1.32 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 1.33 Example of slack variables for including constraints

The cost function can be written as..

Figure 1.34 A subroutine for cost function calculation