About the Definition of an Optimization

The optimization is the process of searching for the minimum, maximum, or for a target value of an Objective function of one or several variables while satisfying certain restrictions or constraints.

See Also
Searching for a Minimum Value
Searching for a Maximum Value
Searching for a Minimum Value

A good example of optimization is the minimum weight design of structures in aerospace industry where aircraft structural designs often prevail on cost considerations. The notion of optimization presupposes that the operation to be improved or optimized is described by a function whose variation can be expressed with respect to a group of parameters, also called variables or free parameters.

Given f(x) a parameter expressed in terms of other parameters: 

Min f(x1, ..., xn) 
such that:

          gi (x1, ...) >= Ki
         hj (x1, ..., xn) ==  Kj
         LB < xi < UB

Where: f(x) is a Engineering Rules Capture formula (Optimization objective function).

x= (x1, ..., xn)

xi is a Engineering Rules Capture parameter (Optimization free parameters).

g, h are constraints (optional).

LB: Lower bound

UB: Upper bound

Design Optimization offers three operating modes whereby you can search for the:

  • f(x) minimum,
  • f(x) maximum,
  • a given value of f(x) or a
  • constraints satisfaction.

These operating modes are respectively called the Minimization, the Maximization and the Target Value and the Constraints only modes.