# Objective function vs fitness function.

What is the difference between an Objective Function and a Fitness Function?

Are Objective Functions only used in Linear Programming?

Are Fitness Functions only used in Genetic Algorithm?

Do we need to apply any operation on a mathematical function to discover Objective/Fitness Functions?

Can you give any concise but versatile example to explain the ideas?

## 1 Answer

In some fields they may be synonyms but in evolutionary computing it can be an important distinction.

The objective function is the function being optimised while the fitness function is what is used to guide the optimisation. Depending on the selection method being used the objective function may need to be scaled. The fitness function is traditionally positive values with higher being better. This is more a concern with methods using proportional selection. Most recent research I've read uses rank based methods such as tournament selection because it avoids issues like scaling.

Quoting a book I'm reading at the moment, Evolutionary Algorithms in Theory and Practice (1996):

Genetic Algorithms need a scaling function $\delta: \mathbb{R} \times \Theta_\delta \rightarrow \mathbb{R}^+$ to map objective function values $f(\Upsilon(\vec{x}))$ to positive real values, since the standard selection mechanism of Genetic Algorithms requires positive fitness values and highest fitness values for the best individuals.