ComplexityFunction is an option for Simplify and FullSimplify which gives a function to rank the complexity of different forms of an expression.
With the default setting ComplexityFunction->Automatic, forms are ranked primarily according to their LeafCount, with corrections to treat integers with more digits as more complex.
Simplify[expr, ComplexityFunction->f] applies f to each intermediate expression generated by Simplify, treating the one which yields the smallest numerical value as simplest.
See The Mathematica Book: Section 3.3.9.
See also: Length, StringLength, TimeConstraint, ExcludedForms, TransformationFunctions.