In applied mathematics, highly optimized tolerance (HOT) is a method of generating power law behavior in systems by including a global optimization principle.
It was developed by Jean M. Carlson and John Doyle in the early 2000s.
[1] For some systems that display a characteristic scale, a global optimization term could potentially be added that would then yield power law behavior.
It has been used to generate and describe internet-like graphs, forest fire models and may also apply to biological systems.
We then want to minimize subject to the constraint Using Lagrange multipliers, this gives giving us a power law.
The global optimization of minimizing the energy along with the power law dependence between
gives us a power law distribution in probability.