Optimization Algorithms Based on Renormalization Group

TL;DR

This paper reviews heuristic optimization algorithms that utilize real-space renormalization group transformations, exploring their relation to low-energy excitations and phase transitions affecting computational complexity.

Contribution

It introduces a class of optimization algorithms based on renormalization group ideas and analyzes their connection to physical phenomena like phase transitions.

Findings

Global updates can be effectively implemented via renormalization group transformations.

The structure of low-energy excitations influences algorithm performance.

Finite-temperature phase transitions impact the complexity of finding ground states.

Abstract

Global changes of states are of crucial importance in optimization algorithms. We review some heuristic algorithms in which global updates are realized by a sort of real-space renormalization group transformation. Emphasis is on the relationship between the structure of low-energy excitations and ``block-spins'' appearing in the algorithms. We also discuss the implication of existence of a finite-temperature phase transition on the computational complexity of the ground-state problem.