Renormalization for Discrete Optimization

TL;DR

This paper introduces a novel algorithm combining renormalization and genetic methods to improve discrete optimization, effectively solving complex problems like TSP and spin glasses by self-consistent multi-scale optimization.

Contribution

It adapts renormalization group techniques into a genetic algorithm framework for discrete optimization, a new approach not previously explored.

Findings

High success rate in finding ground states

Effective on traveling salesman and spin glass problems

Demonstrates power of multi-scale optimization

Abstract

The renormalization group has proven to be a very powerful tool in physics for treating systems with many length scales. Here we show how it can be adapted to provide a new class of algorithms for discrete optimization. The heart of our method uses renormalization and recursion, and these processes are embedded in a genetic algorithm. The system is self-consistently optimized on all scales, leading to a high probability of finding the ground state configuration. To demonstrate the generality of such an approach, we perform tests on traveling salesman and spin glass problems. The results show that our ``genetic renormalization algorithm'' is extremely powerful.