Monte Carlo simulation and global optimization without parameters

TL;DR

This paper introduces a parameter-free Monte Carlo ensemble that enhances global optimization and critical behavior detection, demonstrated on complex problems like TSP and spin glasses.

Contribution

A novel ensemble for Monte Carlo simulations with robust ergodicity and no parameter tuning, improving optimization and critical phenomena analysis.

Findings

Effective in solving hard optimization problems

Capable of estimating free energies at all temperatures

Detects critical behavior without parameter tuning

Abstract

We propose a new ensemble for Monte Carlo simulations, in which each state is assigned a statistical weight $1/k$, where $k$ is the number of states with smaller or equal energy. This ensemble has robust ergodicity properties and gives significant weight to the ground state, making it effective for hard optimization problems. It can be used to find free energies at all temperatures and picks up aspects of critical behaviour (if present) without any parameter tuning. We test it on the travelling salesperson problem, the Edwards-Anderson spin glass and the triangular antiferromagnet.