Monte Carlo Simulation and Global Optimization without Parameters

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 behavior (if present) without any parameter tuning. We test it on the traveling salesperson problem, the Edwards-Anderson spin glass, and the triangular antiferromagnet.