Landscape encodings enhance optimization

TL;DR

This paper demonstrates that using redundant, non-invertible encodings in combinatorial optimization can improve search efficiency by increasing low-energy states and creating smoother landscapes for local search algorithms.

Contribution

It introduces the concept that non-invertible encodings, contrary to traditional invertible ones, can enhance optimization by enriching low-energy states and smoothing the landscape.

Findings

Redundant encodings increase the density of low-energy states.

Non-invertible encodings can create smoother optimization landscapes.

Enhanced landscape properties guide local search towards optimal solutions.

Abstract

Hard combinatorial optimization problems deal with the search for the minimum cost solutions (ground states) of discrete systems under strong constraints. A transformation of state variables may enhance computational tractability. It has been argued that these state encodings are to be chosen invertible to retain the original size of the state space. Here we show how redundant non-invertible encodings enhance optimization by enriching the density of low-energy states. In addition, smooth landscapes may be established on encoded state spaces to guide local search dynamics towards the ground state.