Optimization by thermal cycling

TL;DR

Thermal cycling is an heuristic optimization method combining heating and quenching with decreasing amplitude, effective for discrete and continuous problems, outperforming simulated annealing in certain tasks.

Contribution

This paper introduces the application of thermal cycling to continuous variable problems, extending its use beyond discrete cases and demonstrating its efficiency.

Findings

Thermal cycling outperforms simulated annealing in combinatorial tasks.

Effective for both discrete and continuous optimization problems.

Applicable to Lennard-Jones cluster energy minimization.

Abstract

Thermal cycling is an heuristic optimization algorithm which consists of cyclically heating and quenching by Metropolis and local search procedures, respectively, where the amplitude slowly decreases. In recent years, it has been successfully applied to two combinatorial optimization tasks, the traveling salesman problem and the search for low-energy states of the Coulomb glass. In these cases, the algorithm is far more efficient than usual simulated annealing. In its original form the algorithm was designed only for the case of discrete variables. Its basic ideas are applicable also to a problem with continuous variables, the search for low-energy states of Lennard-Jones clusters.