Energy landscapes of atomic clusters as black box optimization benchmarks

Area of Science:

• Computational Physics
• Materials Science
• Optimization Theory

Background:

• Energy minimization of atomic clusters is a fundamental problem in physics and chemistry.
• Geometry optimization and packing problems, including atomic clusters, are generally NP-complete.
• Current black box optimization benchmarks lack specific features found in physical systems.

Purpose of the Study:

• To introduce atomic cluster energy minimization as a benchmark for continuous black box optimization.
• To propose Cohn-Kumar and Lennard-Jones clusters as specific problem instances.
• To highlight the unique properties of these cluster problems for optimization.

Main Methods:

• Defining potential energies based on distance-dependent pairwise interactions.
• Analyzing the resulting energy landscapes for various topologies (single-funnel, double-funnel).
• Investigating the impact of isospectral symmetry on optimization.

Main Results:

• Cohn-Kumar and Lennard-Jones clusters present diverse energy landscapes, including smooth, rugged, and tunable double-funnel topologies.
• These cluster problems exhibit isospectral symmetry, where atomic arrangements are defined by distance spectra.
• This symmetry is a novel feature not present in existing synthetic optimization test functions.

Conclusions:

• Atomic cluster energy minimization problems are suitable for continuous black box optimization benchmarks.
• The proposed cluster instances offer valuable test cases due to their complex topologies and isospectral symmetry.
• Including these problems in benchmark suites will advance the field of black box optimization.