Energy Landscapes of Atomic Clusters as Black Box Optimization Benchmarks

We present the energy minimization of atomic clusters as a promising problem class for continuous black box optimization benchmarks. Finding the arrangement of atoms that minimizes a given potential energy is a specific instance of the more general class of or , which are generally NP-complete. Atom...

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Bibliographic Details
Published in:Evolutionary computation 2012-12, Vol.20 (4), p.543-573
Main Authors: Müller, C. L., Sbalzarini, I. F.
Format: Article
Language:English
Subjects:
Algorithms
atomic cluster
Atomic clusters
Benchmarking - methods
Benchmarks
Black box optimization benchmark
Cluster Analysis
Clusters
CMA-ES
energy landscape
ground state
Landscapes
Mathematical analysis
Models, Chemical
Optimization
Potential energy
Thermodynamics
Topology
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Summary:We present the energy minimization of atomic clusters as a promising problem class for continuous black box optimization benchmarks. Finding the arrangement of atoms that minimizes a given potential energy is a specific instance of the more general class of or , which are generally NP-complete. Atomic clusters are a well-studied subject in physics and chemistry. From the large set of available cluster optimization problems, we propose two specific instances: Cohn-Kumar clusters and Lennard-Jones clusters. The potential energies of these clusters are governed by distance-dependent pairwise interaction potentials. The resulting collection of landscapes is composed of smooth and rugged single-funnel topologies, as well as double-funnel topologies. In addition, all problems possess a feature that is not covered by the synthetic functions in current black box optimization test suites: . This property implies that any atomic arrangement is uniquely defined by the pairwise distance spectrum, rather than the absolute atomic positions. We hence suggest that the presented problem instances should be included in black box optimization benchmark suites.
ISSN:1063-6560
1530-9304
DOI:10.1162/EVCO_a_00086