ACM Transactions on Graphics (TOG)
Global Optimization on Funneling Landscapes
Journal of Global Optimization
Spin-flip symmetry and synchronization
Evolutionary Computation
Benchmarking a BI-population CMA-ES on the BBOB-2009 noisy testbed
Proceedings of the 11th Annual Conference Companion on Genetic and Evolutionary Computation Conference: Late Breaking Papers
Benchmarking the nelder-mead downhill simplex algorithm with many local restarts
Proceedings of the 11th Annual Conference Companion on Genetic and Evolutionary Computation Conference: Late Breaking Papers
Particle swarm CMA evolution strategy for the optimization of multi-funnel landscapes
CEC'09 Proceedings of the Eleventh conference on Congress on Evolutionary Computation
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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 geometry optimization or packing problems, 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 tunable 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: isospectral symmetry. 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.