Authors:
Christian L. Müeller
and
Ivo F. Sbalzarini
Affiliation:
ETH Zurich, Switzerland
Keyword(s):
Benchmark, Multi-funnel landscape, Lennard-Jones cluster, CMA-ES, Parallel island model.
Related
Ontology
Subjects/Areas/Topics:
Artificial Intelligence
;
Computational Intelligence
;
Concurrent Co-Operation
;
Evolution Strategies
;
Evolutionary Computing
;
Soft Computing
;
Swarm Intelligence
Abstract:
A common shortcoming in the Evolutionary Computation (EC) community is that the publication of many search heuristics is not accompanied by rigorous benchmarks on a balanced set of test problems. A welcome effort to promote such test suites are the IEEE CEC competitions on real-valued black-box optimization. These competitions prescribe carefully designed synthetic test functions and benchmarking protocols. They do, however, not contain tunable real-world examples of the important class of multi-funnel functions. We argue that finding minimum-energy configurations of 38-atom Lennard-Jones (LJ38) clusters could serve as such a benchmark for real-valued, single-objective evolutionary optimization. We thus suggest that this problem be included in EC studies whenever general-purpose optimizers are proposed. The problem is tunable from a single-funnel to a double-funnel topology. We show that the winner of the CEC 2005 competition, the Evolution Strategy with Covariance Matrix Adaptation
(CMA-ES), works on the single-funnel version of this test case, but fails on the double-funnel version. We further argue that this performance loss of CMA-ES can be relaxed by using parallel island models. We support this hypothesis by simulation results of a parallel island CMA-ES, the Particle Swarm CMA-ES, on a subset of the multi-funnel functions in the CEC 2005 benchmark.
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