HappyCat - A Simple Function Class Where Well-Known Direct Search Algorithms Do Fail

A new class of simple and scalable test functions for unconstrained real-parameter optimization will be proposed. Even though these functions have only one minimizer, they yet appear difficult to be optimized using standard state-of-the-art EAs such as CMA-ES, PSO, and DE. The test functions share properties observed when evolving at the edge of feasibility of constraint problems: while the step-sizes (or mutation strength) drops down exponentially fast, the EA is still far way from the minimizer giving rise to premature convergence. The design principles for this new function class, called HappyCat, will be explained. Furthermore, an idea for a new type of evolution strategy, the Ray-ES, will be outlined that might be able to tackle such problems.

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