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M. Gaviano, D. E. Kvasov, D. Lera and Y. D. Sergeyev, “Algorithm 829: Software for Generation of Classes of Test Functions with Known Local and Global Minima for Global Optimization,” ACM Transactions on Mathematical Software, Vol. 29, No. 4, 2003, pp. 469-480. doi:10.1145/962437.962444

has been cited by the following article:

• TITLE: Empirical Review of Standard Benchmark Functions Using Evolutionary Global Optimization

  AUTHORS: Johannes M. Dieterich, Bernd Hartke

  KEYWORDS: Optimization; Genetic Algorithms; Benchmark Functions; Dimensionality Scaling; Crossover Operators

  JOURNAL NAME: Applied Mathematics, Vol.3 No.10A, November 1, 2012

  ABSTRACT: We have employed a recent implementation of genetic algorithms to study a range of standard benchmark functions for global optimization. It turns out that some of them are not very useful as challenging test functions, since they neither allow for a discrimination between different variants of genetic operators nor exhibit a dimensionality scaling resembling that of real-world problems, for example that of global structure optimization of atomic and molecular clusters. The latter properties seem to be simulated better by two other types of benchmark functions. One type is designed to be deceptive, exemplified here by Lunacek’s function. The other type offers additional advantages of markedly increased complexity and of broad tunability in search space characteristics. For the latter type, we use an implementation based on randomly distributed Gaussians. We advocate the use of the latter types of test functions for algorithm development and benchmarking.