A Generator for Multimodal Test Functions with Multiple Global Optima

The topic of multimodal function optimization, where the aim is to locate more than one solution, has attracted a growing interest especially in the evolutionary computing research community. To experimentally evaluate the strengths and weaknesses of multimodal optimization algorithms, it is important to use test functions representing different characteristics and of various levels of difficulty. However, the available selection of multimodal test problems with multiple global optima is rather limited at the moment and no general framework exists. This paper describes our attempt in constructing a test function generator to allow the generation of easily tunable test functions. The aim is to provide a general and easily expandable environment for testing different methods of multimodal optimization. Several function families with different characteristics are included. The generator implements new parameterizable function families for generating desired landscapes and a selection of well known test functions from literature, which can be rotated and stretched. The module can be easily imported to any optimization algorithm implementation compatible with C programming language.

[1]  Alain Pétrowski,et al.  A clearing procedure as a niching method for genetic algorithms , 1996, Proceedings of IEEE International Conference on Evolutionary Computation.

[2]  William H. Press,et al.  Numerical Recipes in C, 2nd Edition , 1992 .

[3]  Edmund K. Burke,et al.  Parallel Problem Solving from Nature - PPSN IX: 9th International Conference, Reykjavik, Iceland, September 9-13, 2006, Proceedings , 2006, PPSN.

[4]  Zbigniew Michalewicz,et al.  Genetic Algorithms + Data Structures = Evolution Programs , 1992, Artificial Intelligence.

[5]  Marcus Gallagher,et al.  A general-purpose tunable landscape generator , 2006, IEEE Transactions on Evolutionary Computation.

[6]  Zbigniew Michalewicz,et al.  Test-case generator for nonlinear continuous parameter optimization techniques , 2000, IEEE Trans. Evol. Comput..

[7]  Ronald W. Morrison,et al.  Designing Evolutionary Algorithms for Dynamic Environments , 2004, Natural Computing Series.

[8]  Samir W. Mahfoud.  Niching methods for genetic algorithms , 1996 .

[9]  R. K. Ursem.  Multinational evolutionary algorithms , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

[10]  Ralph R. Martin,et al.  A Sequential Niche Technique for Multimodal Function Optimization , 1993, Evolutionary Computation.

[11]  Georges R. Harik,et al.  Finding Multimodal Solutions Using Restricted Tournament Selection , 1995, ICGA.

[12]  Nikolaus Hansen,et al.  Completely Derandomized Self-Adaptation in Evolution Strategies , 2001, Evolutionary Computation.

[13]  Jürgen Branke,et al.  Evolutionary Optimization in Dynamic Environments , 2001, Genetic Algorithms and Evolutionary Computation.

[14]  Zbigniew Michalewicz,et al.  Evolutionary Computation 1 , 2018 .

[15]  William H. Press,et al.  Numerical Recipes in Fortran 77: The Art of Scientific Computing 2nd Editionn - Volume 1 of Fortran Numerical Recipes , 1992 .

[16]  Yaroslav D. Sergeyev,et al.  Algorithm 829: Software for generation of classes of test functions with known local and global minima for global optimization , 2003, TOMS.

[17]  William H. Press,et al.  Numerical recipes in C , 2002 .

[18]  R.W. Morrison,et al.  A test problem generator for non-stationary environments , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

[19]  Samir W. Mahfoud.  A Comparison of Parallel and Sequential Niching Methods , 1995, ICGA.

[20]  David E. Goldberg,et al.  Genetic Algorithms with Sharing for Multimodalfunction Optimization , 1987, ICGA.

[21]  K. Dejong,et al.  An analysis of the behavior of a class of genetic adaptive systems , 1975 .

[22]  D. Wolpert,et al.  No Free Lunch Theorems for Search , 1995 .

[23]  Kalyanmoy Deb,et al.  Comparison of multi-modal optimization algorithms based on evolutionary algorithms , 2006, GECCO.

[24]  P. John Clarkson,et al.  A Species Conserving Genetic Algorithm for Multimodal Function Optimization , 2002, Evolutionary Computation.

[25]  Ofer M. Shir,et al.  Niche Radius Adaptation in the CMA-ES Niching Algorithm , 2006, PPSN.