Genetically controlled random search: a global optimization method for continuous multidimensional functions

A new stochastic method for locating the global minimum of a multidimensional function inside a rectangular hyperbox is presented. A sampling technique is employed that makes use of the procedure known as grammatical evolution. The method can be considered as a “genetic” modification of the Controlled Random Search procedure due to Price. The user may code the objective function either in C++ or in Fortran 77. We offer a comparison of the new method with others of similar structure, by presenting results of computational experiments on a set of test functions.Program summaryTitle of program: GenPriceCatalogue identifier:ADWPProgram summary URL:http://cpc.cs.qub.ac.uk/summaries/ADWPProgram available from: CPC Program Library, Queen's University of Belfast, N. IrelandComputer for which the program is designed and others on which it has been tested: the tool is designed to be portable in all systems running the GNU C++ compilerInstallation: University of Ioannina, GreeceProgramming language used: GNU-C++, GNU-C, GNU Fortran-77Memory required to execute with typical data: 200 KBNo. of bits in a word: 32No. of processors used: 1Has the code been vectorized or parallelized?: noNo. of lines in distributed program, including test data, etc.:13 135No. of bytes in distributed program, including test data, etc.: 78 512Distribution format: tar. gzNature of physical problem: A multitude of problems in science and engineering are often reduced to minimizing a function of many variables. There are instances that a local optimum does not correspond to the desired physical solution and hence the search for a better solution is required. Local optimization techniques are frequently trapped in local minima. Global optimization is hence the appropriate tool. For example, solving a nonlinear system of equations via optimization, employing a “least squares” type of objective, one may encounter many local minima that do not correspond to solutions, i.e. minima with values far from zero.Method of solution: Grammatical Evolution is used to accelerate the process of finding the global minimum of a multidimensional, multimodal function, in the framework of the original “Controlled Random Search” algorithm.Typical running time: Depending on the objective function.