A survey on the global optimization problem using Kruskal–Wallis test

Abstract

The article deals with experimental comparison and verification of stochastic algorithms for global optimization while searching the global optimum in dimensions 3 and 4 of selected testing functions in Matlab computing environment. To draw a comparison, we took the algorithms Controlled Random Search, Differential Evolution that we created for this test and implemented in Matlab, and fminsearch function which is directly built in Matlab. The basic quantities to compare algorithms were time complexity while searching the considered area and reliability of finding the global optimum of the 1st De Jong function, Rosenbrock’s saddle, Ackley’s function and Griewangk’s function. The time complexity of the algorithms was determined by the number of test function evaluations during the global optimum search and we analysed the results of the experiment using the “Kruskal–Wallis test” non-parametric method.