Analyzing convergence performance of evolutionary algorithms: A statistical approach

• Convergence analysis is presented for analyzing evolutionary algorithms’ performance.
• Convergence testing is performed by using the nonparametric Page test.
• An alternative is provided for experiments including functions with reachable optima.
• A case of study is included, demonstrating the uses of the tests.

The analysis of the performance of different approaches is a staple concern in the design of Computational Intelligence experiments. Any proper analysis of evolutionary optimization algorithms should incorporate a full set of benchmark problems and state-of-the-art comparison algorithms. For the sake of rigor, such an analysis may be completed with the use of statistical procedures, supporting the conclusions drawn.In this paper, we point out that these conclusions are usually limited to the final results, whereas intermediate results are seldom considered. We propose a new methodology for comparing evolutionary algorithms’ convergence capabilities, based on the use of Page’s trend test. The methodology is presented with a case of use, incorporating real results from selected techniques of a recent special issue. The possible applications of the method are highlighted, particularly in those cases in which the final results do not enable a clear evaluation of the differences among several evolutionary techniques.