Ranking and comparing evolutionary algorithms with Hellinger-TOPSIS

When multiple algorithms are applied to multiple benchmarks as it is common in evolutionary computation, a typical issue rises, how can we rank the algorithms? It is a common practice in evolutionary computation to execute the algorithms several times and then the mean value and the standard deviation are calculated. In order to compare the algorithms performance it is very common to use statistical hypothesis tests. In this paper, we propose a novel alternative method based on the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) to support the performance comparisons. In this case, the alternatives are the algorithms and the criteria are the benchmarks. Since the standard TOPSIS is not able to handle the stochastic nature of evolutionary algorithms, we apply the Hellinger-TOPSIS, which uses the Hellinger distance, for algorithm comparisons. Case studies are used to illustrate the method for evolutionary algorithms but the approach is general. The simulation results show the feasibility of the Hellinger-TOPSIS to find out the ranking of algorithms under evaluation.