A Statistical Scheme to Support Performance Comparisons between Different Designs of Evolutionary Algorithms

Evolutionary algorithms are stochastic heuristics which can optimize over special functions, known as fitness functions, by manipulating the structure (genotype) of candidate solutions known as individuals. Because of its stochastic nature, this class of algorithms is expected to have different performances when dealing with the same problem, depending on random initial conditions and random decisions taken during execution time, even when converging to proximal solutions. Also, other important factor to a better performance relies on proper designs of the algorithm's steps, its genetic operators, individual representation and the fitness function itself. This work proposes a statistical approach to enable performance comparisons between different evolutionary algorithm designs to the same problem. To help with the design decision process, the statistical hypothesis test for difference of means is performed in order to achieve decision matrices. The concept of Pareto's “statistical dominance” (defined in this work) is useful to point out which variation of design is more appropriated for the problem in question. A case study is presented in this work, an application for computer automated exterior lighting design. It has some concurrent objectives to be optimized: four possible metrics to illumination quality and two possible metrics for energy efficiency. The present statistical scheme was successful in indicating a more appropriate formulation for the multi-objective fitness function in need.