A Simplex Crossover based evolutionary algorithm including the genetic diversity as objective

The key issue for an efficient and reliable multi-objective evolutionary algorithm (MOEA) is the ability to converge to the True Pareto Front with the least number of objective function evaluations, while covering it as much as possible. To this purpose, in a previous paper performance comparisons showed that the Genetic Diversity Evolutionary Algorithm (GeDEA) was at the same level of the best state-of-the-art MOEAs due to it intrinsic ability to properly conjugate exploitation of current non-dominated solutions and the exploration of the search space. In this paper, an improved version, namely the GeDEA-II, is proposed which features a novel crossover operator, the Simplex-Crossover (SPX), and a novel mutation operator, the Shrink-Mutation. Genetic Diversity Evaluation Method (GeDEM) operator was left unchanged and completed using the non-dominated-sorting based on crowding distance. The performance of the GeDEA-II was tested against other different state-of-the-art MOEAs, following a well-established procedure already used in other previous works. When compared to the original proposed test problems, the number of decision variables was increased and the number of generations left to the algorithms was intentionally reduced in order to test the convergence performance of the MOEAs. GeDEA-II and competitors were executed 30 times on each proposed test problem. The final approximation set reached by each algorithm was represented in the objective function space, and the performance, measured in terms of hypervolume indicator, reported in dedicated box plots. Finally, authors aimed at putting in evidence the excellent performance of GeDEA-II on the same test problems, by increasing the decision variables up to 100 times the original proposed number. Results clearly indicates that the performance of GeDEA-II is, at least in these cases, superior. (C) 2012 Elsevier B.V. All rights reserved.