A Simplex-Crossover-Based Multi-Objective Evolutionary Algorithm

Abstract

The key issue for an efficient and reliable multi-objective evolutionary algorithm 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, and a novel mutation operator, the Shrink-Mutation. GeDEM operator was left unchanged and completed using the non-dominated-sorting based on crowding distance. The comparison among GeDEA-II and GeDEA, as well as with three other modern elitist methods, on different extremely multidimensional test problems, clearly indicates that the performance of GeDEA-II is, at least in these cases, superior. In addition, authors aimed at putting in evidence the very good performance of GeDEA-II even in extremely multidimensional landscapes. To do this, four test problems were considered, and the GeDEA-II performance tested as the number of decision variables was increased. In particular, ZDT test functions featured a number of decision variables ranging from the original proposed number up to 1,000, whereas on DTLZ the decision variables were increased up to 100 times the original proposed number. Results obtained contribute to demonstrate further the GeDEA-II breakthrough performance.