Average rank domination relation for NSGAII and SMPSO algorithms for many-objective optimization

The paper introduces the average rank dominance relation that substitutes the Pareto domination relation for many objective optimization. The relation is based on the performances of the solutions in each objective and calculated as the average rank of the solutions on each objective. In addition, the paper studies substituting the Pareto domination relation by this domination relation in the well known multi-objective algorithms NSGAII and SMPSO respectively based on the genetic and particle swarm optimization. The new algorithms are tested on the first four problems of DTLZ family and compared to the original algorithms via new performance indicators. The indicators are constructed so that they measure convergence and spread of the solutions and can be easily computed for high objectives number (≫ 3).