Search Process Analysis of Multiobjective Evolutionary Algorithms using Convergence-Diversity Diagram

Many tasks in the real world are multi-objective optimization problems (MOPs). Population-based approaches are promising for solving MOPs. In particular, multi-objective evolutionary algorithms (MOEAs) are popular and have been actively studied over the last two decades. However, since it is not easy to directly display and compare multi-dimensional solution sets, it is difficult to analyze the search process of MOEAs using direct visualization techniques such as scatter plots. This paper proposes an analytical method to compare multiple search processes in terms of convergence and diversity by extending the authors' previous work, i.e., Convergence-Diversity Diagram. Through computational experiments, the proposed method reveals characteristics and similarities in three representative MOEAs and six test problems. In addition, this paper provides discussions on algorithm design, biases in the DTLZ test suite, and the improvement of visualization based on experimental results.