A Multiobjective Test Suite with Hexagon Pareto Fronts and Various Feasible Regions

The performance of a Multiobjective Evolutionary Algorithm (MOEA) for many-objective optimization is often evaluated by multiobjective scalable test problems like DTLZ and WFG problems. This is because the scalable test problems are quite useful for an MOEA analysis. However, the scalable test problems do not have enough diversity of the shapes of the Pareto front and the feasible region to evaluate the capability of MOEAs. Previous studies showed that these shapes have a great impact on the performance of MOEAs. Thus, MOEAs should be evaluated on more test problems with different shapes of the Pareto front and the feasible region. In this study, the shapes of the Pareto front in the existing scalable test problems are examined from some viewpoints such as the distribution of optimal or worst solutions for each objective and the degree of the correspondence with the distribution of the weight vectors. The shape of the feasible region is also examined from the viewpoint of the spread of an initial population and the existence of dominance resistant solutions. According to the observations, we propose new shapes of the Pareto front and the feasible region to design a new scalable test suite. Experimental results show that the proposed test suite has totally different properties from the existing test problems.