On Reference Set Selection for Constrained Multiobjective Optimization Problems

The Pareto set and Pareto front of a continuous multiobjective optimization problem typically contain infinitely many solutions. Since dealing with infinite sets is impractical, they are commonly approximated by finite reference sets. In this way, the performance of multiobjective optimization algorithms can be assessed using quality indicators. However, the selection of a reference set depends on the intended goal, such as achieving a uniform distribution of solutions along the Pareto set or Pareto front, or optimizing a specific quality indicator. In this paper, we investigate and compare six strategies for reference set construction in constrained bi-objective problems from a recently proposed test problem generator. The approaches are evaluated with respect to multiple quality indicators and computational cost. The experiments are performed on test problems with irregular Pareto sets and fronts. From these experiments, we conclude that the choice of strategy should depend on the intended goal, with the approach that aims to maximize the hypervolume indicator value standing out as the best trade-off in terms of speed and indicator accuracies.