Approximating Multiobjective Optimization Problems with Complex Pareto Fronts

The main goal of multiobjective optimization is to achieve a set of well-converged and evenly-distributed Pareto optimal points. While evolutionary algorithms have been reported to converge well, their distribution performance might not be as uniform as we expected, especially when the problems to be optimized involve complex Pareto fronts. In this paper, with the aid of a set of uniformly-distributed reference points, multiobjective optimization problems (MOPs) can be handled by minimizing least reference distances (LRD), which measure the proximity of solutions to their nearest reference points. This way, the uniformity of approximated solutions is implicitly controlled by the reference point set, and convergence is in the charge of LRD. The proposed LRD algorithm (LRDA) is tested and compared with several popular algorithms on a number of old and newly-developed MOPs that have complex Pareto fronts, showing that this method is very promising to obtain evenly-distributed Pareto optimal points for the problems considered in this paper.