Analyzing Limited Size Archivers of Multi-objective Optimizers

In the context of multi-objective optimization, where there may be many optimal incomparable solutions, most of the optimizers maintain a limited repository, to keep the objective vectors of the solutions found during the execution. There are several methods to decide which vectors remain in that limited size archive, and these different techniques may have properties that guarantee the diversity and quality of their outcomes. This paper examines some of those strategies, analyzing their properties, and comparing empirically their outputs based on two quality indicators, additive epsilon and hypervolume. Most of the archiving techniques studied in this work cannot ensure that at the end of the process their vectors are all optimal. Due to this fact, a new approach is presented, based on a second archive to store the points which would be discarded. The main idea is verify how much the recycled vectors could improve the generated set. In the realized tests, the method had not a significant time cost regardless the adopted archiving technique.