On the Evaluation of the Quality of Non-dominated Sets


There are many published multi-objective evolutionary algorithms (also known as MOEAs). A natural question is what algorithm performs better? If we ignore other factors such as computational complexity, the evaluation of the performance of a MOEA only depends on the output of the algorithm. The output of a MOEA is a set of vectors (usually known as non-dominated sets) with some special properties derived from the Pareto Optimality Cri- teria (POC). Unfortunately, evaluating and comparing these non-dominated sets is not an easy task and is an open research problem. Many performance measures have been proposed in the past, but they are sensitive to misleading cases and sometimes, hard to use. Some theoret- ical studies have been developed in order to determine what we want from a good performance measure. Unfortunately, many of the performance mea- sures derived from those studies are too conservative and have a very limited capacity to distinguish between good and bad sets. The goal of this thesis is to analyze the problem and introduce a new method for the evaluation of non-dominated sets, named G-Ranker. The G-Ranker is designed having in mind most of the desired properties of a non-dominated set, needs no extra information about the multi-objective problem and is more robust to misleading cases compared to other methods. Also, we introduce a set of test cases to evaluate the effectiveness of a performance measure. The results of the experiments demonstrate the supe- riority of the G-Ranker with respect to state-of-the-art approaches reported in specialized literature.