An Overview of Weighted and Unconstrained Scalarizing Functions


Scalarizing functions play a crucial role in multi-objective evolutionary algorithms (MOEAs) based on decomposition and the R2 indicator, since they guide the population towards nearly optimal solu- tions, assigning a fitness value to an individual according to a predefined target direction in objective space. This paper presents a general review of weighted scalarizing functions without constraints, which have been proposed not only within evolutionary multi-objective optimization but also in the mathematical programming literature. We also investigate their scalability up to 10 objectives, using the test problems of Lamé Su- perspheres on the MOEA/D and MOMBI-II frameworks. For this pur- pose, the best suited scalarizing functions and their model parameters are determined through the evolutionary calibrator EVOCA. Our expe- rimental results reveal that some of these scalarizing functions are quite robust and suitable for handling many-objective optimization problems.