Designing Scalarizing Functions Using Grammatical Evolution
Amín V. Bernabé Rodríguez, Carlos A. Coello Coello · 2023
In this paper, we present a grammatical evolution-based framework to produce new scalarizing functions, which are known to have a significant impact on the performance of both decomposition-based multi-objective evolutionary algorithms (MOEAs) and indicator-based MOEAs which use R2. We perform two series of experiments using this framework. First, we produce many scalarizing functions using different benchmark problems to explore the behavior of the resulting functions according to the geometry of the problem adopted to generate them. Then, we perform a second round of experiments adopting two combinations of problems which yield better results in some test instances. We present the experimental validation of these new functions compared against the Achievement Scalarizing Function (ASF), which is known to provide a very good performance. For this comparative study, we adopt several benchmark problems and we are able to show that our proposal is able to generate new scalarizing functions that can outperform ASF in different problems.