Study of the approximation of the fitness landscape and the ranking process of scalarizing functions for many-objective problems

Although surrogate models have been successfully adopted by evolutionary algorithms to solve time-consuming multiobjective problems, their use has been confined to solving problems with a low number of objectives. On the other hand, scalarizing functions have proved to work well with many-objective problems. This paper presents a novel study on many-objective optimization concerning the use of surrogate models to approximate both (1) the fitness landscape of traditional multiobjective approaches and (2) the ranking relation imposed by such approaches. Our methodology involves a thorough comparison of four popular surrogate modeling techniques in order to approximate the fitness landscape and the ranking relations of three different scalarizing functions. Additionally, we explored the interactions of these methods through four well-known scalable test problems with four, six, eight, and ten objectives. Besides finding that Tchebycheff scalarizing function and Gaussian processes for machine learning are accurate methods to handle many-objective problems, one of our most important findings involves the capabilities of metamodeling techniques to approximate the ranking procedure from the information gathered from the parameter space. Such a capability can be effectively used for pre-screening purposes on MOEAs.

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