Verification of Applicability of MOEAs to Many-Objective GP Problem

In this paper, an trial application on Multi-Objective Evolutionary Algorithms (MOEAs) to a Many-Objective Genetic Programming (MaOGP) Problem and their effectiveness verification. In several works, Multi-Objective GP (MOGP) using MOEAs is effective on such a function estimation problem for the cutting process of steel, a modeling of a non-linear systems and a truss optimization. However, their targets are two or three objective GP problems. There is not many researches on GP problems with more than four objectives, or MaOGP. Recent studies have reported that MOEAs are inappropriate for Many-Objecitve Optimization Problems (MaOPs), which includes four or more objectives. Although MOEA/D and NSGA-III, which are one of MaOEA, are known as effective algorithms for MaOPs, these algorithms, for example, require an many scalarization vectors or appropriate reference set to obtain a Pareto front that is widely and evenly distributed, they are not always easy to apply to real world problems. The MaOEAs are actually very sensitive techniques to the vectors or the reference set in the real problems. On the other hand, although it has been pointed out that MOEAs are not suitable for MaOP in verification reports with several benchmarks, there is no fact that MOEAs have been applied to MaOGP problems and their effectiveness has been denied. Therefore, this paper tries to apply MOEAs, NSGA-II and SPEA2, to a test MaOGP problem and verify their effectiveness. Since we can easily change the difficulty and/or also parameters such as the number of objectives of the test problem, it is also expected to contribute to MaOGP research in the future.