Abstract
Solving many-objective optimization problems is challenging due to the increase in the number of objectives. The challenges include the increased complexity in the structure of the Pareto front, the increased number of solutions needed to represent the Pareto front, and the selection of solutions. Many-objective optimization becomes even more challenging when they are expensive and must be solved with the assistance of surrogates. This chapter introduces three surrogate-assisted many-objective optimization algorithms, where the surrogates are used to approximate the objective functions or distinguish between nominated and non-dominated solutions. The benefit of the latter is that it needs to build only one surrogate regardless of the number of objectives. The last algorithm presented in this Chapter adopts a dropout neural network to predict the fitness and estimate the uncertainty of the fitness predictions. Compared to the Gaussian process, dropout neural networks are scalable to the increase in the number of decision variables and the number of objectives, and are more suited to incremental learning, making it particularly attractive for solving high-dimensional many-objective expensive optimization problems.