Bayesian Approaches to Surrogate-Assisted Evolutionary Multi-objective Optimization: A Comparative Study

Both evolutionary Bayesian optimization (EBO) and Bayesian evolutionary optimization (BEO) are used to solve time-consuming optimization problems, where in the EBO method, the evolutionary algorithm is adopted to optimize the acquisition function for finding its optimal solution to be evaluated using the time consuming objective functions, while in the BEO approach, surrogates are utilized to replace the expensive objective functions and the acquisition function is used in the model management to choose individuals for evaluations using the expensive objective functions. In this paper, we perform comparisons on these two approaches to see which method is better for solving computationally expensive multi-objective problems. The expected improvement (EI) is used as the acquisition function in both EBO and BEO approaches. Two strategies are proposed to select individuals to be evaluated using the real computationally expensive objectives. The experimental results conducted on ZDT and DTLZ test problems showed that the BEO approach is more efficient than the EBO approach for solving multi-objective problems.