A New Approach to Building the Gaussian Process Model for Expensive Multi-objective Optimization

A novel approach to building a Gaussian process (GP) model for each objective more precisely is proposed in this study for expensive multi-objective optimization, where there may be little apparent similarity or correlation among objectives. These objectives are mapped to tasks where a similarity or correlation exists among them, and then these tasks are used to build the GP model jointly using multi-task GP (MTGP). This approach facilitates a mutual knowledge transfer across tasks and helps avoid tabula rasa learning for a new task and capture the structure in tasks that covary. The estimated value for each objective can be derived from the estimated values of the built MTGP model of the tasks with a reverse mapping. It also has been shown that the GP models of the well-known MOEA/D-EGO and ParEGO are both special cases of our approach. To solve the expensive multi-objective optimization problem, a multi-objective optimization framework based on this approach with MOEA/D is also developed. Experimental results show that the proposed algorithm performs better than several state-of-the-art multi-objective evolutionary algorithms.