Conjugate Surrogate for Expensive Multiobjective Optimization

The Kriging surrogate (KS) has been widely used in surrogate-assisted multiobjective evolutionary algorithms (SAMOEAs) for solving expensive multiobjective optimization problems (EMOPs). Typically, when tackling an M-objective EMOP, a KS consists of M Kriging models, in which each model is used to approximate one objective function to replace the expensive fitness evaluation. Since such a KS is only efficient in solving low-dimensional EMOPs, the dimension reduction method has been adopted to construct the reduction surrogate (RS) to reduce training costs. However, both KS and RS can only approximate the mapping from variables to different objectives (i.e., objective function) but ignore the potential relationship between objectives. For practical applications, it is necessary to take into account the mapping between different objectives for the reliability of the surrogate. Therefore, we for the first time propose the concept of the conjugate surrogate (CS) and construct a simple CS to realize the approximated mapping from objectives to objectives. Different from KS or RS, all models in CS are conjugate symbiosis. In collaboration with RS, CS can not only benefit the light training cost, but also improve the convergence speed. Compared with five state-of-the-art SAMOEAs, the CS-assisted algorithm shows its effectiveness and competitiveness in solving EMOPs.