A Comparison-Relationship-Surrogate Evolutionary Algorithm for Multi-Objective Optimization

Evolutionary algorithms often struggle to find high-quality solutions to multi-objective optimization problems on a limited budget of function evaluations (here, a few hundred). A promising direction to improve the efficiency of these methods is to augment the objective functions with a data-driven surrogate model. These ``surrogate-assisted'' optimization algorithms can achieve better solutions than conventional algorithms for the same number of function evaluations on a wide variety of test problems. In this work, we continue to explore the area of surrogate-assisted multi-objective optimization by introducing and testing an algorithm driven by a new type of surrogate model: a comparison-relationship-surrogate model. This model predicts the truth values of the comparison operator evaluated on the objective functions for two candidate solutions. These predictions can be used to infer the domination relationships that power the non-dominated sorting mechanism used by many multi-objective genetic algorithms to select fit individuals. Several numerical experiments are performed on this algorithm using well-known test suites plus a real-world problem from the field of accelerator physics. Statistical analysis of the results demonstrates that the new algorithm can, on average, achieve better-converged solutions to many medium-scale, biobjective problems than existing state-of-the-art methods for a limited budget of function evaluations.