Metamodeling for multimodal selection functions in evolutionary multi-objective optimization

Most real-world optimization problems involve computationally expensive simulations for evaluating a solution. Despite significant progress in the use of metamodels for single-objective optimization, metamodeling methods have received a lukewarm attention for multi-objective optimization. A recent study classified various metamodeling approaches, of which one particular method is interesting, challenging, and novel. In this paper, we study this so-called M6 method in detail. In this approach, a selection operator's assignment function, as it is implemented in an evolutionary multi-objective optimization (EMO) algorithm, is directly metamodeled. Thus, this methodology requires only one selection function to be metamodeled irrespective of multitude of objective and constraint functions in a problem. However, the flip side of the methodology is that the resulting function is multimodal having a different optimum for every desired Pareto-optimal solution. We have used two different selection functions based on two recent ideas: (i) KKT proximity measure function and (ii) multimodal based evolutionary multi-objective (MEMO) selection function. The resulting meta-modeling methods are applied to a number of standard two and three-objective constraint and unconstrained test problems. Near Pareto-optimal solutions are found using only a fraction of high-fidelity solution evaluations compared to usual EMO applications.