Classifying Metamodeling Methods for Evolutionary Multi-objective Optimization: First Results

In many practical optimization problems, evaluation of objectives and constraints often involve computationally expensive procedures. To handle such problems, a metamodel-assisted approach is usually used to complete an optimization run in a reasonable amount of time. A metamodel is an approximate mathematical model of an objective or a constrained function which is constructed with a handful of solutions evaluated exactly. However, when comes to solving multi-objective optimization problems involving numerous constraints, it may be too much to metamodel each and every objective and constrained function independently. The cumulative effect of errors from each metamodel may turn out to be detrimental for the accuracy of the overall optimization procedure. In this paper, we propose a taxonomy of various metamodeling methodologies for multi-objective optimization and provide a comparative study by discussing advantages and disadvantages of each method. The first results presented in this paper are obtained using the well-known Kriging metamodeling approach. Based on our proposed taxonomy and an extensive literature search, we also highlight new and promising methods for multi-objective metamodeling algorithms.