A Taxonomy for Metamodeling Frameworks for Evolutionary Multiobjective Optimization

One of the main difficulties in applying an optimization algorithm to a practical problem is that evaluation of objectives and constraints often involve computationally expensive procedures. To handle such problems, a metamodel is first formed from a few exact (high-fidelity) solution evaluations and then optimized by an algorithm in a progressive manner. However, in solving multiobjective or many-objective optimization problems involving multiple constraints, a simple extension of the idea to form one metamodel for each objective and constraint function may not constitute the most efficient approach. 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 different plausible metamodeling frameworks for multiobjective and many-objective optimization and provide a comparative study by discussing advantages and disadvantages of each framework. The results presented in this paper are obtained using the well-known Kriging metamodeling approach. Based on our extensive simulation studies on proposed frameworks, we report intriguing observations about the behavior of each framework, which may provide salient guidelines for further studies in this emerging area within evolutionary multiobjective optimization.