A Generative Kriging Surrogate Model for Constrained and Unconstrained Multi-objective Optimization

Surrogate models are effective in reducing the computational time required for solving optimization problems. However, there have been a lukewarm interest in finding multiple trade off solutions for multi-objective optimization problems using surrogate models. The literature on surrogate modeling for constrained optimization problems is also rare. The diffculty lies in the requirement of building and solving multiple surrogate models, one for each Pareto-optimal solution. In this paper, we first provide a brief introduction of the past studies and suggest a computationally fast, Kriging-based, and generative procedure for finding multiple near Pareto optimal solutions in a systematic manner. The expected improvement metric is maximized using a real-parameter genetic algorithm for finding new solutions for high-fidelity evaluations. The approach is computationally fast due to the interlinking of building multiple surrogate models and in its systematic sequencing methodology for assisting one model with another. In standard two and three-objective test problems with and without constraints, our proposed methodology takes only a few hundreds of high-fidelity solution evaluations to find a widely distributed near Pareto optimal solutions compared to the standard EMO methods requiring tens of thousands of high-fidelity solution evaluations. The framework is generic and can be extended to utilize other surrogate modeling methods easily.