Surrogate-Assisted Multi-Objective Optimization for Handling Objectives with Heterogeneous Evaluation Times: Unconstrained Problems

Balija Santoshkumar, Kalyanmoy Deb

Abstract: Surrogates are commonly used in single and multi-objective optimization studies for quickly evaluating objective functions which are otherwise expensive to evaluate. Starting with a set of high-fidelity evaluated solutions, optimization algorithms generate new in-fill solutions for further high-fidelity evaluations to improve the previous surrogate models towards the optimal regions of the search space. In terms of evaluating in-fill solutions, most current optimization algorithms must evaluate all objectives using high-fidelity means, irrespective of relative differences in their evaluation times. In this paper, we address the issue of handling objective functions having heterogeneous high-fidelity evaluation times and propose a framework which combines evaluation time and surrogate accuracy of each objective to decide which population members should undergo a high-fidelity evaluation and for which objectives. Our proposed approach deals with heterogeneously evaluated solutions - some objectives with high-fidelity and some with surrogates - in a generic way. Initial results on a number of two and three-objective problems, presented in this paper, show promise for approach and encourages to launch a deeper study on more complex and constrained problems.