Surrogate-assisted evolutionary biobjective optimization for objectives with non-uniform latencies

We consider multiobjective optimization problems where objective functions have different (or heterogeneous) evaluation times or latencies. This is of great relevance for (computationally) expensive multiobjective optimization as there is no reason to assume that all objective functions should take an equal amount of time to be evaluated (particularly when objectives are evaluated separately). To cope with such problems, we propose a variation of the Kriging-assisted reference vector guided evolutionary algorithm (K-RVEA) called heterogeneous K-RVEA (short HK-RVEA). This algorithm is a merger of two main concepts designed to account for different latencies: A single-objective evolutionary algorithm for selecting training data to train surrogates and K-RVEA's approach for updating the surrogates. HK-RVEA is validated on a set of biobjective benchmark problems varying in terms of latencies and correlations between the objectives. The results are also compared to those obtained by previously proposed strategies for such problems, which were embedded in a non-surrogate-assisted evolutionary algorithm. Our experimental study shows that, under certain conditions, such as short latencies between the two objectives, HK-RVEA can outperform the existing strategies as well as an optimizer operating in an environment without latencies.