Abstract Interactive multiobjective optimization methods have proven promising in solving optimization problems with conflicting objectives since they iteratively incorporate preference information of a decision maker in the search for the most preferred solution. To find the appropriate interactive method for various needs involves analysis of the strengths and weaknesses. However, extensive analysis with human decision makers may be too costly and for that reason, we propose an artificial decision maker to compare a class of popular interactive multiobjective optimization methods, i.e., reference point based methods. Without involving any human decision makers, the artificial decision maker works automatically to interact with different methods to be compared and evaluate the final results. It makes a difference between a learning phase and a decision phase, that is, learns about the problem based on information acquired to identify a region of interest and refines solutions in that region to find a final solution, respectively. We adopt different types of utility functions to evaluation solutions, present corresponding performance indicators and propose two examples of artificial decision makers. A series of experiments on benchmark test problems and a water resources planning problem is conducted to demonstrate how the proposed artificial decision makers can be used to compare reference point based methods.

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.