Handling Objectives With Heterogeneous Evaluation Times in Surrogate-Assisted Evolutionary Multi-Objective Optimization

Many practical optimization problems involve multiple objectives involving heterogeneous evaluation times. To handle such problems, most evolutionary multi-and many-objective optimization (EMO/EMaO) algorithms do not take into account the heterogeneity in evaluation times, rather they execute a high-fidelity evaluation of all objectives for promising population members identified by the associated surrogate-assisted optimization algorithm. Although this provides a complete and error-free evaluation of a solution, we argue that such an approach may not produce the most computationally efficient procedure. This paper proposes a probabilistic ranking procedure for determining which population member and which objective functions are to be high-fidelity evaluated so that they would produce the best chance of improving convergence and diversity preservation within an EMO/EMaO generation. The ranking metric uses three properties of a population member: (i) relative evaluation times, (ii) the probability of the member being non-dominated in its neighborhood, and (iii) each objective’s surrogate prediction error. Details of the resulting heterogeneous EMO (HET-EMO) algorithm are presented with pseudo-codes, sketches, and discussions. Thereafter, results of HET-EMO are compared with four state-of-the-art surrogate-assisted EMOs, including the one that handles heterogeneity in evaluation times and an original EMO (without any surrogate) on a total of 234 test and engineering problem instances having two to eight-objectives. Results indicate superior performance of HET-EMO, indicating the effectiveness of the proposed procedure. The paper also raises several future research directions demonstrating the need and motivation for further studies on the topic.