Semi-supervised learning assisted particle swarm optimization of computationally expensive problems

In many real-world optimization problems, it is very time-consuming to evaluate the performance of candidate solutions because the evaluations involve computationally intensive numerical simulations or costly physical experiments. Therefore, standard population based meta-heuristic search algorithms are not best suited for solving such expensive problems because they typically require a large number of performance evaluations. To address this issue, many surrogate-assisted meta-heuristic algorithms have been proposed and shown to be promising in achieving acceptable solutions with a small computation budget. While most research focuses on reducing the required number of expensive fitness evaluations, not much attention has been paid to take advantage of the large amount of unlabelled data, i.e., the solutions that have not been evaluated using the expensive fitness functions, generated during the optimization. This paper aims to make use of semi-supervised learning techniques that are able to enhance the training of surrogate models using the unlabelled data together with the labelled data in a surrogate-assisted particle swarm optimization algorithm. Empirical studies on five 30-dimensional benchmark problems show that the proposed algorithm is able to find high-quality solutions for computationally expensive problems on a limited computational budget.