Surrogate-based Distributed Optimisation for Expensive Black-box Functions

This paper considers distributed optimisation problems with black-box functions using surrogate-assisted methods. Since the cost functions and their derivatives are usually impossible to be expressed by explicit functions due to the complexity of modern systems, function calls have to be performed to obtain those values. Moreover, the cost functions are often expensive to evaluate, and therefore designers prefer to reduce the number of evaluations. In this paper, surrogate-based methods are utilised to approximate the true functions, and conditions for constructing smooth and convex surrogates are established, by which the requirements for explicit functions are eliminated. To improve the quality of surrogate models, a distance-based infill strategy is proposed to balance the exploitation and exploration, which guarantees the density of the decision sequence in a compact set. Then, a distributed optimisation algorithm is developed to solve the reformulated auxiliary sub-problems, and the convergence of the proposed algorithm is established via Lyapunov theory. Simulation examples are provided to validate the effectiveness of the theoretical development and demonstrate the potential significance of the framework.