Multi-Objective Bayesian Optimization using Deep Gaussian Processes with Applications to Copper Smelting Optimization

Copper smelting is a complex industrial process that involves a lot of long procedures and inter-process connections. Moreover, there are non-stationary, noisy, and multi-objective challenges in copper smelting optimization. The traditional methods of process optimization rely on experience to adjust repeatedly, which is time-consuming and laborious, as well as difficult to find the optimal point. Bayesian optimization is an effective method to discover the optimal point of an expensive black-box function using few samples. In this paper, Bayesian optimization is introduced to solve the copper smelting optimization problem. The surrogate model is constructed based on noisy deep Gaussian processes to cope with the non-stationary process and observational noise of copper smelting. Then, the expected hypervolume improvement is used as the acquisition function, considering multiple objectives when selecting the new sampling point. We conduct experiments on standard test functions and a simulation model of copper flash smelting. The experimental results demonstrate that the proposed method performs well in terms of convergence and diversity.