A cooperative approach to efficient global optimization

The efficient global optimization (EGO) algorithm is widely used for solving expensive optimization problems, but it has been frequently criticized for its incapability of solving high-dimensional problems, i.e., problems with 100 or more variables. Extending the EGO algorithm to high dimensions encounters two major challenges: the training time of the Kriging model goes up rapidly and the difficulty of solving the infill optimization problem increases exponentially as the dimension of the problem increases. In this work, we propose a simple and efficient cooperative framework to tackle these two problems simultaneously. In the proposed framework, we first randomly decompose the original high-dimensional problem into several sub-problems, and then train the Kriging model and solve the infill optimization problem for each sub-problem. Context vectors are used to link the sub-problems such that the Kriging models are trained and the infill optimization problems are solved in a cooperative way. Once all the sub-problems have been solved, we start another random decomposition again and repeat the divide-and-conquer process until the computational budget is reached. Experiment results show that the proposed cooperative approach can bring nearly linear speedup with respect to the number of sub-problems. The proposed approach also shows competitive optimization performance when compared with the standard EGO and six high-dimensional versions of EGO. This work provides an efficient and effective approach for high-dimensional expensive optimization.