Controlling the Exploitation/Exploration Trade-Off in Global Optimization: A Set Membership Approach

Trading off exploration and exploitation is a crucial task in global (or black-box) optimization, to balance the search for better local optimizers with the refinement of already-found ones. Often, such a trade-off is not easily controlled by the user, as it depends non-trivially on the tuning parameters of the selected algorithm. A new concept is proposed here, where the share of exploitation moves over the total number of iterations is regulated by a feedback control law, to achieve a user-defined set-point. This concept is applied to the recently proposed Set Membership Global Optimization (SMGO) technique, resulting in a modified algorithm. Additional computational improvements are presented as well, and the resulting approach is extensively tested and compared with other methods. The statistical tests indicate that the new algorithm has better iteration-based optimization performance than the original one, at the same time shortening the computational times by around one order of magnitude.