Subspace dynamic-simplex linear interpolation search for mixed-integer black-box optimization problems

Abstract

Design and management of complex systems with both integer and continuous decision variables can be guided using mixed-integer optimization models and analysis. We propose a new mixed-integer black-box optimization (MIBO) method, subspace dynamic-simplex linear interpolation search (SD-SLIS), for decision making problems in which system performance can only be evaluated with a computer black-box model. Through a sequence of gradient-type local searches in subspaces of solution space, SD-SLIS is particularly efficient for such MIBO problems with scaling issues. We discuss the convergence conditions and properties of SD-SLIS algorithms for a class of MIBO problems. Under mild conditions, SD-SLIS is proved to converge to a stationary solution asymptotically. We apply SD-SLIS to six example problems including two MIBO problems associated with petroleum field development projects. The algorithm performance of SD-SLIS is compared with that of a state-of-the-art direct-search method, NOMAD, and that of a full space simplex interpolation search, Full-SLIS. The numerical results suggest that SD-SLIS solves the example problems efficiently and outperforms the compared methods for most of the example cases. © 2017 Wiley Periodicals, Inc. Naval Research Logistics 64: 305–322, 2017