Branch-and-Model: a derivative-free global optimization algorithm

Kaiwen Ma, Luis Miguel Rios, Atharv Bhosekar, Nikolaos V. Sahinidis, Sreekanth Rajagopalan

Abstract: This paper presents a novel derivative-free global optimization algorithm Branch-and-Model (BAM). The BAM algorithm partitions the search domain dynamically, builds surrogate models around carefully selected evaluated points, and uses these models to exploit local function trends and speed up convergence. For model construction, BAM employs Automated Learning of Algebraic Models (ALAMO). The ALAMO algorithm generates algebraic models of the black-box function using various base functions and selection criteria. BAM’s potentially optimal identification scheme saves computational effort and prevents delays in searching for optimal solutions. The BAM algorithm is guaranteed to converge to the globally optimal function value under mild assumptions. Extensive computational experiments over 500 publicly open-source test problems and one industrially-relevant application show that BAM outperforms state-of-the-art DFO algorithms regardless of problem convexity and smoothness, especially for higher-dimensional problems.