Lipschitz-inspired HALRECT algorithm for derivative-free global optimization

This article considers a box-constrained global optimization problem for Lipschitz-continuous functions with an unknown Lipschitz constant. Motivated by the famous DIRECT (DIviding RECTangles), new HALRECT (HALving RECTangles) algorithm is introduced. A deterministic approach combines halving (bisection) multi-point sampling scheme in contrast to trisection and midpoint used most existing DIRECT-type algorithms. partitioning uses more comprehensive information on objective function. Four different strategies selecting potentially optimal hyper-rectangles are introduced exploit function’s effectively. The original other variations (twelve total) tested compared twelve recently algorithms 96 benchmark from DIRECTGOLib v1.1, perturbed their versions. Extensive experimental results advantageous state-of-the-art optimization. New approaches offer high robustness across problems of degrees complexity, varying simple—uni-modal low dimensional complex—multi-modal higher dimensionality.