  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), a new HALRECT (HALving RECTangles)
algorithm is introduced. A new deterministic approach combines halving
(bisection) with a new multi-point sampling scheme in contrast to trisection
and midpoint sampling used in the most existing DIRECT-type algorithms. A new
partitioning and sampling scheme utilizes more comprehensive information about
the objective function. Four different strategies of selecting potentially
optimal hyper-rectangles are introduced to exploit the information about the
objective function effectively. The original HALRECT algorithm and other
introduced HALRECT variations (twelve in total) are tested and compared with
the other twelve recently introduced DIRECT-type algorithms on $96$
box-constrained benchmark functions from DIRECTGOLib v1.1, and 96 perturbed
their versions. The extensive experimental results show a very promising
performance compared to state-of-the-art DIRECT-type global optimization. New
HALRECT approaches offers high robustness across problems of different degrees
of complexity, varying from simple - uni-modal and low dimensional to complex -
multi-modal and higher dimensionality.
