A New Multisection Technique in Interval Methods for Global Optimization

A new multisection technique in interval methods for global optimization is investigated, and numerical tests demonstrate that the efficiency of the underlying global optimization method can be improved substantially. The heuristic rule is based on experiences that suggest the subdivision of the current subinterval into a larger number of pieces only if it is located in the neighbourhood of a minimizer point. An estimator of the proximity of a subinterval to the region of attraction to a minimizer point is utilized. According to the numerical study made, the new multisection strategies seem to be indispensable, and can improve both the computational and the memory complexity substantially. Received May 31, 1999; revised January 20, 2000