Numerical Experiences with a New Generalized Subinterval Selection Criterion for Interval Global Optimization

Abstract

The convergence properties are studied for interval global optimization algorithms that select the next subinterval to be subdivided with the largest value of the indicator pf(f k, X) = $$\frac{{f_k - \underline F \left( X \right)}}{{\overline F \left( X \right) - \underline F \left( X \right)}}$$ . In contrast to previous work, here the more general case is investigated, when the global minimum value is unknown, and thus its estimation f k in the iteration k has an important role. Extensive numerical tests on 40 problems confirm that substantial improvements can be achieved both on simple and sophisticated algorithms by the new method (not utilizing the minimum value).