  In many important design problems, some decisions should be made by finding
the global optimum of a multiextremal objective function subject to a set of
constrains. Frequently, especially in engineering applications, the functions
involved in optimization process are black-box with unknown analytical
representations and hard to evaluate. Such computationally challenging
decision-making problems often cannot be solved by traditional optimization
techniques based on strong suppositions about the problem (convexity,
differentiability, etc.). Nature and evolutionary inspired metaheuristics are
also not always successful in finding global solutions to these problems due to
their multiextremal character. In this paper, some innovative and powerful
deterministic approaches developed by the authors to construct numerical
methods for solving the mentioned problems are surveyed. Their efficiency is
shown on solving both the classes of random test problems and some practical
engineering tasks.
