Deterministic approaches for solving practical black-box global optimization problems

Abstract

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.