Deterministic Global Optimization Methods for Solving Engineering Problems

Abstract

In many important practical problems, some decision should be made by finding the global optimum of a multiextremal objective function subject to a set of constraints. 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.). In this paper, some innovative and powerful approaches developed by the authors to construct efficient numerical methods for solving the mentioned problems are presented.

Deterministic approaches for solving practical black-box global optimization problems

“…This paper is based upon the work [43] presented at the Eleventh International Conference on Computational Structures Technology (Dubrovnik, Croatia, 4-7 September 2012) and extends the previous research in both the theoretical and the experimental directions, thus offering to the optimal design community competitive tools to tackle real-life engineering decisionmaking tasks.…”

“…In this Section, some innovative deterministic approaches developed by the authors for constructing efficient global optimization techniques are briefly presented as in [43]. The consolidated success of these ideas, confirmed by important international publications and presentations around the world, allows the authors' group, on the one hand, to develop promising optimization approaches over a solid scientific basis, thus eliminating the theoretical faults risks, and, on the other hand, to tackle difficult black-box practical optimization problems (e.g., from control theory, environmental sciences and geological mechanics, electrical engineering and telecommunications, gravitational physics, etc.)…”