Solution space characterization and mathematical analysis of complex engineering optimization models
Keywords:
Solution space characterization, engineering optimization, mathematical analysis, optimizationAbstract
Nonlinear relationship, constraints and high dimensionality pose major challenges in identifying solutions and analyzing performance of complex engineering optimization models. In this study, a solution space characterization framework is proposed to investigate characteristics of feasible region, optimization landscape, convergence and stability of complex engineering systems. The framework takes advantage of the fundamental concepts of mathematical optimization such as convex analysis, constraint qualifications, duality, sensitivity and optimality conditions to gain insight into the structural behavior of complex optimization models. The proposed solution space characterization framework considers objective function, design constraints, feasible solution space and optimality conditions to investigate engineering optimization problems in a structured manner. It is demonstrated that appropriate continuity, convexity and regularity conditions guarantee existence and stability of optimal solutions and facilitate the investigation of structural properties of solution space through theoretical studies. In addition, dual relationships and sensitivity analysis are carried out to investigate the effect of parameter variation on optimization performance. Two-bar structural optimization problem considering compliance constraint is solved as a case study in order to illustrate the efficiency of the proposed framework. The obtained results reveal that there is no change in the stability of optimal design against compliance variation between 0.60 and 1.40 whereas the performance of objective is deteriorating from 6.6667 to 2.8571 due to increased design freedom. Stability of optimal design with respect to the parameter variation is verified through sensitivity analysis.
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