Development of a multi-objective optimization algorithm based on lichtenberg figures

Abstract

This doctoral dissertation presents the most important concepts of multi-objective optimization and a systematic review of the most cited articles in the last years of this subject in mechanical engineering. The State of the Art shows a trend towards the use of metaheuristics and the use of a posteriori decision-making techniques to solve engineering problems. This fact increases the demand for algorithms, which compete to deliver the most accurate answers at the lowest possible computational cost. In this context, a new hybrid multi-objective metaheuristic inspired by lightning and Linchtenberg Figures is proposed. The Multi-objective Lichtenberg Algorithm (MOLA) is tested using complex test functions and explicit contrainted engineering problems and compared with other metaheuristics. MOLA outperformed the most used algorithms in the literature: NSGA-II, MOPSO, MOEA/D, MOGWO, and MOGOA. After initial validation, it was applied to two complex and impossible to be analytically evaluated problems. The first was a design case: the multi-objective optimization of CFRP isogrid tubes using the finite element method. The optimizations were made considering two methodologies: i) using a metamodel, and ii) the finite element updating. The last proved to be the best methodology, finding solutions that reduced at least 45.69% of the mass, 18.4% of the instability coefficient, 61.76% of the Tsai-Wu failure index and increased by at least 52.57% the natural frequency. In the second application, MOLA was internally modified and associated with feature selection techniques to become the Multi-objective Sensor Selection and Placement Optimization based on the Lichtenberg Algorithm (MOSSPOLA), an unprecedented Sensor Placement Optimization (SPO) algorithm that maximizes the acquired modal response and minimizes the number of sensors for any structure. Although this is a structural health monitoring principle, it has never been done before. MOSSPOLA was applied to a real helicopter’s main rotor blade using the 7 best-known metrics in SPO. Pareto fronts and sensor configurations were unprecedentedly generated and compared. Better sensor distributions were associated with higher hypervolume and the algorithm found a sensor configuration for each sensor number and metric, including one with 100% accuracy in identifying delamination considering triaxial modal displacements, minimum number of sensors, and noise for all blade sections.