Development of a new hybrid optimization method for solution of structural optimization problems

Optimization can be defined as the process of finding the best solution among all possible solutions for a given problem under certain conditions. To make an optimization problem more manageable, mathematical models are created based on the problem's structure. The uncertainty and irregularity in the behavior of nature-inspired metaheuristic optimization algorithms can provide solutions for various optimization applications and problems. The fundamental components of metaheuristic optimization algorithms are exploration, which involves generating various solutions through global search, and exploitation, which focuses on local search to select the best candidate solutions. This study proposes a new hybrid optimization algorithm to solve structural optimization problems. The goal was to integrate chaotic maps into the Artificial Rabbits Optimization (ARO) algorithm, a current and well-known metaheuristic optimization algorithm, to improve its convergence speed. This new hybrid algorithm was then applied to solve various structural optimization problems. In this study, the random parameters in the mathematical equations of the Artificial Rabbit Optimization (ARO) algorithm were hybridized with 10 well-known chaotic maps and 4 proposed modification methods and this hybrid algorithm developed in this thesis is named as the Chaotic Artificial Rabbits Optimization (CARO) algorithm. The performance of the CARO algorithm was tested by using 23 classical test functions. Subsequently, the CARO algorithm was applied to 5 fundamental engineering design problems; pressure vessel, bearing, tension/compression spring, cantilever beam, and gear train. The CARO algorithm was compared with 6 current and popular metaheuristic algorithms in the literature; Artificial Rabbits Optimization (ARO) algorithm, Particle Swarm Optimization (PSO), Grey Wolf Optimization (GWO), Moth-Flame Optimization (MFO), Harris Hawks Optimization (HHO) and Genetic Algorithm (GA). In the scope of the thesis, the structural optimization of a new brake pedal was performed using the CARO algorithm, aiming to create a light weight brake pedal that meets the stress requirements under working conditions compared to an existing brake pedal. The mathematical model of the brake pedal's structural optimization problem was created by using latin hypercube sampling method and radial basis functions meta-modeling method. 6 holes were drilled in the brake pedal according to topology and shape optimization, reducing the weight and determining the design variables. Using the latin hypercube sampling method, 100 different brake pedal models were created. Mathematical equations for the objective function (weight) and the constraint function (stress) were obtained using the radial basis functions meta-modeling method. Using these mathematical equations, CARO algorithm was solved in terms of the mass minimization of the brake pedal, by comparing with 6 well-known metaheuristic algorithms in the literature. As a result, the optimum design weight of the brake pedal was obtained as 983.30 grams, which is 18.2% lighter than the initial design weight of 1202 grams. Thus, the newly developed Chaotic Artificial Rabbits Optimization (CARO) algorithm was used for the first time in the literature to solve a structural optimization problem for a vehicle part. Keywords: Metaheuristic optimization, Artificial rabbits optimization algorithm, Chaotic maps, Chaotic artificial rabbits optimization algorithm, Topology optimization, Shape optimization, Mechanical design, Brake pedal