## 3 Sensitivity Analysis and Genetic Algorithms for Design Optimization of the MRE-Based ATDVA
### Application of Sensitivity Analysis and Genetic Algorithms for Optimization of the MRE-Based ATDVA  
Genetic algorithms are based on the principle of biological evolution theory and genetics that individuals of superior quality tend to adapt well to the natural world and produce superior descendants. Because genetic algorithms have a group of individuals composed of binary combinations, they can  
Figure 15: Cross section of coil part. provide a wide variety of cases when expressed in binary numbers and do not use gradients unlike conventional optimization algorithms. In most cases, engineering optimization problems exhibit nonlinear behavior, and accordingly, gradient-based search techniques often reach local optimum points. In contrast, genetic algorithms are more likely to find global optimum points because they search the whole of a given design space without using gradients. A genetic algorithm involves the processes of propagation, selection, crossover and mutation. The propagation process generates a predetermined number (n) of design parameters. The value of \(n\) representing the number of generated design parameters is converted into binary. The selection process determines how fit each individual is for the objective function and concludes that the higher the fitness of individuals, the more likely they are to influence their descendants. The basic idea of the roulette wheel model as the most widely used selection method is that individuals leave offspring in proportion to their fitness. The selection process finds the value of an objective function by substituting generated design parameters into the objective function. If the process is to find values of the design parameters that maximize the objective function, the selection probability for each design parameter is calculated by dividing the value of each design parameter by the sum of all function values. In addition, a cumulative probability is calculated for each design parameter. The cumulative probability is the sum of the first to kth selection probabilities. Each of the calculated cumulative probabilities is compared with a randomly generated number between 0 and 1. If the first cumulative probability is greater than the first random number, the first design parameter is selected; likewise, if the kth cumulative probability is greater than the second random number, then the kth design parameter is selected. This process is repeated m times. As a result, m design parameters are selected after the selection process. Subsequently, the crossover process selects random positions for random design parameters and crosses them over each other. The mutation process provides a global search effect by searching spaces other than the combination space of early genes by means of genetic modification occurring with a constant probability. Moderate mutations increase the rate of convergence towards the objective function and the diversity of groups. The mutations can be divided into two classes: static and dynamic. Static mutations take place with fixed mutation probabilities, whereas the probability of dynamic mutation varies from time to time. Typically, the mutations occur with a probability of 0.5-1 per bit. The mutation process is a process wherein the binary value of 0 or 1 for a random position is converted into 1 or 0. If the genetic algorithm fails to reach a predetermined number of repeats, design parameters are propagated again and in turn undergo the processes of selection, crossover and mutation. Once the predetermined number of repeats is finally reached, the algorithm finds the values of design parameters that maximize the objective function. It is necessary to perform a sensitivity analysis for selecting design parameters of the MRE-based ATDVA. The sensitivity analysis was conducted for each of the design parameters in equation (14) as a formula for the magnetic field of the MRE-based ATDVA's mass part (Figure 16). Figure 16: Design parameter sensitivity analysis of adaptive tuned MRE vibration absorber.