###### Abstract  
A design engineer has to deal with increasingly complex design tasks on a daily basis, for which the available design time is shrinking. Market competitiveness can be improved by using optimization if the design process can be automated. If there is limited information about the behavior of the objective function, global search methods such as simulated annealing (SA) should be used. This algorithm requires the selection of a number of parameters based on the task. A procedure for reducing the time spent on tuning the SA algorithm for computationally expensive, simulation-driven optimization tasks was developed. The applicability of the method was demonstrated by solving a shape optimization problem of a rubber bumper built into air spring structures of berries. Due to the time-consuming objective function call, a support vector regression (SVR) surrogate model was used to test the performance of the optimization algorithm. To perform the SVR training, samples were taken using the maximin Latin hypercube design. The SA algorithm with an adaptive search space and different cooling schedules was implemented. Subsequently, the SA parameters were fine-tuned using the trained SVR surrogate model. An optimal design was found using the adapted SA algorithm with negligible error from a technical aspect.  
finite element analysis; hyperelastic material model; support vector regression; engineering optimization; simulated annealing; parameter tuning +
Footnote †: journal: Applied  
background and hyperelastic material model available [1; 2; 3], trials can be carried out by applying finite element analysis. The rubber product can be simulated with a simplified model due to the axisymmetric geometric and boundary conditions, so the running time is not significant despite the nonlinear simulation.  
Design optimization uses a mathematical formulation of a design problem to support the selection of the optimal design [4]. For the selection, the objective function is used, which is a scalar value formulated from a set of design responses; thus, it has different behaviors for a variety of problems. Several local and global search methods can be used if the computational cost of the optimization algorithm allows it to run on the model [5]. Because the gradient of the objective function calculated by finite element simulation is not given in the analytical form, but with approximate differences, gradient-based methods such as nonlinear programming by quadratic Lagrangian [6], mixed-integer sequential quadratic programming [7] or robust optimization [8] can be used to efficiently find the single global optimum. Direct methods, such as [PERSON]'s method [9] and the Nelder-Mead simplex method [10; 11], can approach the local minimum by using the value of the objective function. If limited information is available about the objective function behavior, it is recommended to use global optimal search methods. These include nature-inspired metaheuristic search methods such as the genetic algorithm [12], differential evolution [13] or simulated annealing (SA) which guarantees approaching the global optimum with the right settings. On the other hand, these algorithms require the selection of a number of parameters based on the task.