# Multi-Objective Pareto Optimization of Tensile Membrane Architecture for Energy Harvesting
## 3 Methodology
### Configuration for Goals  
The simulation had two objectives: maximization of the acceleration and stiffness. These terms are defined in the following sections. If the surface of the TMA simulation has uniform gaps and crossing lines above the gaps on both axes, vertices can be generated at the intersections. The vertices of the surface are suitable for locating energy harvesters because the harvesters can be equally distributed on the surface. Thus, the acceleration values can be measured for all parts of the surface. Prior to a consideration of layout and numbers of energy harvesters on the membrane, this study assumed to spread harvesters uniformly and with defined optimal shape, material and region for maximizing the electric generation. It is also an important scope and worthwhile to research the \"optimal location of energy harvesters\" after the wind pattern is realized precisely. Nonetheless, the used wind pattern was a periodic frequency form which simplified the actual wind. Thus, we were in a prior step before discussing the precise number, location, or type of harvesters and we were able to grasp the trend of energy harvesting TMA from a macroscopic point of view. The hyper and barrel-vault shapes have 613 vertices and types, whereas the conic shape has 800. The acceleration is the sum of the number of vertices whose acceleration values exceed a defined value during the 400 iterations. Because the Kangaroo solver runs in its own iterations and not in actual time, the values defined for the acceleration measurements are set to display the simulation results as clearly as possible. According to the literature, the acceleration is not exactly proportional to the amount of energy generated but has the same direction [27]. Thus, comparing the accelerations among different geometries can be useful for evaluating different forms of energy generation.  
The material stiffness refers to the degree of stiffness of the membrane material. It is proportional to Young's modulus when the values of cross-sectional area and the length of the structural components are assumed to be constant, in accordance with the equation spring strength = EA/L(kN/m) presented in Section 3.3. According to [PERSON] [30], the elastic modulus (or Young's modulus) is inversely correlated with the tensile stress of the TMA. Therefore, when the elastic modulus, i.e., Young's modulus, increases, the deflection value decreases, indicating that the TMA is becoming stable. Thus, a higher stiffness corresponds to a more stable TMA. One goal of the simulation was the maximization of the stiffness because as the TMA becomes more stable, the probability of failure decreases, and an equilibrium condition is maintained. As reported in our previous paper [12], the acceleration increases with the magnitude of the TMA flatter, but for this to occur, the stiffness value must be low. In contrast, a higher material stiffness corresponds to a more stable TMA and a lower acceleration. Thus, a tradeoff must be achieved between the two goals of the simulation. Therefore, when genetic Pareto optimization is performed, TMA alternatives that optimally satisfy both goals can be identified.