# Topology Optimisation Using MPBILs and Multi-Grid Ground Element
## 2 Topological Designs with Single-and Multi-Ground Design Approaches  
### Topological Designs with Ground Element Filtering  
Topology optimization is one mathematical tool used in the conceptual design stage of engineering systems for finding the best structural layout from a given design domain. Topological design can perform using an optimization method and finite element analysis. This technique is started by defining design domain represented as the discrete structural members such as panels, truss, and frame as shown in Figure 1. The optimization method can be performed by varying the width or thickness of each element in the design domain between zero and the maximum value. All elements were discarded, if the element width/thickness value was zero. Otherwise, the element was retained. With this concept, optimization of the structural layout and component sizes is performed. Two popular, well known topological methods are the solid isotropic material with penalization (SIMP) approach and the homogenization method, which use gradient-based optimizers. Later, an alternative optimizer is evolutionary algorithms due to the fact they are robust, simple to use, derivative-free, and free from intermediate pseudo densities [8]. Complicated problems, such as partial topology, simultaneous topology, shape, and sizing optimization, can be performed within one optimization run [3; 8; 16; 17] by using such algorithms. In this paper [8], they presented the comparative performance of multi-objective evolutionary algorithms (MOEAs) for solving structural topology optimization test problems based on ground element filtering technique. It has been found that MPBIL is the best optimizer in their study, which outperforms other MOEAs [8], so MPBIL is the only MOEA selected to improve its search performance in this research. Furthermore, the ground element filtering technique is also used in this study. The ground element filtering technique (GEF technique) is a simple numerical scheme that can apply to all kinds of optimizers, which can prevent the checkerboard pattern problem and at the same time decrease the number of design variables [8; 18; 19]. The idea uses two mesh grids of design domain with different resolutions. The lower resolution grid is provided for design variables, whereas the higher resolution is used as a finite element grid. The conversion between two grids relates to threshold value (\(\varepsilon\)) that is defined at the first time before optimization run. Therefore, this technique has been proved to be an efficient technique to suppress the checkerboard problem. Next, the details of GEF technique are seen in [8; 18; 19]. Later, a method for solving checkerboard pattern was presented by [PERSON] and [PERSON] [20]. They proposed that derivative-freelevel-set method for solving structural topology can solve the checkerboard problem. This new technique can avoid the main limitations of non-gradient methods: dependence on the objective value. Moreover, the boundaries of structure are smooth, but it does not directly depend on the decision variables. A very recent work in multi-objective topology optimization has been proposed to address the limitations of generating infeasible structures and expensive computational cost by using the technique called \"graphics processing unit (GPU)\" [21]. On the contrary, this technique has been commented on usefulness in the case of truss-like structures and the solved examples are simple, and obtained results are sub-optimal solutions [22]. Recent applications of topology optimization appeared in design of composite molding processes [23]. More recently, applications of topology optimization appeared in many fields, e.g., composite molding processes [23], optimal design of piezoelectric [24], phononic crystals design [25] and stator configurations [26].