> For the complete documentation index, see [llms.txt](https://albertlidesign.gitbook.io/ibeso/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://albertlidesign.gitbook.io/ibeso/tutorial/multi-solution-system.md).
# Topology Optimization
[**Topology optimization (TO)**](https://en.wikipedia.org/wiki/Topology_optimization) is a mathematical method that optimizes material layout within a given design space, for a given set of [loads](https://en.wikipedia.org/wiki/Structural_load), [boundary conditions](https://en.wikipedia.org/wiki/Boundary_conditions) and [constraints](https://en.wikipedia.org/wiki/Constraint_\(mathematics\)) with the goal of maximizing the performance of the system (wiki).
iBESO imports multi-solution methods, which allows users to create diverse optimal topologies simultaneously. The solutions can bring about rich design diversity for designers.
### Tutorial
The main interface is show in Fig. 1. It includes three parts: a iBESO LOGO, a side bar and four optimizers. The side bar has multiple useful functions (a detailed introduction can be found [here](/ibeso/gui/main-interface.md)).
The four optimizers are used to display the topologically optimized results. The name of four optimizers are Solution A, Solution B, Solution C and Solution D, repecrtively. Generally, they use four different multi-solution algorithms. Users can change their algorithm in the [Options Panel](/ibeso/gui/options-panel.md). Moreover, the size of the opotimizers is adaptively adjusted according to the pre-defined resolution (changed in the [Options Panel](/ibeso/gui/options-panel.md)).
Click 
can launch the four optimizers and obtain the corresponding results, as shown in Fig. 2. During the optimization process, users can click 
to pause the program or click 
to reset all optimizers. Note that the optimization process doesn't allow users to change parameters and settings. Thus, most of buttons are inactive.
Besides, users can change the optimization parameters in the [Parameter Panel](/ibeso/gui/parameter-panel.md), such as target volume, filter radius and resolution. For example, Fig. 3 shows another example with different resolution.
### Default Parameters
iBESO defines a cantiliver beam as the default example. Its optimization parameters are shown in the table below.
| Parameter | Default value | Function |
| ---------------------------------------------------------------- | ---------------------- | ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |
| Resolution | 64 x 40 | The number of elements in the width (64) and the height (40) directions |
| Filter radius | 3 | |
| Target volume | 0.5 | The final volume of results |
| [Young's modulus](https://en.wikipedia.org/wiki/Young's_modulus) | 1 | A mechanical property that measures the tensile or compressive [stiffness](https://en.wikipedia.org/wiki/Stiffness) of a [solid](https://en.wikipedia.org/wiki/Solid) material when the force is applied lengthwise. |
| [Poisson's ratio](https://en.wikipedia.org/wiki/Poisson's_ratio) | 0.3 | A measure of the [deformation](https://en.wikipedia.org/wiki/Deformation_\(engineering\)) (expansion or contraction) of a material in directions perpendicular to the specific direction of [loading](https://en.wikipedia.org/wiki/Structural_load). |
| Scoring weight | 1 | Defines the weight of the [Scoring System](/ibeso/tutorial/scoring-system.md) |
| Drawing weight | 0.3 | Defines the weight of the [Drawing System](/ibeso/tutorial/drawing-system.md) |
| Save path | | |
| Smoothing | True | |
| Minimum random value | 75% | |
| Maximum random value | 100% | |
| Random seed | 2 | |
| Solution A Algorithms | Original BESO | |
| Solution B Algorithms | Random Perturbation | |
| Solution C Algorithms | Random Initial Designs | |
| Solution D Algorithms | Random Perturbation | |
| Brush radius | 2 | |
| Brush hardness | 50% | |
| Brush opacity | 100% | |