# Development of a Power and Communication Bus Using HIL and Computational Intelligence
## 5 HIL-Based Optimization Method for Bus Prototyping
The second group of software decision variables are data processing methods, like \(p_{s_{5}}\) where mathematical operations of the input data are chosen, \(p_{s_{6}}\), where the source of data for analysis is chosen, and \(p_{s_{7}}\), where the target manner for addressing is chosen. Prior research has thoroughly investigated how the following addresses will look; two obvious trends ware noticed--following addresses will rise or fall--as well as another two not so obvious trends--in the rising trend the lower value is the last one, and in the falling trend, the higher avlue is the last one. An example is shown in Figure 9.  
Figure 9: One of the characteristic trends of the addresses value. Generally, multi-objective functions very often have an infinite number of local as well as global extrema and therefore one should investigate a set of points, each of which satisfies the objectives. Because of this, the predominant Pareto optimality concept is adopted. The Pareto-optimal solution is often considered the same as a non-dominated solution; it exists if there is no solution that improves at least one objective function without worsening the others. In this research, it is sufficient to apply the following fundamental measures as objectives:  
* \(c_{1}\), which is based on addressable factor: \[c_{1}(\mathbf{p}_{h},\mathbf{p}_{s})=\left\{ \begin{array}{l}\frac{1}{\sum \limits_{i=2}^{n-1}\left(1\,\mathrm{if}\,a_{i}>a_{i+1}\right)}\ \mathrm{if}\,p_{s\gamma}=2\ \mathrm{or}\ 4\\ \frac{1}{\sum\limits_{i=2}^{n-1}\left(1\,\mathrm{if}\,a_{i}>a_{i+1}\right)}\ \mathrm{other}\, \end{array} \right.\] (6) where elements of the vector \(\mathbf{a}\) are computed using the proposed rule in the form as follows: \[a_{n}(\mathbf{a})=\left\{ \begin{array}{l}a_{n}=\max(\mathbf{a})+1\ \mathrm{if}\ a_{n}=\min(\mathbf{a})\ \mathrm{and}\ p_{s\gamma}=3\\ a_{n}=\min(\mathbf{a})-1\ \mathrm{if}\ a_{n}=\max(\mathbf{a})\ \mathrm{and}\ p_{s\gamma}=4\\ \mathrm{no change\ in\ other,}\end{array} \right.\] (7) and \(n\) represents the number of nodes, \(p_{s\gamma}\) defines the addresses trend (see Table 2), and \(a_{i}\) measures address value of the \(i\)-th node. * \(c_{2}\) is based on the minimal difference between addresses: \[c_{2}(\mathbf{p}_{h},\mathbf{p}_{s})=\frac{1}{\Delta_{max}+1},\] (8) where \(\Delta_{max}\) describes the difference in addresses between neighbour nodes. * \(c_{3}\) is used to show the overall cost of the system: \[c_{3}(\mathbf{p}_{h})=\
u(\mathbf{p}_{h_{M}},\mathbf{p}_{h_{C}},n),\] (9) where \(\
u\) is the function which calculates a cost of each element used in the current approach. On the other hand, the global criterion method can be successfully applied to transform a multiple objective function into a single objective one. This way, an indirect utility function can be expressed in its simplest form as the weighted sum of objectives:  
\[C(\mathbf{p}_{h},\mathbf{p}_{s})=\frac{\mathbf{w}\mathbf{C}^{T}(\mathbf{p})}{ \mathbf{1}\mathbf{w}^{T}}=\left\{ \begin{array}{l}5c_{1}\ \mathrm{if}\ c_{1}\geq\frac{1}{n}-1\\ w_{1}c_{2}+w_{2}c_{3}\ \mathrm{other},\end{array} \right. \tag{10}\]  
where \(\mathbf{w}\) is a row vector with weights indicating the relative significance of the objective functions; in this study, \(w_{1}\) and \(w_{2}\) indicate the weights for the second and third criteria, respectively. The optimal solution is found if the criterion function \(\mathbf{C}\) has a relative minimum value at \(\mathbf{p}^{*}\), that means if:  
\[\mathbf{p}^{*}=[\mathbf{p}_{h}^{*}\ \mathbf{p}_{s}^{*}]=\underset{p\in\Omega}{ \mathrm{argmin}}\ \mathbf{C}(\mathbf{p}_{h},\mathbf{p}_{s}). \tag{11}\]  
It has been decided to apply intelligent computing and hardware in the loop techniques due to several difficulties in bus prototyping discussed in Section 2.