## 3 Evolutionary Techniques for Intelligent Sensor Systems Design
### Assessment Functions and Multi-objective Problem  
The evaluation of solutions obtained by the optimization algorithms of ADIMSS is commonly based on classification accuracy. Basically, any classifier can be applied as an assessment function. However, algorithms that possess few parameters are favorable and offer a reliable convergence in training. For instance, the voting _k_-NN classifier is often applied as an assessment function in automatic feature selection. In the voting _k_-NN classifier, a test sample is classified in the class represented by a majority of the k number of selected samples. One variant of nearest neighbor methods is the volumetric _k_-NN, where a test sample is classified in the class represented by the smallest distance among distances between the test sample and the _k_-th sample in each class. Another variant is the sum-volumetric _k_-NN [34], which employs the sum of all the \(k\) nearest neighbors per class for its decision. The classification performance measure is implemented using the balance accuracy rate, which takes into account the correct classification rate per class. This prevents the searching optimization algorithms from selecting biased models in imbalanced datasets. The assessment function using classification measure is the average of the correct classification as described in the following equation:  
\[q_{t}= \frac{q_{a_{1}}+q_{a_{2}}+\ldots+q_{a_{L}}}{L} \tag{15}\]where \(\Omega=(\omega_{1}\), \(\omega_{2}\),..., \(\omega_{L})\) gives the class affiliation of patterns and \(q_{\omega}\) denotes the classification accuracy of a set of patterns with the same class affiliation \(\omega\). The non-parametric overlap measure (NPOM), which is inspired by the nearest neighbor concepts, provides a very fine-grained value range. The NPOM measures the quality of the discriminant data classes in the feature space, where it gives values close to one for non-overlapping class regions and decreases towards zero proportional to increasingly overlapping of class regions. The NPOM is computed by:  
\[q_{o}=\frac{1}{L}\sum_{c=1}^{L}\frac{1}{N_{c}}\sum_{i=1}^{N_{c}}\frac{\sum_{j=1 }^{k}R_{i,j}+\sum_{j=1}^{k}n_{j}}{2\sum_{j=1}^{k}n_{j}} \tag{16}\]  
\[n_{j}=1-\frac{D_{i,j}}{D_{i,k}} \tag{17}\]  
\[R_{i,j}= \begin{cases}n_{i}&\omega_{i}=\omega_{j}\\ -n_{i}&\omega_{i}\
eq\omega_{j}\end{cases}  \tag{18}\]  
where \(n_{j}\) computes the weighting factor for the position of the \(j\)-th nearest neighbor. \(D_{i,j}\) is the Euclidean distance between the \(i\)-th pattern and its \(j\)-th nearest neighbor. Ri,j denotes the measure contribution of the \(i\)-th pattern with regard to the \(j\)-th nearest neighbor. \(\omega_{i}\) denotes the class affiliation of the \(i\)-th sample, \(L\) is the number of classes, and \(N_{c}\) is the number of patterns in the \(c\)-th class. Typically, the number of parameter \(k\) of this quality measure is set in the range of 5 to 10 [34]. The nonparametric compactness measure (NPCM) is inspired by linear and non-linear discriminant analysis. The NPCM is applied to measure the quality of the class compactness and separation in the feature space. However, this assessment function still suffers from lack of normalization. The extended version of NPCM is done employing normalized distances (Euclidean distance) [16, 34], as shown in the following equation:  
\[dn_{i,j}=\frac{d_{max}-d_{i,j}}{d_{max}-d_{min}} \tag{19}\]  
where \(d_{i,j}\) is the Euclidean distance between the I-th and the j-th samples.