*2.4. Feature Selection*

The objective of feature selection is to find a subset of the features that were obtained with the feature extraction method. The feature selection method attempts to find a parsimonious feature subset that results in accurate classification. However, subset size and classification accuracy are conflicting objectives. A small feature subset will probably result in high classification error, whereas a large feature subset will probably result in lower classification error. Therefore, feature selection can be viewed as a multi-objective optimization (MOO) problem. In MOO problems, no single solution can simultaneously optimize all objectives. The solutions comprise a set of possible alternative solutions known as the optimal Pareto set [21].

We seek the most informative but parsimonious subset of features for gait mode classification. Note that exhaustive search is not practical in cases with a high-dimensional set of features. A set of *<sup>n</sup>* features has 2*<sup>n</sup>* − 1 different subsets (excluding the null subset). Many heuristic search strategies, such as sequential forward selection, sequential backward elimination, and evolutionary search, have been suggested for this type of combinatorial problem [42]. Evolutionary algorithms (EAs) have been demonstrated as an efficient global search strategy for feature selection [43]. They generally outperform sequential forward selection and sequential backward elimination [22]. However, EA-based search strategies are computationally expensive due to the need for many cost function evaluations. To reduce computational complexity, we propose a new method called gradient-based multi-objective feature selection (GMOFS) for UIR. In addition, we propose the application of four EA-based search strategies, using multi-objective biogeography-based optimization (MOBBO), for feature selection. We then use two systematic approaches to compare the performance of the GMOFS search strategy with four variants of MOBBO.
