# Comparison of Profit-Based Multi-Objective Approaches for Feature Selection in Credit Scoring
## 1 Introduction  
Credit-scoring evaluations are an important part of the lending process, allowing financial institutions to manage risks [1]. Feature selection, a crucial part of the credit-scoring process, typically aims to minimize the number of features, thereby reducing model complexity, data acquisition costs, and computation time [2]. Traditionally, feature selection is conducted as a separate step before model training and is used to improve a single statistical measure, such as the area under the receiver operating curve (AUC) [3]. Beyond this, other factors, such as the profitability of the resulting model [4, 5], have been the focus of the feature-selection process. These factors, which depend on data and applications, can be incorporated into the feature-selection process as objectives in multi-objective optimizations (MOOs).  
MOO algorithms allow designers to balance several, often conflicting, objectives [6]. These methods have been applied to simultaneously consider the number of features and another training objective, such as profit, in feature selection [7]. Several algorithms have been developed to handle MOO problems, including the Strength Pareto Evolutionary Algorithm (SPEA-II), non-dominated sorting genetic algorithm (NSGA-II) [8, 9], and its reference-based adaptation for many-objective problems, NSGA-III. Hybrid algorithms, which integrate aspects of two or more optimization methods, have also been employed. An example is the adaptation of the continuous Grasshopper Optimization Algorithm (GOA)for filter-based feature selection through the introduction of binary conversion [10; 11]. Further examples used non-dominated strategies to convert Cuckoo Optimization Algorithm (COA) [12]. A non-dominated sorting binary GOA, NSBGOA, was proposed for feature selection with optimization of multiple objective [13].  
Existing research has shown that even for closely related multi-objective algorithms, performance varies depending on the test problem [14]. However, there is limited research comparing performance of different multi-objective algorithms for feature selection. In particular, existing research tends to use on one base classifier, with the base classifier used depending on the analyst's discretion. Changes in performance due to different base classifiers require further examination. This research aims to fill the gap by comparing the performance of several multi-objective methods on feature selection in credit scoring, namely NSGA-II, NSGA-III, and the newly proposed hybrid meta-heuristic, NSBGOA. Secondly, the effect of different base classifiers on performance is considered to determine the most suitable. Third, these multi-objective methods are compared to conventional feature-selection techniques. Three common objectives for credit-scoring feature selection are employed: maximizing profit, selecting features that are more easily explained to stakeholders, and minimizing number of features [4; 15].  
Related research is considered in Section 2, while Section 3 introduces the methods used in this research. Detailed in Section 4 is the problem formulation and empirical evaluation. Results of the evaluation are shown in Section 5 and discussed in Section 6. Lastly, the conclusion is given in Section 7.