Multiobjective genetic programming for maximizing ROC performance

In binary classification problems, receiver operating characteristic (ROC) graphs are commonly used for visualizing, organizing and selecting classifiers based on their performances. An important issue in the ROC literature is to obtain the ROC convex hull (ROCCH) that covers potentially optima for a given set of classifiers [1]. Maximizing the ROCCH means to maximize the true positive rate (tpr) and minimize the false positive rate (fpr) for every classifier in ROC space, while tpr and fpr are conflicting with each other. In this paper, we propose multiobjective genetic programming (MOGP) to obtain a group of nondominated classifiers, with which the maximum ROCCH can be achieved. Four different multiobjective frameworks, including Nondominated Sorting Genetic Algorithm II (NSGA-II), Multiobjective Evolutionary Algorithms Based on Decomposition (MOEA/D), Multiobjective selection based on dominated hypervolume (SMS-EMOA), and Approximation-Guided Evolutionary Multi-Objective (AG-EMOA) are adopted into GP, because all of them are successfully applied into many problems and have their own characters. To improve the performance of each individual in GP, we further propose a memetic approach into GP by defining two local search strategies specifically designed for classification problems. Experimental results based on 27 well-known UCI data sets show that MOGP performs significantly better than single objective algorithms such as FGP, GGP, EGP, and MGP, and other traditional machine learning algorithms such as C4.5, Naive Bayes, and PRIE. The experiments also demonstrate the efficacy of the local search operator in the MOGP framework.