CNN-HT: A Two-Stage Algorithm Selection Framework

Abstract

The No Free Lunch theorem tells us that no algorithm can beat other algorithms on all types of problems. The algorithm selection structure is proposed to select the most suitable algorithm from a set of algorithms for an unknown optimization problem. In this paper, an innovative algorithm selection approach called the CNN-HT two-stage algorithm selection framework is introduced. In the first stage, a Convolutional Neural Network (CNN) is employed to classify problems. In the second stage, the Hypothesis Testing (HT) technique is used to suggest the best-performing algorithm based on the statistical analysis of the performance metric of algorithms that address various problem categories. To provide a more general structure for the classification model, we adopt Exploratory Landscape Analysis (ELA) features of the problem as the input and utilize feature selection techniques to reduce the redundant ones. In problem classification, our proposed algorithm selection framework achieves an average accuracy of 96% for the classification of unknown black-box problems, and it improves to 98.8% after feature selection. This shows that our proposed classification method can accurately classify BBOB problems into 24 classes of problems and thus can correctly recommend algorithms accordingly. The performance of CNN-HT is compared with a single optimization algorithm on a continuous black-box optimization problem set, and the average ranking of CNN-HT is superior, demonstrating its effectiveness.