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. This paper introduces an innovative algorithm selection approach called the CNN-HT, which is a two-stage algorithm selection framework. 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. The two-stage approach can adapt to different algorithm combinations without the need to retrain the entire model, and modifications can be made in the second stage only, which is an improvement of one-stage approaches. To provide a more general structure for the classification model, we adopt Exploratory Landscape Analysis (ELA) features of the problem as input and utilize feature selection techniques to reduce the redundant ones. In problem classification, the average accuracy of classifying problems using CNN is 96%, which demonstrates the advantages of CNN compared to Random Forest and Support Vector Machines. After feature selection, the accuracy increases to 98.8%, further improving the classification performance while reducing the computational cost. This demonstrates the effectiveness of the first stage of the CNN-HT method, which provides a basis for algorithm selection. In the experiments, CNN-HT shows the advantages of the second stage algorithm as well as good performance with better average rankings in different algorithm combinations compared to the individual algorithms and another algorithm combination approach.
Keywords: algorithm selection; classification; convolutional neural network; exploratory landscape analysis; feature selection; hypothesis testing.