Granular Box Regression Using Simulated Annealing and Genetic Algorithm: A Comparative Study

Representation of compound information in a truthful, coarse way forms the layout of the granular computing paradigm. In granular computing, the continuous variables are mapped into intervals to be utilized in the extraction of fuzzy graphs from the given dataset. The objective of Granular Box Regression is to establish a relationship between the predictor and the target variables using multidimensional boxes. However, the traditional box regression technique uses a greedy approach due to which the algorithm tends to converge to some local optima, and optimal box configuration may not be obtained. In this article, we suggest overcoming the problem of getting stuck into local optima using randomized search and optimization techniques of Simulated Annealing and Genetic Algorithms. The major advantage of using Simulated Annealing is that it allows occasional acceptance of poor solutions to avoid getting trapped into some local optima. Genetic Algorithms also provide efficient, robust search optimization techniques that minimize the chances of a local optimum problem. A comparative analysis is conducted while implementing Granular Box Regression using Simulated Annealing and Genetic Algorithm, and the results are demonstrated on some artificial datasets, economic datasets, and some datasets of COVID-19 cases. As per the quantitative analysis of the Granular Box Regression (GBR) methods, both GBR-SA and GBR-GA significantly outperformed the baseline GBR algorithm across various datasets. For instance in the 3DED1 dataset, GBR-SA and GBR-GA showed an improvement of 16.02 % while for 2DCD2, they showed an improvement of 22.22 % . However, the execution time varied for GBR-GA by 95.4 % with the GBR-SA algorithm, which in turn took about 26 % average time more than the base algorithm of GBR.