A Support Vector Machine-based Approach to Chance Constrained Problems using Huge Data Sets

Abstract

In this paper, a new approach to solve data-driven Chance Constrained Problems (CCPs) is proposed. First of all, a large data set is used to formulate CCP because such a large data set is available nowadays due to advanced information technologies. However, since the size of the data set is too large, a Support Vector Machine (SVM) is used to estimate the probability of meeting all constraints of CCP for the large data set. In order to generate a training data set for the SVM, a sampling technique called Space Stratified Sampling (SSS) is proposed in this paper. According to the first principal component obtained by Principal Component Analysis (PCA), SSS divides the large data into several strata and selects some data from each stratum. The SVM trained by SSS is called S SVM. In order to solve CCPs based on large data sets efficiently, a new optimization method called Adaptive Differential Evolution with Pruning technique (ADEP) is also proposed.