Abstract
In this paper, a new approach to solve Chance Constrained Problems (CCPs) using huge data sets is proposed. Specifically, instead of the conventional mathematical model, a huge data set is used to formulate CCP. This is because such a large data set is available nowadays due to advanced information technologies. Since the data set is too large to evaluate the probabilistic constraint of CCP, a new data reduction method called Weighted Stratified Sampling (WSS) is proposed to describe a relaxation problem of CCP. An adaptive Differential Evolution combined with a pruning technique is also proposed to solve the relaxation problem of CCP efficiently. The performance of WSS is compared with a well known method, Simple Random Sampling. Then, the proposed approach is applied to a real-world application, namely the flood control planning formulated as CCP.
Highlights
In real-world applications, a wide range of uncertainties have to be taken into account
The proposed approach is applied to a real-world application, namely the flood control planning formulated as Chance Constrained Problems (CCPs) [5]
If the inflow of water is estimated through a complex mathematical computation taking hours [36] or the amount of rainfall is predicted from a huge weather data set [37], we must realize the advantage of the pruning technique that surely reduces the run time of Adaptive DE (ADE) without harming the quality of the obtained solution
Summary
In real-world applications, a wide range of uncertainties have to be taken into account. In many real-world applications, the variance of observed data is caused by some uncertainties These applications are probably formulated as CCP more accurately by using a large data set instead of the mathematical model. By using the new data reduction method called WSS, the above CCP based on the full data set is converted into a relaxation problem of CCP. In order to solve the relaxation problem of CCP efficiently, a new optimization method based on Differential Evolution (DE) [18] is contrived in this paper. It is shown that the theoretical sample size is too large in practice; (2) By using larger data sets, the performance of WSS is examined more intensively by comparison with SRS.
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