An approach to chance constrained problems using weighted empirical distribution and differential evolution with application to flood control planning

Abstract

This paper proposes a new approach to solve chance constrained problems (CCPs) efficiently. Specifically, the probabilistic constraint in CCP can be evaluated directly if the cumulative distribution function (CDF) of uncertain function value is known. Therefore, the CDF is approximated by using weighted empirical CDF (W ECDF). Then a powerful evolutionary algorithm, namely differential evolution, combined with W ECDF is used to solve CCP. In order to demonstrate the performance of the proposed method, it is applied to flood control planning problems. K E Y W O R D Schance constrained problem, differential evolution, empirical distribution, stochastic programming Electron Comm Jpn. 2019;102:45-55.

An Approach to Chance Constrained Problems Based on Huge Data Sets Using Weighted Stratified Sampling and Adaptive Differential Evolution

“…It is difficult to solve CCP in (5). In real-world applications, the function value g m (x, ξ ) in (4) has to be evaluated for each of the data ξ ∈ B through a time-consuming computer simulation.…”

“…Supposing thatp(x, B) p(x, Ω) holds, we can estimate theoretically a necessary sample size for SRS. Let x ∈ X be a solution of CCP in (5). By using random samples…”

“…In addition to the reservoir, the water-retaining capacity of forest is counted to prevent the flood caused by heavy rainfall. Thereby, the flood control planning is formulated as CCP [5]. Figure 12 shows a topological river model.…”

“…Specifically, CCP ensures that the probability of meeting all constraints is above a certain level. Since the balance between optimality and reliability can be designated by CCP, many real-world applications have been formulated as CCPs [3][4][5].…”

“…The proposed approach is applied to a real-world application, namely the flood control planning formulated as CCP [5]. In addition to the conventional reservoir, the water-retaining capacity of the forest is considered in the flood control planning.…”