New approach for uncertain random multi-objective programming problems based on C_ESD criterion

Abstract

To overcome the defects that the traditional approach for multi-objective programming under uncertain random environment (URMOP) neglects the randomness and uncertainty of the problem and the volatility of the results, a new approach is proposed based on expected value-standard deviation value criterion (C ESD criterion). Firstly, the effective solution to the URMOP problem is defined; then, by applying sequence relationship between the uncertain random variables, the UR-MOP problem is transformed into a single-objective programming (SOP) under uncertain random environment (URSOP), which are transformed into a deterministic counterpart based on the C ESD criterion. Then the validity of the new approach is proved that the optimal solution to the SOP problem is also efficient for the URMOP problem; finally, a numerical example and a case application are presented to show the effectiveness of the new approach.

Method for constructing typical operation scenarios in power systems considering spatiotemporal correlation of renewable energy generation

“…Different from the proportional dot product method, the dimension d is divided into h equal parts, d/h = dv = dk, and the multi-head attention mechanism calculates Equation (6)…”

“…Traditional scenario analysis methods, such as Markov chain [5] and scenario tree [6], are based on statistical assumptions of a specific probability density function. However, it is difficult for deterministic hypothetical probabilistic models to fully characterize the characteristics of renewable energy output [7].…”