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

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 URMOP 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.