Worst Case Optimization Using Chebyshev Inequality

In real-world optimization problems, a wide range of uncertainties have to be taken into account. The presence of uncertainty leads to different results for repeated evaluations of the same solution. Therefore, users may not always be interested in the so-called best solutions. In order to find the robust solutions which are evaluated based on the predicted worst case, Worst Case Optimization Problem (WCOP) is formulated by using Chebyshev inequality from samples. Besides, a new evolutionary algorithm based on Differential Evolution is proposed to solve WCOP efficiently. The difference between the nominal solutions and the robust solutions is demonstrated through engineering design problems.