Constrained robust optimal design using a multiobjective evolutionary algorithm

A major fraction of evolutionary optimization methods aim to find solutions that maximize performance. However, a solution that solely maximizes performance is of no practical use as it may be too sensitive to parametric variations (non-uniform material properties, inexact physical dimensions, uncertainties in loading and operating conditions, etc.). Furthermore, for design problems with constraints, a robust solution needs to be feasible and remain feasible under parametric variations. In this paper, a new evolutionary algorithm is proposed that is capable of handling constrained robust optimal design problems. A multiobjective formulation is introduced that considers an individuals' performance, mean performance of its neighbors and the standard deviation of its neighbors' performance as three objectives for optimization. In order to handle feasibility, an innovative constraint-handling scheme based on Pareto concept is introduced that considers an individual's self-feasibility and its neighborhood feasibility. Robust optimal solutions to two engineering design examples are reported in this paper. Results of simulation are also presented to illustrate the differences between an optimal solution and a robust optimal solution.