Many-Objective Hybrid Optimization Under Uncertainty With Applications

Abstract

A novel method for solving many-objective optimization problems under uncertainty was developed. It is well known that no single optimization algorithm performs best for all problems. Therefore, the developed method, a many-objective hybrid optimizer (MOHO), uses five constitutive algorithms and actively switches between them throughout the optimization process allowing for robust optimization. MOHO monitors the progress made by each of the five algorithms and allows the best performing algorithm more attempts at finding the optimum. This removes the need for user input for selecting algorithm as the best performing algorithm is automatically selected thereby increasing the probability of converging to the optimum. An uncertainty quantification framework, based on sparse polynomial chaos expansion, to propagate the uncertainties in the input parameter to the objective functions was also developed and validated. Where the samples and analysis runs needed for standard polynomial chaos expansion increases exponentially with the dimensionality, the presented sparse polynomial chaos approach efficiently propagates the uncertainty with only a few samples, thereby greatly reducing the computational cost. The performance of MOHO was investigated on a total of 65 analytical test problems from the DTLZ and WFG test suite, for which the analytical solution is known. MOHO is also applied to two additional real-life cases of aerodynamic shape design of subsonic and hypersonic bodies. Aerodynamic shape optimization is often computationally expensive and is, therefore, a good test case to investigate MOHO`s ability to reduce the computational time through robust optimization and accelerated convergence. The subsonic design optimization had three objectives: maximize lift and minimize drag and moment. The hypersonic design optimization had two objectives: maximize volume and minimize drag. Two accelerated solvers based on fast multipole method and Newton impact theory are developed for simulating subsonic and hypersonic flows. The results show that MOHO performed, on average, better than all five remaining algorithms in 52% of the DTLZ+WFG problems. The results of robust optimization of a subsonic body and hypersonic bodies were in good agreement with theory. The MOHO developed is capable of solving many-objective, multi-objective and single objective, constrained and unconstrained optimization problems with and without uncertainty with little user input.