Adaptive Bilevel Approximation Technique for Multiobjective Evolutionary Optimization

The computational intensiveness of evolutionary algorithms (EAs) in dealing with large-scale problems has been of great concern over the years. In order to reduce the computational burden associated with EAs initially, an anchored ANOVA decomposition model was integrated with the elitist nondominated sorting genetic algorithm (NSGA-II). Later, an improved version of the former framework, a novel approximation technique was developed and specialized to solve typical case scenarios often encountered, such as problems with nonconvex and disconnected Pareto optimal fronts. This proposed tool has been referred to as adaptive bilevel error-sensitivity based anchored ANOVA decomposition (ABE-ANOVA). ABE-ANOVA has been developed by the amalgamation of anchored ANOVA decomposition and Gaussian process (GP) model. They are coupled in such a way that anchored ANOVA handles the global behavior of the model using a set of component functions and GP interpolates local variations as a function of sample points, resulting in a two-level approximation. The study proves that ABE-ANOVA assisted NSGA-II is much more robust as compared to ANOVA assisted NSGA-II, especially in handling complex scenarios. Implementation of the proposed approaches have been demonstrated with the help of several multiobjective analytical examples and a few finite element problems. Performance has been assessed by comparing simulation of the actual model with NSGA-II and a few other algorithms. Excellent results in terms of accuracy and computational effort makes the proposed method potential for real-time applications. (C) 2016 American Society of Civil Engineers.