An MaOEA/Local Search Hybrid Based on a Fast, Stochastic BFGS Using Achievement Scalarizing Search Directions

We consider the problem of multiobjective and many-objective optimization in the unconstrained, continuous-variable setting. Can modern EAs designed for this setting (such as NSGA-III) that arguably have proven performance be improved by incorporating local search, and can this be achieved in a general way not requiring excessive tuning of parameters? Optimization in this setting is usually found to be increasingly challenging as the number of objectives is increased (albeit some works suggest the contrary) and this is believed to be because of the weakness of selection pressure available from Pareto comparisons, challenges in maintaining diversity and/or, in decomposition-based methods, due to the number of search ``directions'' that must be managed. To investigate our problem, we propose integrating a many-objective evolutionary algorithm (MaOEA) with local-search techniques based on derivative-free BFGS-like algorithms. This is done in two slightly different ways both using achievement scalarizing functions. Our results on well-known benchmark functions suggest a significant improvement is possible with reasonable assumptions about how to choose the base MaOEA parameters and a principled and general approach to choosing the remaining parameters in the hybrid algorithm. Our findings underline the effectiveness of hybrid methods and suggest powerful algorithms from mathematical programming can be used even without gradients.