A centerline symmetry and double-line transformation based algorithm for large-scale multi-objective optimization

The search space of large-scale multi-objective optimization problems (LSMOPs) is huge because of the hundreds or even thousands of decision variables involved. It is very challenging to design efficient algorithms for LSMOPs to search the whole space effectively and balance the convergence and diversity at the same time. In this paper, to tackle this challenge, we develop a new algorithm based on a weighted optimization framework with two effective strategies. The weighted optimization framework transforms an LSMOP into multiple small-scale multi-objective optimization problems based on a problem transformation mechanism to reduce the dimensionality of the search space effectively. To further improve its effectiveness, we firstly propose a centerline symmetry strategy to select reference solutions to transform the LSMOPs. It takes not only some non-dominated solutions but also their centerline symmetric points as the reference solutions, which can enhance the population diversity to avoid the algorithm falling into local minima. Then, a new double-line transformation function is designed to expand the search range of the transformed problem to further improve the convergence and diversity. With the two strategies, more widely distributed potential search areas are provided and the optimal solutions can be found easier. To demonstrate the effectiveness of our proposed algorithm, numerical experiments on widely used benchmarks are executed and the statistical results show that our proposed algorithm is more competitive and performs better than the other state-of-the-art algorithms for solving LSMOPs.