High-Dimensional Multi-objective PSO Based on Radial Projection

Abstract

When solving multi-objective problems, traditional methods face increased complexity and convergence difficulties because of the increasing number of objectives. This paper proposes a high-dimensional multi-objective particle swarm algorithm that utilizes radial projection to reduce the dimensionality of high-dimensional particles. Firstly, the solution vector space coordinates undergo normalization. Subsequently, the high-dimensional solution space is projected onto 2-dimensional radial space, aiming to reduce computational complexity. Following this, grid partitioning is employed to enhance the efficiency and effectiveness of optimization algorithms. Lastly, the iterative solution is achieved by utilizing the particle swarm optimization algorithm. In the process of iteratively updating particle solutions, the offspring reuse-based parents selection strategy and the maximum fitness-based elimination selection strategy are used to strengthen the diversity of the population, thereby enhancing the search ability of the particles. The computational expense is significantly diminished by projecting the solution onto 2-dimensional radial space that exhibits comparable characteristics to the high-dimensional solution, while simultaneously maintaining the distribution and crowding conditions of the complete point set. In addition, the offspring reuse-based parents selection strategy is used to update the external archive set, further avoiding premature convergence to local optimal solution. The experimental results verify the effectiveness of the method in this paper. Compared with four state-of-the-art algorithms, the algorithm proposed in this paper has high search efficiency and fast convergence in solving high-dimensional multi-objective optimization problems, and can also obtain higher quality solutions.