Multi-Gbest Decomposition for Many-Objective Optimization

This paper proposes MIDMOPSO۲, a novel many-objective optimization algorithm integrating indicator-based selection and direction vectors to balance convergence and diversity. Unlike conventional approaches relying solely on Pareto dominance, MIDMOPSO۲ employs the Iε+ indicator to enhance individual evaluation and utilizes direction vectors to decompose the problem into single-objective subproblems, effectively preserving population diversity. Each particle is assigned a unique direction vector, reducing chaos in the search space. While traditional swarm algorithms guide the population with a single global best (Gbest), MIDMOPSO۲ dynamically selects personalized guides from an external archive based on minimal vectorial distance, mimicking natural evolutionary diversity. The archive is updated iteratively using a fitness indicator to maintain elite solutions. Tested on DTLZ benchmark problems (۳–۱۵ objectives), MIDMOPSO۲ demonstrates superior adaptability and efficiency compared to state-of-the-art methods (e.g., NSGA-III, MOEA/D) in Hypervolume (HV) and Inverted Generational Distance (IGD) metrics. Key innovations include: Directional decomposition for structured search, Iε+-based archive management to prioritize high-quality solutions, Particle-specific guidance to avoid premature convergence. Results confirm significant improvements in scalability and solution diversity for high-dimensional objectives, addressing critical challenges in many-objective optimization

Keywords:

optimization , binary indicator , direction vectors , aggregation of particles , different patterns