Large-scale many-objective particle swarm optimizer with fast convergence based on Alpha-stable mutation and Logistic function

Elite Directed Particle Swarm Optimization with Historical Information for High-Dimensional Problems

High-dimensional optimization problems are ubiquitous in every field nowadays, which seriously challenge the optimization ability of existing optimizers. To solve this kind of optimization problems effectively, this paper proposes an elite-directed particle swarm optimization (EDPSO) with historical information to explore and exploit the high-dimensional solution space efficiently. Specifically, in EDPSO, the swarm is first separated into two exclusive sets based on the Pareto principle (80-20 rule), namely the elite set containing the top best 20% of particles and the non-elite set consisting of the remaining 80% of particles. Then, the non-elite set is further separated into two layers with the same size from the best to the worst. As a result, the swarm is divided into three layers. Subsequently, particles in the third layer learn from those in the first two layers, while particles in the second layer learn from those in the first layer, on the condition that particles in the first layer remain unchanged. In this way, the learning effectiveness and the learning diversity of particles could be largely promoted. To further enhance the learning diversity of particles, we maintain an additional archive to store obsolete elites, and use the predominant elites in the archive along with particles in the first two layers to direct the update of particles in the third layer. With these two mechanisms, the proposed EDPSO is expected to compromise search intensification and diversification well at the swarm level and the particle level, to explore and exploit the solution space. Extensive experiments are conducted on the widely used CEC’2010 and CEC’2013 high-dimensional benchmark problem sets to validate the effectiveness of the proposed EDPSO. Compared with several state-of-the-art large-scale algorithms, EDPSO is demonstrated to achieve highly competitive or even much better performance in tackling high-dimensional problems.