Adaptive projection plane and reference point strategy for multi-objective particle swarm optimization

Achieving a balance between convergence and diversity and their mutual enhancement is a complex task in the process of algorithm improvement. This is crucial because it is directly related to the effectiveness of the algorithm in obtaining accurate and uniformly distributed Pareto frontiers. Although significant progress has been made in particle swarm algorithms, exploring new approaches is necessary. In this paper, we construct a projection plane (projection line in 2D) based on the extreme values of the non-dominated solutions, select a set of uniform reference points on the projection plane, and then project the non-dominated solutions onto the constructed projection plane to form projection points. The reference points and projection points on the projection plane are thus utilized to guide the updating of the population as well as the maintenance of the external archive, a strategy that enhances the algorithm's global exploration and local exploitation capabilities. Secondly, we aggregate the target values of particles into a single scalar value and combine the idea of particle fusion to design a scheme for the particle selection of individual optimal particles. This paper further improves the algorithm's overall performance by using the information between populations to select individual optimal particles. Lastly, it is evaluated against a number of multi-objective algorithms that are currently in use and perform well on 22 test problems. The findings demonstrate that the algorithm this paper proposes performs better when solving multi-objective problems.