Abstract
It is difficult to balance the convergence and diversity at the same time and select the globally optimal particle (gbest) in the multiobjective particle swarm optimization (MOPSO) process. In this paper, a novel method based on adaptive angle division is proposed targeting at archive maintenance and gbest selection. According to the number of particles in the current archive, the angle region of the target space is adaptively adjusted and uniformly divided. The globally optimal particle is selected from the low-density angle region of the particle distribution; in the meanwhile, the superfluous particles are deleted from the high-density angle region. Consequently, the selection of gbest and update of external archive set which including the generation of the optimal solution set and maintenance of external archive set are synchronized. The convergence and diversity are ensured while improving the uniformity of the optimal solution set. In addition, the current highest non-dominated particles in each angle region are preserved, and the particles in adjacent regions are selected to conduct global guidance for such regions and regions of the particle-free distribution area. Through these two ways, the diversity of the population is maintained while the coverage spreadability of the optimal solution set in the target space is enhanced. Four state-of-the-art evolution multiobjective optimization (EMO) algorithms and the two classic EMO algorithms are selected as the peer algorithms to validate multiobjective particle swarm optimization based on adaptive angle division (AADMOPSO) algorithm. A series of extensive experiments are conducted on five groups of standard test functions. The experimental results show the effectiveness and competitiveness of the proposed AADMOPSO in balancing convergence and diversity.
Highlights
Multiobjective optimization problems (MOPs) widely exist in many fields, such as industry, economy, management, medicine and so on
DEVELOPMENT OF THE PROPOSED ALGORITHM we introduce some concepts and definitions used in AADMOPSO firstly
3) The method based on meshing uses random deletion to process the extra particles in the mesh, and the method based on adaptive angle region division has one and only one particle in each angular region, which is beneficial to improve the uniformity of the optimal solution set in the target space
Summary
Multiobjective optimization problems (MOPs) widely exist in many fields, such as industry, economy, management, medicine and so on. The fourth type is based on Pareto sorting which is a multiobjective evolutionary algorithm in view of non-dominated sorting The advantage of this method is that it can find multiple solutions in a run, and it is easy to combine with various evolutionary algorithms. The choice of gbest and the maintenance of external archive set are completed synchronously according to the particle distribution in the angle region Compared with the former algorithm, the main contributions of AADMOPSO algorithm are summarized as follows. As the number of non-dominant solutions in the external archive set increases, in view of the number of particles and iteration times the angle region is divided in the target space adaptively, which benefit to improving the coverage and distribution of the optimal solution set.
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