Many-objective Optimization Problems (MaOPs) often involve more than three objectives. As the number of objectives increases, traditional algorithms face critical challenges: weakened selection pressure due to the explosion of non-dominated solutions, difficulty in balancing convergence and diversity and inefficient search in many objective spaces. This paper addresses these issues by proposing an angle-penalty distance and polarity-division guided algorithm for many-objective electric field optimization (PD-MaOEFO). Firstly, a charge function representing the quality of particles has constructed based on the angle-penalty distance(APD), such that the better the particle, the greater the charge it carries. Secondly, a particle polarity division strategy is introduced. Non-dominant solutions with smaller APD values are classified as protons, particles with smaller APD values in the solution set are classified as electrons, and particles with larger APD values in the solution set are classified as neutrons. Electrons move under the influence of proton Coulomb attraction and neighboring electron Coulomb repulsion, while neutrons move under the influence of proton nuclear force, the algorithm achieves a balance between development and exploration capabilities. Finally, a proton pool update strategy based on reference vectors and APD is introduced to achieve a balance between protons convergence and diversity. To validate the effectiveness of the proposed algorithm, we conducted comparative experiments with seven many-objective optimization algorithms, covering 13 many-objective optimization test problems. The experimental results demonstrate that the proposed algorithm can effectively solve many-objective optimization problems and exhibits good stability under varying numbers of objectives.

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An Angle-Penalty Distance and Polarity-Division Guided Algorithm for Many-Objective Electric Field Optimization

  • Yue Zhang,
  • Liping Xie

摘要

Many-objective Optimization Problems (MaOPs) often involve more than three objectives. As the number of objectives increases, traditional algorithms face critical challenges: weakened selection pressure due to the explosion of non-dominated solutions, difficulty in balancing convergence and diversity and inefficient search in many objective spaces. This paper addresses these issues by proposing an angle-penalty distance and polarity-division guided algorithm for many-objective electric field optimization (PD-MaOEFO). Firstly, a charge function representing the quality of particles has constructed based on the angle-penalty distance(APD), such that the better the particle, the greater the charge it carries. Secondly, a particle polarity division strategy is introduced. Non-dominant solutions with smaller APD values are classified as protons, particles with smaller APD values in the solution set are classified as electrons, and particles with larger APD values in the solution set are classified as neutrons. Electrons move under the influence of proton Coulomb attraction and neighboring electron Coulomb repulsion, while neutrons move under the influence of proton nuclear force, the algorithm achieves a balance between development and exploration capabilities. Finally, a proton pool update strategy based on reference vectors and APD is introduced to achieve a balance between protons convergence and diversity. To validate the effectiveness of the proposed algorithm, we conducted comparative experiments with seven many-objective optimization algorithms, covering 13 many-objective optimization test problems. The experimental results demonstrate that the proposed algorithm can effectively solve many-objective optimization problems and exhibits good stability under varying numbers of objectives.