基于扩容和双距离决策的多目标粒子群优化算法

为了更好地改善多目标粒子群优化算法的收敛性和多样性，提出一种基于扩容和双距离决策的多目标粒子群优化算法。利用扩容的方法对目标空间中目标函数值的上下限进行扩大，得到新的上下限后再建立网格，这样可以计算出边界点的坐标。在小网格中选择引导粒子或者劣质粒子时，利用小网格中粒子到理想点和当前小网格最优点的距离进行决策筛选，这样充分利用目标空间中的信息来对粒子的优先级进行判断。对新的粒子进行差分变异，增加了整体的多样性，并通过阈值控制其变异的频率。将算法和当前具有代表性的多目标粒子群优化算法进行对比实验，提出的算法效果更佳。实验表明，提出算法的收敛性和多样性不仅得到较大提高，而且较为稳定。

Multi-objective particle swarm optimization algorithm based on expansion and dual distance

In order to improve the convergence and diversity of multi-objective particle swarm optimization algorithm, a new multi-objective particle swarm optimization algorithm based on expansion and dual distance is proposed. The main innovations of this paper are as follows: firstly,the upper and lower limits of the objective function value in the target space are expanded by the expansion, and after the grid is established by the new upper and lower limits, the coordinates of the boundary point can be calculated. Then, when selecting the leader or the inferior particles in a small grid,the decision is made by the two distances from the small grid to the ideal point and the current small grid. In this way, the information in the target space is fully utilized to judge the priority of the particles; Finally, the differential mutation of the new particles increases overall diversity and the frequency of their mutation is controlled by a threshold. The algorithm is compared with the current representative multi-objective particle swarm optimization algorithm, and the results show that the algorithm proposed in this paper is better than the comparison algorithm. Experiments show that the convergence and diversity of the proposed algorithm are not only improved, but also stable.