基于自适应网络与动态拥挤距离的多目标粒子群算法及应用

针对传统方法不易收敛到真实Pareto前端和解的多样性较差的问题，提出了一种基于自适应网络和动态拥挤距离的多目标粒子群优化算法。该算法能在外部种群的数量超过种群规模时，将目标函数空间均匀地划分为间隔相同的网格，统计每个网格中粒子的数量进而估计粒子的密度，限制外部档案的规模；然后引入粒子的方差信息，设计了基于动态拥挤距离的算法，避免了一次性淘汰所有拥挤距离小的个体而使解的分布性变差的问题，提高了解的多样性。函数优化实验及该算法在成品油调和经济效益问题中的应用都验证了改进后的算法具有很好的效果。

Multi objective Particle Swarm Optimization Algorithm Based on Adaptive Network and Dynamic Crowding Distance and Its Application

The traditional particle swarm optimization (PSO) algorithm has some shortcomings, e.g. not easy to converge to the true Pareto front, and the poor diversity of the solutions. This paper presents a multi objective PSO algorithm based on adaptive network and dynamic crowding distance. For the case that the number of external population exceeds the population size, the proposed algorithm can divide the objective function space into the grids with the same interval, and then, estimate the density of particles by computing the number of particles in each grid so as to limit the size of the external archive. Moreover, the variance of particle is introduced and a dynamic crowding distance based algorithm is designed. That can avoid the problem that the distribution of solution become worse due to eliminating all individuals with small crowded distance in one time. Hence, the diversity of the solutions can be improved. Both the experiment on function optimization and the application in reconciling refined petroleum products validate the effectiveness of the proposed algorithm.