基于角度坐标的多目标粒子群优化算法

为了在保证多目标粒子群优化(multi-objective particle swarm optimization, MOPSO)算法所求解集分布性的前提下提高算法的收敛性，依据辅助适应度赋值策略，提出了基于角度坐标的多目标粒子群优化(intelligent MOPSO, IMOPSO)算法。通过建立角度坐标系，确定了不同维优化目标下目标向量的角度坐标及角度参数，给出了求取目标函数空间中参考线角度参数的方法，并定义了目标向量的辅助适应度值，以对处于非劣支配关系的个体进行综合比较。结果表明,IMOPSO算法较好地维护了Pareto解的分布性与收敛性，且在求解小规模的最优个体时仍能在整个Pareto前沿均匀分布，未出现“聚集”现象，运行时间小于NSGA2、SPEA2、MOEA/D，充分验证了IMOPSO算法的有效性。

Method of multi-objective particle swarm optimization based on angular coordinates

In order to improve the convergence of multi-objective particle swarm optimization (MOPSO) while ensuring well distribution, a new method of MOPSO based on auxiliary fitness value is proposed. By establishing an angular coordinate, the angular coordinate parameters of the objective vector are ascertained as well as angular reference line’s parameters in various dimensional spaces. And an auxiliary fitness value is defined  to compare non-dominating individuals. Simulation results indicate that IMOPSO commendably balances the conflicts of convergence and distribution even for the small size of archive. Moreover, its pareto solutions would not get crowded in a small region along the Pareto front in test functions. Consequently, IMOPSO is validated and proven effective while its runtime is less than NSGA2, SPEA2 and MOEA/D.