中文摘要：

在多目标粒子群算法中,粒子的飞行由自身的最优位置和指导粒子决定,如何定义适应度选出合适的指导粒子,指导搜索过程向全局Pareto最优区域飞行,并保持种群在最优前端的多样性是算法的关键问题.针对上述问题,构造了同时考虑粒子的Pareto占优情况和目标空间邻近密集度的表现型共享适应度函数,在此基础上提出一个基于表现型共享的多目标粒子群优化算法（MOPSO）.为了验证算法的有效性,采用占优等级指标来分析近似解集的占优情况,并采用EPS、HYP和R2指标来衡量解集的分布情况.实验结果表明,算法具有较强的全局搜索能力,能在较小的计算代价下获得较好的Pareto前端近似.

英文摘要：

In multi-objective particle swarm optimization, a particle flies according to its history best position and the leaders, therefore how to define the fitness function in order to guide the search to- wards the global Pareto-optimal region and maintain population diversity in the non-dominated front is the key to success. To solve the above problem, a fitness function based on the phenotype sharing is designed considering both the Pareto dominance and the neighborhood density of the objective space. Then a multi-objective particle swarm optimization algorithm based on the phenotype fitness function is proposed. In order to validate the proposed algorithm, the Dominance ranks indicator is used to ana- lyze the dominance relation of the approximation set, and the EPS, HYP and R2 indicators are applied to compare the distribution of the approximation set. Results indicate that the proposed MOPS0 can lead to a good approximation of Pareto front with less computational cost in general.