粒子群优化算法因形式简洁、收敛快速和参数调节机制灵活等优点,同时一次运行可得到多个解,且能逼近非凸或不连续的 Pareto 最优前端,因而被认为是求解多目标优化问题最具潜力的方法之一。但当粒子群优化算法从单目标问题扩展到多目标问题时,Pareto最优解集的存储与维护、全局和个体最优解的选择以及开发与开采的平衡等问题亦随之出现。通过目标空间变换方法,采用 Pareto 前端在被称为平行格坐标系统的新目标空间中的分布熵及差熵评估种群的多样性及进化状态,并以此为反馈信息来设计进化策略,使得算法能够兼顾近似 Pareto 前端的收敛性和多样性。同时,引入格占优和格距离密度的概念来评估Pareto最优解的个体环境适应度,以此建立外部档案更新方法和全局最优解选择机制,最终形成了基于Pareto熵的多目标粒子群优化算法。实验结果表明：在IGD性能指标上,与另外8种对等算法相比,该算法在由ZDT和DTLZ系列组成的12个多目标测试问题集中表现出了显著的性能优势。%Due to its concise formation, fast convergence, and flexible parameters, particle swarm optimization (PSO) with the ability to gain multiple solutions at a run and to approximate the Pareto front of those non-convex or discontinuous multiobjective optimization problems (MOPs) is considered to be one of the most promising techniques for MOPs. However, several challenges, such as maintaining the archive, selecting the global and personal best solutions, and balancing the exploration and exploitation, occur when extending PSO from single-objective optimization problems to MOPs. In this paper, the distribution entropy and its difference of an approximate Pareto front in a new objective space, named parallel cell coordinate system (PCCS), are proposed to assess the diversity and evolutionary status of the population. The feedback information from evolutionary environment is served in the evolutionary strategies to balance the convergence and diversity of an approximate Pareto front. Meanwhile, the new concepts, such as cell dominance and individual density based on cell distance in the PCCS, are introduced to evaluate the individual environmental fitness which is the metric using in updating the archive and selecting the global best solutions. The experimental results illustrate that the proposed algorithm in this paper significantly outperforms the other eight peer competitors in terms of IGD on 12 test instances chosen from the ZDT and DTLZ test suites.
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