基于NSGA-II和MOPSO融合的一种多目标优化算法

用多目标粒子群优化(MOPSO)算法的粒子位置更新模式替代NSGA Ⅱ的交叉操作，获得一个新的算法（NSGA Ⅱ MOPSO）。为使这两种差异较大的算法实现无缝融合，在NSGA Ⅱ算法范围内对MOPSO中特有的概念粒子及其速度、Pbest、引导者进行处理: 1)粒子对应于NSGA Ⅱ中子代群体的个体； 2)不再使用粒子速度概念； 3)不再使用粒子Pbest概念，代之以从父代群体中为每个粒子的每一维寻找一个最近的该粒子非支配个体; 4)每一个粒子的引导者可以是父代群体中稀疏程度最大的个体或者是按照二进制随机竞赛选择方法从父代群体中选择的一个个体，具体哪一种方式发挥作用依赖于预先设定的概率。另外，引入稀疏程度概念来评价粒子在目标函数空间的分布。6个算例的结果表明，与NSGA Ⅱ及最新的两种MOPSO算法（CLMOPSO 和 EM MOPSO）相比，新算法是一个有效、稳定的算法。

Multi-objective optimization algorithm based on the combination of NSGA-Ⅱ and MOPSO

A new algorithm was developed through replacing the crossover operation in NSGA-Ⅱ with the mode of position updating in multi objective particle swarm optimizer (MOPSO). In order to seamlessly combine NSGA Ⅱand the greatly different MOPSO, the special concepts (particle and its velocity, Pbest and leader) for MOPSO were dealt with within the scope of NSGA-Ⅱ: 1) particle in MOPSO was considered to be equivalent to offspring individual in NSGA-Ⅱ; 2) the concept of velocity fell into disuse; 3) the concept of Pbest also came into disuse. Instead of that, for each dimension of a particle, the nearest one among its nondominated individuals in parent population was used; 4) the leader of a particle was the individual with largest sparse degree among parent population or selected from parent population by binary tournament selection method, which of them taking effect lies on the predefined probability. In addition, a new concept, i.e., sparse degree, was introduced to evaluate the distribution of particles in objective function space. Experiments on six benchmark problems indicate that the new algorithm is an effective and stable one when compared with NSGA-Ⅱ and two of the latest MOPSOs (CLMOPSO and EM-MOPSO).