多目标优化(Multi-objective Optimization，MO)算法的目的是在解空间中找到一组最优的，互不支配的，且分布均匀的解。在数据挖掘，图像分割，图像聚类等领域中，往往需要选取合适的参数，此时运用多目标优化算法，能够得到一个最优的参数集合，这样有利于选取合适的参数。为了提高多目标优化算法的性能，许多学者分别采用不同的策略对多目标优化算法进行了研究，目前，经典的多目标优化算法有NSGA-II，SPEA2，MOPSO和MOEA/D等。同时，在实际问题中，往往受到约束条件的制约，因此约束处理策略也受到了广大学者的关注。目前有多个评价多目标优化算法的性能指标，但各有利弊，如何有效地评价多目标优化算法的性能也是众多学者研究的热点。本文首先对NSGA-II的拥挤度值计算方法进行了改进，之后在免疫克隆算法的基础上提出了修正免疫克隆约束多目标优化算法，最后对多目标优化算法在多分类中的应用做了进一步的研究。 本文的主要内容包括： (1) 针对NSGA-II在优化三维测试问题时，拥挤度值计算方法的不足，提出了一种新的拥挤度值计算方法。该方法通过引进局部拥挤度值策略完成对种群的更新操作，并通过引进全局拥挤度值策略完成对子代种群的选取操作。实验结果显示，该拥挤度值计算方法使NSGA-II处理三维测试问题的性能得到了很大的提高。 (2) 针对约束多目标优化问题，提出新的免疫克隆约束多目标优化算法。该算法通过引进一个约束处理策略，用一个修正算法对个体的目标函数值进行修正， 并对修正后的目标函数值采用免疫克隆多目标优化算法进行优化。通过实验证明了该算法的有效性。 (3) Cai等人在2010年提出了多目标同时聚类和分类框架(MSCC)，通过引进聚类和分类两个目标函数，并采用MOPSO优化这两个目标函数达到设计多分类器的目的。由于MOPSO在优化MSCC框架中的多目标问题时，只能得到少量的非支配解，而在此情况下，著名的NSGA-II由于采用了Pareto排序方法，种群中会保留大量优秀的支配解，这样有利于种群的优化，所以为了进一步研究MSCC框架，引进了NSGA-II优化MSCC框架中的多目标问题。实验结果表明，在NSGA-II的优化下，MSCC分类器的性能好于MOPSO优化MSCC框架的情况，而且也发现了MSCC框架在处理部分数据集时出现的问题。

Multi-objective optimization (MO) algorithm is to find a set of nondominated and well distributed solutions. In the area of data mining, image sengmentation and image clustering, we always need to find proper parameters, and multi-objective optimization algorithms can help us find a set of solutions, then we select which one to use. In order to improve the performance of multi-objective optimization algorithms, a lot of researchers brought in different kinds of strategies. So far, there are some kind of famous multi-objective optimization algotihoms such as NSGA-II, SPEA2, MOPSO and MOEA\D. Meanwhile, in pratical problems, there are always constraints, and how to deal with the constraints is a hotspot for many researchers. Firstly, this paper improved the crowding-distance computation, secondly, based on Immune Clonal algorithm, this paper proposed a new constrained multi-objective optimization algorithm, finally, this paper made a deeper analysis in the application of multi-objective optimization algorithms in multi-class classification. The primary coverage of this article includes: (1) In recent years, NSGA-II is one of the most famous multiobjective evolutionary algorithms, but when dealing with three-objective test problems, it can not find a well distributed population because of the drawback of the method for the crowding-distance computation. Aiming at this, we proposed a new method for the crowding-distance computation. By bringing in a local crowding-distance value, this method completes the updating operation of the population, and the selection of the sub-population from the parent population is done through a global crowding-distance value. Then we made a brief analysis of the new algorithm’s parameter. Finally, at the appropriate parameter, the new proposed algorithm was tested on two and three dimensional test problems, and compared with the other three famous multiobjective optimization algorithms. The test result shows that the new proposed algorithm achieves a better convergence and diversity than NSGA-II and other two algorithms. (2) Proposed a new Immune Clonal Constrained Multi-objective Algorithm for constrained multi-objective optimization problems. By bringing in a new constrained handling strategy to modify the objective values of individuals, the new proposed algorithm optimizes the individuals with the modified objective values, and stores the non-dominated feasible individuals in an elitist population. In the optimization process, the algorithm not only preserves the non-dominated feasible individuals, but also utilizes the infeasible solutions with smaller constrained violation values; Meanwhile the new algorithm introduces the overall cloning strategy to improve the distribution diversity of the solutions. The new proposed algorithm is tested on several popular constrained test problems, and compared with the other two constrained multi-objective optimization algorithms. The results show that the optimal solutions of the new proposed algorithm have better diversity than the other two algorithms, and get improvement in convergence and uniformity. (3) In 2010, Cai et al. proposed a multiobjective simultaneous learning framework (MSCC) for both clustering and classification learning to design a multi-class classifier. She chose two minimization objective functions: Clustering function and classification function, and used MOPSO to optimize the two functions. Because there are only a few nondominated solutions in MOPSO population, and in this situation, NSGA-II can keep a lot of good dominated solutions in the population, which will help the population optimize, for further study of MSCC framework, this paper brought in NSGA-II as the optimization algorithm. The results of experiments show that, under the optimization of NSGA-II, MSCC framework can get better multi-class classifiers and the dominated solutions can get better classifiers than nondominated solutions. By observing the changing curves of the maximum classification accuracy rate following with the optimization of populations, this paper found that, when dealing with most of the data sets, the maximum accuracy is not improved following the optimization of populations.