Multi-objective Optimization Based On NSGA-Ⅱ And Immune Algorithm And Classification

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, finalll, 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) In2010, 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.