Research On Wavelet-based Immune Multi-objective Optimization Algorithm

Immune algorithms imitate the body’s immune system, and solve optimization problems by using swarm intelligence-based search methods. Thus, using immune algorithms to solve multi-objective optimization problems is becoming the focus of evolutionary computing research. Compared to classical multi-objective evolutionary algorithms, Immune algorithms have obvious advantages on dealing with complex problem, but still a little off when the number of objective function is greater or the Pareto front is more complicated, such as slow convergence and bad performance. Therefore, the improved immune algorithms have high theoretical and practical value. In this paper, wavelet-based immune algorithm is designed to meet those shortfalls, and applied to solve multi-objective optimization problems and fuzzy clustering issues.The nondominated sorting multi-objective evolutionary algorithms can solve two-objective optimization problems successfully, but their performance will deteriorate badly when the number of objectives exceeds four. In this paper, wavelet-based Immune Algorithm (WIA) is proposed for many-objective optimization by using a novel elite extraction operator (EEO) and a descent reproductive mode (DRM). Using the locality and multi-resolution of wavelet to extract the distribution information of the nondominated individuals, the EEO guides the searching process of the true Pareto-optimal front effectively. Taking advantage of nondominated individuals’relative positional relationship in different ranks, the DRM extends an elite individual to a population in the approximate fastest descent direction of objective function values. In case of two sets of test problems with the number of objectives changing from 3 to 20, experimental results show the efficiency and effectiveness of the WIA compared to other three current state-of-the-art MOEAs.Fuzzy clustering can express ambiguity of sample category, and better reflect the actual needs of data mining. Wavelet-based Immune Fuzzy C-means Algorithm (WIFCM) is proposed for overcoming the imperfections of fuzzy clustering, such as falling easily into local optimal solution, slower convergence speed and initialization-dependence of clustering centers. Innovations of WIFCM are elite extraction operator (EEO) and descent reproductive mode (DRM). Using the locality and multi-resolution of wavelet transform, the EEO explores the distribution and density information of spatial data objects in multi-dimensional space to guide the search of optimal solution. Taking advantage of the relationship between the relative positions of elite antibodies and inferior antibodies, the DRM obtains the approximate fastest descent direction of objective function values, and assures fast convergence of algorithm. Compared to the classic fuzzy C-means algorithm, experiments show that WIFCM has obvious advantages in average number of iterations and accuracy.