The Improved Evolutionary Multi-objective Optimization Algorithms Based On Invasive Weed Optimization Operator And For Clustering

Evolutionary Algorithms are a type of algorithms which are inspired by the natural phenomena. Now, they have been widely used in various fields:optimization, machine learning, pattern recognition and so on. In the field of multi-objective optimization, evolutionary algorithms reflect the huge advantage. After the1990s, with the development of the evolutionary algorithms, many scholars have dedicated to the study of evolutionary multi-objective algorithms and proposed many algorithms. With the deepening of the research, the evolutionary multi-objective optimization algorithms show new features, such as the algorithms based on the artificial immune system, introducing the operator of local search, proposed the multi-objective optimization evolutionary algorithm based on decomposition, and so on. Invasive Weed Optimization Algorithm proposed by Mehrabian and Lucas in2006is a novel numerical stochastic optimization algorithm inspired by the phenomenon of the invasive weed colonization. This algorithm combines the global and local search ideas and has been used in some practical problems. It is easy to operate and modify the multi-objective optimization algorithms.The work of this paper mainly includes:1. Improve Nondominated Neighbor Immune Algorithm (NNIA) which was proposed by Gong et al. by introducing in a modified IWO operator. There are three points in this modified I WO operator:1) associated parent weed (individual) is proposed, in order to extend the searching space,2) the associated parent weed is adjusted by the number which is obey Cauchy distribution,3) introducing an oscillating factor proposed by Basak et al. The main aim of the modification is not only to improve the global search ability, but also maintain the advantages of the local search. Without increasing the number of function evalutions and the size of the population, the performance of NNIA is modified by introducing the modified IWO operator, the stability of the algorithm is improved and the results of some test problems have been improved obviously.2. Another modified IWO operator is introduced in Multi-objective Evolutionary Algorithm Based on Decomposition (MOEA/D) which was proposed by Zhang et al to improve the convergence of the algorithm and maintain the diversity of the output solutions. Here, it is adopted the ability of IWO operator in which the searching space is changing from global to local during the iteration of the algorithm. There are two modilications in the new IWO operator:1) the location of the seed generated by the parent weed is changed, it means applying IWO operation on the individual produced by DE operator,2) a new equation for calculating the standard deviation of the normal distribution is proposed in the IWO operator. In the modification1), it is mainly focus on the ability of local search of the IWO operator and in order to expend the capability of global and local search of the individual generated by DE operator. And the modification2) is mainly to adapt to the characteristics of the producing new individual method of MOEA/D, and retain the characteristics of the original IWO operator at the same time. When the number of the generation equals to certain number, we perform the modified IWO operator and combined the technique of Pareto dominate with the original update method of MOEA/D to update the individuals. From the analysis of experiments, the results of the modified MOEA/D have a better performance for some of the complex functions than the original algorithm, and especially the comparison between the algorithms which are the one introduced the modified IWO operator and the original one respectively.3. A new multi-objective IWO algorithm is proposed to solve the clustering problem in which the cluster number is uncertainty. In this algorithm, the IWO operator optimizes two clustering objective functions simultaneously, and a variable length real coded scheme is adopted, the variable individuals are the cluster centers with different cluster numbers. A new mechanism called feedback-update mechanism is proposed to keep the diversity of the individuals which have different cluster numbers. Finally, the Silhouette index is used to select the optimal solution. From the results of the experiments, the algorithm performs a better performance than the other algorithms for comparing.