Research On Multi-objective Optimization Problems Based On Evolutionary Algorithm

The typical idea of solving multi-objective problems(MOPs)is based on the mathematical modeling.Many multi-objective optimization algorithms have been proposed and obtained good results in different environments.However,the numerical calculation method which can deal with many complex functions,taking into account both the distribution and convergence index is still in the exploratory stage.Fuzzy cognitive map can be used to establish a computable model for the causal relationship,transfer knowledge through the nodes and the representation of the causal relationship in the system with the arc,so that the expression of causal relations more formal.Because it does not have the capability of non monotonic reasoning,when encountered practical problems,fuzzy cognitive map can not find the exact weight and easy to form a large model error.In this paper,the above problems are studied and the corresponding solutions are put forward.(1)In this paper,a multi-objective evolutionary algorithm based on the coordinate transformation in the objective space(MOEA/CT)is introduced for better managing convergence and distribution of solutions when MOEA is used for solving MOPs.The coordinate transformation strategy is proposed for finding more efficient solutions that can accelerate convergence process.Based on the coordinate transformation strategy,a novel update strategy and density estimation approach for selecting solutions from external archive which is storing the non-dominated solutions is integrated in MOEA/CT for getting better distribution of the solutions.The proposed MOEA/CT is compared with four state-of-art algorithms,the comparative experimental results demonstrate that MOEA/CT outperforms the other four competitors and it can achieve solutions with better distribution and better convergence to PF.(2)In learning of fuzzy cognitive maps(FCMs),the traditional optimization algorithms mainly rely on the data error of the weights between two concepts in the weighted graph,which usually leads to the low accuracy of the fitted model of FCMs.In this paper,the idea of multiobjective optimization is used in the learning of FCMs.Therefore,the learning problem is modeled with two objectives,which are the data error of the weights of directed arcs and the proportion of the data error.The dependence of the weights is reduced by using the multiobjective optimization model.In order to effectively solve the multi-objective optimization problem,a multi-objective evolutionary algorithm based on the coordinate transformation(MOEA/CT)is proposed.Experimental results show that learning of FCMs by using the proposed MOEA/CT can effectively decrease the data error and the model error and reflect the causal relationship between concepts accurately.