Solving Complex Multi-Objective Optimization Problems By Evolutionary Algorithms

Many problems in scientific research and engineering applications involve multiple objectives to be optimized simultaneously,which are collectively known as multi-objective optimization problems.In the last two decades,evolutionary algorithms and other meta-heuristics have exhibited satisfactory performance in solving multi-objective optimization problems.Nevertheless,they may encounter difficulties when tackling complex multi-objective optimization problems,such as those with many objectives,a large number of decision variables,and irregular Pareto fronts.To address this issue,this thesis tailors a number of multi-objective evolutionary algorithms for solving several types of complex multi-objective optimization problems.The main contributions of this thesis contain the following five parts:(1)Many-objective optimization problems are the most popular type of complex multi-objective optimization problems,which contain many objectives to be optimized.This thesis proposes a strengthened dominance relation for solving many-objective optimization problems,called SDR.The proposed SDR uses an adaptive niching technique based on the angles between objective vectors to detect the dominance relations of solutions,which can not only highly improve the selection pressure in high-dimensional objective space,but also strike a good balance between convergence and diversity of the non-dominated solution set.Experimental results show that SDR outperforms existing dominance relations on many benchmark problems;moreover,the SDR based NSGA-II is also competitive to state-of-the-art many-objective evolutionary algorithms.(2)Large-scale multi-objective optimization problems are another popular type of complex multi-objective optimization problems,which contain a large number of decision variables.This thesis proposes a decision variable clustering based evolutionary algorithm for solving large-scale multi-objective optimization problems,called LMEA.The proposed LMEA starts with the clustering of decision variables,where all the decision variables are divided into convergence-related variables and diversity-related variables,and all the convergence-related variables are further divided into several subgroups that are not interacted with each other.During the optimization procedure,LMEA alternately optimizes each group of convergence-related variables and diversity-related variables by different strategies.Experimental results demonstrate the superiority of LMEA over existing algorithms in solving large-scale benchmark problems.(3)There exist some complex multi-objective optimization problems having irregular Pareto fronts.In order to better solve this type of problems,this thesis proposes a reference point adaptation based evolutionary algorithm,called AR-MOEA.The proposed AR-MOEA is based on an enhanced IGD indicator,where a set of points sampled on unit simplex are adopted as the reference points for the calculation of indicator value.The main idea of AR-MOEA lies in the reference point adaptation method,which can adaptively adjust the distribution of the reference points according to the shape of the current population in objective space,and thus make the reference points capable of capturing different shapes of Pareto fronts.Experimental results demonstrate that AR-MOEA has promising versatility on problems with regular or irregular Pareto fronts.(4)There also exist some complex multi-objective optimization problems with both many-objectives and irregular Pareto fronts.This thesis proposes a generic front modeling based evolutionary algorithm for solving many-objective optimization problems with irregular Pareto fronts,called GFM-MOEA.The proposed GFM-MOEA learns the shape of the Pareto front via a mathematical model,which uses the non-dominated solutions in the current population as the training set,and employs the Levenberg-Marquardt algorithm to train the model.Experimental results demonstrate that the proposed front modeling method can effectively estimate various PFs with many objectives,and result in a competitive performance of GFM-MOEA in comparison to existing algorithms.(5)For a complex multi-objective optimization problem in real-world applications(i.e.,feature selection),this thesis proposes an evolutionary algorithm called AR-MOEA-FS.The feature selection problem is characterized by many decision variables,complex objective functions,and computationally expensive functions.According to the characteristics of feature selection problem,the proposed AR-MOEA-FS inherits the framework of AR-MOEA,and uses new population initialization strategy,crossover operator,and mutation operator to accelerate the convergence.Experimental results show that AR-MOEA-FS can obtain better results than traditional feature selection approaches and classical multi-objective evolutionary algorithms on various datasets.